%%% ====================================================================

%%% BibTeX-file{
%%%     author          = "Nicholas J. Higham",
%%%     version         = "1.00",
%%%     date            = "28 August 2002",
%%%     filename        = "acc-stab-num-alg-2ed.bib",
%%%     address         = "Department of Mathematics
%%%                        University of Manchester
%%%                        Manchester M13 9PL
%%%                        England",
%%%     telephone       = "+44 (0)161 275 5800",
%%%     FAX             = "+44 (0)161 275 5819",
%%%     checksum        = ""
%%%     email           = "higham at ma.man.ac.uk (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "bibliography, numerical analysis, N. J. Higham",
%%%     supported       = "yes",
%%%     docstring       = "BibTeX bibliography for the book
%%%                        \cite{Higham:2002:ASN}:
%%%                        Accuracy and Stability of Numerical Algorithms
%%%                        by Nicholas J. Higham, SIAM, 2002"
%%%     }

%%% ====================================================================

%%% The URL (Uniform Resource Locator) of this file is

%%%

%%%   URL = "http://www.ma.man.ac.uk/~higham/asna/acc-stab-num-alg-2ed.bib"



@Preamble{"\def\noopsort#1{}" # "\def\l{\char32l}" #
                 "\def\v#1{{\accent20 #1}} \let\^^_=\v" #
                 "\def\hbk{hardback}" # "\def\pbk{paperback}"}

%=======================================================================

% Journal abbreviations:



@String{j-ACM =  "J. Assoc. Comput. Mach."}

@String{j-Adv-Comp-Math = "Adv. in Comput. Math."}

@String{j-AHC =  "Annals of the History of Computing"}

@String{j-AMM =  "Amer. Math. Monthly"}

@String{j-ANN-NUM-MATH = "Annals of Numerical Mathematics"}

@String{j-ANN-STAT = "Ann. Statist."}

@String{j-APP-MATH-COMP = "Appl. Math. Comput."}

@String{j-APP-MATH-LETT = "Applied Mathematics Letters"}

@String{j-APP-NUM-MATH = "Appl. Numer. Math."}

@String{j-APPROX = "J. Approximation Theory"}

@String{j-ASA =  "J. Amer. Statist. Assoc."}

@String{j-BAMS = "Bull. Amer. Math. Soc."}

@String{j-BIT =  "BIT"}

@String{j-CACM = "Comm. ACM"}

@String{j-CMJ =  "College Mathematics Journal"}

@String{j-COMP-MATH-APPL = "Computers Math. Applic."}

@String{j-COMPUT-GRAPH-STAT = "Journal of Computational and Graphical
                 Statistics"}

@String{j-COMPUTING = "Computing"}

@String{j-COMP-J = "Comput. J."}

@String{j-CSE =  "Computing in Science and Engineering"}

@String{j-EL =   "Electronics Letters"}

@String{j-ELA =  "The Electronic Journal of Linear Algebra"}

@String{j-ETNA = "Electron. Trans. Numer. Anal."}

@String{j-FOCM = "Found. Comput. Math."}

@String{j-IEEE-AC = "IEEE Trans. Automat. Control"}

@String{j-IEEE-AHC = "IEEE Annals of the History of Computing"}

@String{j-IEEE-ASSP = "IEEE Trans. Acoust., Speech, Signal Processing"}

@String{j-IEEE-C = "IEEE Trans. Comput."}

@String{j-IEEE-MG = "IEEE Trans. Magnetics"}

@String{j-IEEE-PC = "IEEE Trans. Prof. Commun."}

@String{j-IEEE-SE = "IEEE Trans. Software Engrg."}

@String{j-IEEE-SP = "IEEE Trans. Signal Processing"}

@String{j-IMA-BULL = "IMA Bulletin"}

@String{j-IMAJNA = "IMA J. Numer. Anal."}

@String{j-INFPL = "Inform. Process. Lett."}

@String{j-IJC =  "Internat. J. Control"}

@String{j-IJNME = "Internat. J. Numer. Methods Eng."}

@String{j-IJSA = "Internat. J. Supercomputer Appl."}

@String{j-INTEL-TECH-J = "Intel Technology Journal"}

@String{j-JAMS = "J. Amer. Math. Soc."}

@String{j-JIMA = "J. Inst. Maths. Applics."}

@String{j-JCAM = "J. Comput. Appl. Math."}

@String{j-JCOMP-PHYS = "J. Comput. Phys."}

@String{j-JMAA = "J. Math. Anal. and Appl."}

@String{j-JNLAA = "Journal of Numerical Linear Algebra with
                 Applications"}

@String{j-JOTA = "J. Optimization Theory and Applications"}

@String{j-JSV =  "Journal of Sound and Vibration"}

@String{j-JUCS = "Journal of Universal Computer Science"}

@String{j-LAA =  "Linear Algebra Appl."}

@String{j-LMA =  "Linear and Multilinear Algebra"}

@String{j-MATH-COMP = "Math. Comp."}

@String{j-MATH-GAZ = "Mathematical Gazette"}

@String{j-MATH-PROG = "Math. Programming"}

@String{j-MATH-TODAY = "Mathematics Today"}

@String{j-MTAC = "M.T.A.C."}

@String{j-NAMS = "Notices Amer. Math. Soc."}

@String{j-Nature = "Nature"}

@String{j-NUM-ALG = "Numerical Algorithms"}

@String{j-NFAO = "Numerical Functional Analysis and Optimization"}

@String{j-NLAA = "Numerical Linear Algebra with Applications"}

@String{j-NUM-MATH = "Numer. Math."}

@String{j-PAR-COMP = "Parallel Comput."}

@String{j-PROC-AMS = "Proc. Amer. Math. Soc."}

@String{j-PSYCHO = "Psychometrika"}

@String{j-QJMAM = "Quart. J. Mech. Appl. Math."}

@String{j-REE =  "The Radio and Electronic Engineer"}

@String{j-SIGNUM = "ACM SIGNUM Newsletter"}

@String{j-SCIENCE = "Science"}

@String{j-SIAM = "J. Soc. Indust. Appl. Math."}

@String{j-SIAD = "SIAM J. Alg. Discrete Methods"}

@String{j-SICOMP = "SIAM J. Comput."}

@String{j-SICOPT = "SIAM J. Control Optim."}

@String{j-SIDM = "SIAM J. Disc. Math."}

@String{j-SIAM-NEWS = "SIAM News"}

@String{j-SIMA = "SIAM J. Math. Anal."}

@String{j-SIAMA = "SIAM J. Appl. Math."}

@String{j-SIMAX = "SIAM J. Matrix Anal. Appl."}

@String{j-SINUM = "SIAM J. Numer. Anal."}

@String{j-SIOPT = "SIAM J. Optim."}

@String{j-SIREV = "SIAM Rev."}

@String{j-SISC = "SIAM J. Sci. Comput."}

@String{j-SISSC = "SIAM J. Sci. Statist. Comput."}

@String{j-SCL =  "Systems and Control Letters"}

@String{j-TOMS = "ACM Trans. Math. Software"}

@String{j-TPLS = "ACM Trans. Program. Lang. Syst."}

@String{j-ZAMM = "Z. Angew. Math. Mech."}

@String{j-ZAMP = "Z. Angew. Math. Phys."}

%=======================================================================

% Type abbreviations:



@String{t-NAREP = "Numerical Analysis Report"}

%=======================================================================

% Departments/Institutions and their addresses:



@String{inst-ATT = "AT\&T Bell Laboratories"}

@String{inst-ATT:adr = "Murray Hill, NJ, USA"}

@String{inst-CS-Lucent = "Computing Sciences Research Center, Bell
                 Laboratories"}

@String{inst-CS-Lucent:adr = "Murray Hill, NJ"}

@String{inst-Bell = "Bell Laboratories"}

@String{inst-Belladr = "Murray Hill, NJ, USA"}

@String{inst-Berkeley-CS = "Department of Computer Science, University
                 of California"}

@String{inst-Berkeley-Math = "Department of Mathematics, University of
                 California"}

@String{inst-Berkeley = "University of California"}

@String{inst-Berkeley:adr = "Berkeley, CA, USA"}

@String{inst-U-Bremen-ZT = "Zentrum f{\"u}r Technomathematik,
                 Universit{\"a}t Bremen"}

@String{inst-U-Bremen-ZT:adr = "Bremen, Germany"}

@String{inst-CERFACS = "CERFACS"}

@String{inst-CERFACS:adr = "Toulouse, France"}

@String{inst-Cornell = "Cornell University"}

@String{inst-Cornell:adr = "Ithaca, NY, USA"}

@String{inst-DAMTP = "Department of Applied Mathematics and Theoretical
                 Physics, University of Cambridge"}

@String{inst-DAMTP:adr = "Cambridge, UK"}

@String{inst-U-Dundee = "Department of Mathematics and Computer Science,
                 University of Dundee"}

@String{inst-U-Dundee:adr = "Dundee, Scotland"}

@String{inst-ENSEEIHT = "Dept. Informatique et Maths Appls.,
                 ENSEEIHT-IRIT"}

% L'Institut National Polytechnique De Toulouse,  D\'{e}partment Informatique N7 - IRIT} }
@String{inst-ENSEEIHT:adr = "31071 Toulouse Cedex, France"}

@String{inst-HARWELL = "{AERE} {Harwell} Laboratory"}

% @String{inst-HARWELL:adr        = "Chilton, Oxon, England"}



@String{inst-IAN = "Istituto di Analisi Numerica del CNR"}

@String{inst-IAN:adr = "Pavia, Italy"}

@String{inst-IMA = "Institute for Mathematics and Its Applications,
                 University of Minnesota"}

@String{inst-IMA:adr = "Minneapolis, MN, USA"}

@String{inst-IMA-UK = "The Institute of Mathematics and Its
                 Applications"}

@String{inst-IMA-UK:adr = "Southend-On-Sea, Essex, UK"}

@String{inst-CS-U-KY = "Department of Mathematics, University of
                 Kentucky"}

@String{inst-CS-U-KY:adr = "Lexington, KY, USA"}

@String{inst-MCCM = "Manchester Centre for Computational Mathematics"}

@String{inst-MCCM:adr = "Manchester, England"}

%%% Numerical Analysis Reports: ISSN 1360-1725



@String{inst-MCS-Argonne = "Mathematics and Computer Science Division,
                 Argonne National Laboratory"}

@String{inst-MCS-Argonne:adr = "Argonne, IL, USA"}

@String{inst-NAG = "NAG Ltd."}

@String{inst-NAG:adr = "Oxford, UK"}

@String{inst-NPL = "National Physical Laboratory"}

@String{inst-NPL:adr = "Teddington, UK"}

@String{inst-ORNL = "Oak Ridge National Laboratory"}

@String{inst-ORNL:adr = "Oak Ridge, TN, USA"}

@String{inst-OUCL = "Numerical Analysis Group, Oxford University
                 Computing Laboratory"}

@String{inst-OUCL:adr = "Oxford, UK"}

@String{inst-U-Manchester = "University of Manchester"}

@String{inst-U-Manchester:adr = "Manchester, England"}

@String{inst-CS-U-MARYLAND = "Department of Computer Science, University
                 of Maryland"}

@String{inst-CS-U-MARYLAND:adr = "College Park, MD, USA"}

@String{inst-NASA-Ames = "NASA Ames Research Center"}

@String{inst-NASA-Ames:adr = "Moffett Field, CA, USA"}

@String{inst-RICE-CAM = "Department of Computational and Applied
                 Mathematics"}

@String{inst-RICE-CAM:adr = "Rice University, Houston, TX, USA"}

@String{inst-CS-U-STANFORD = "Department of Computer Science, Stanford
                 University"}

@String{inst-OR-U-STANFORD = "Department of Operations Research,
                 Stanford University"}

@String{inst-U-STANFORD:adr = "Stanford, CA, USA"}

@String{inst-CS-U-Tenn = "Department of Computer Science, University of
                 Tennessee"}

@String{inst-CS-U-Tenn:adr = "Knoxville, TN, USA"}

@String{inst-Math-UCLA = "Department of Mathematics, University of
                 California"}

@String{inst-Math-UCLA:adr = "Los Angeles, USA"}

@String{inst-Math-UCSD = "Department of Mathematics, University of
                 California"}

@String{inst-Math-UCSD:adr = "San Diego, USA"}

@String{inst-CS-U-Umea = "Institute of Information Processing,
                 University of Ume{\aa}"}

@String{inst-CS-U-Umea:adr = "Ume{\aa}, Sweden"}

@String{inst-RAL = "Atlas Centre, Rutherford Appleton Laboratory"}

@String{inst-RAL:adr = "Didcot, Oxon, UK"}

@String{inst-Math-U-Strath = "Department of Mathematics, University of
                 Strathclyde"}

@String{inst-Math-U-Strath:adr = "Glasgow, Scotland"}

@String{inst-TU-Chemnitz = "Fak. f. Mathematik, Technische
                 Universit{\"a}t Chemnitz-Zwickau"}

@String{inst-TU-Chemnitz:adr = "Chemnitz, FRG"}

@String{inst-M-Utrecht = "Department of Mathematics, Utrecht
                 University"}

@String{inst-M-Utrecht:adr = "Utrecht, Netherlands"}

%=======================================================================

% Publishers and their addresses:



@String{pub-ACM = "ACM Press"}

@String{pub-ACM:adr = "New York"}

@String{pub-AMS = "American Mathematical Society"}

@String{pub-AMS:adr = "Providence, RI, USA"}

@String{pub-AP = "Academic Press"}

@String{pub-AP:adr-NY = "New York"}

@String{pub-AP:adr-B = "Boston, MA, USA"}

@String{pub-AP:adr-S = "San Diego, CA, USA"}

@String{pub-AP:adr-L = "London"}

@String{pub-AW = "Ad{\-d}i{\-s}on-Wes{\-l}ey"}

% @String{pub-AW:adr              = "Reading, Massachusetts"}

@String{pub-AW:adr = "Reading, MA, USA"}

@String{pub-AWLongman = "Addison Wesley Longman"}

@String{pub-AWLongman:adr = "Harlow, Essex, UK"}

@String{pub-BH = "Birkh{\"{a}}user"}

@String{pub-BH:adr = "Boston, MA, USA"}

@String{pub-BH:adr-Basel = "Basel, Switzerland"}

@String{pub-Blaisdell = "Blaisdell"}

@String{pub-Blaisdell:adr-MA = "Waltham, MA, USA"}

@String{pub-Blaisdell:adr-NY = "New York"}

@String{pub-BrooksCole = "Brooks/Cole"}

@String{pub-BrooksCole:adr = "Pacific Grove, CA, USA"}

@String{pub-CH = "Chapman and Hall"}

@String{pub-CHCRC = "Chapman and Hall/CRC"}

@String{pub-CH:adr-L = "London"}

@String{pub-CH:adr-NY = "New York"}

@String{pub-CUP = "Cambridge University Press"}

@String{pub-CUP:adr = "Cambridge, UK"}

@String{pub-CRC = "CRC Press"}

@String{pub-CRC:adr = "Boca Raton, FL, USA"}

@String{pub-DCH = "D. C. Heath"}

@String{pub-DCH:adr = "Lexington, MA, USA"}

@String{pub-Dover = "Dover"}

@String{pub-Dover:adr = "New York"}

@String{pub-EH = "Ellis Horwood"}

@String{pub-EH:adr = "New York"}

@String{pub-ELS = "Elsevier"}

@String{pub-ELSNH = "Elsevier/North-Hol{\-}land"}

@String{pub-ELS:adr = "Amsterdam, The Netherlands"}

@String{pub-Freeman = "W. H. Freeman"}

@String{pub-Freeman:adr = "New York"}

@String{pub-Gruyter = "Walter de Gruyter"}

@String{pub-Gruyter:adr = "Berlin"}

@String{pub-Harvard = "Harvard University Press"}

@String{pub-Harvard:adr = "Cambridge, MA, USA"}

@String{pub-HMSO = "Her Majesty's Stationary Office"}

@String{pub-HMSO:adr = "London"}

@String{pub-HRW = "Holt, Rinehart and Winston"}

@String{pub-HRW:adr = "New York"}

@String{pub-IEC = "International Electrotechnical Commission"}

@String{pub-IEC:adr = "Geneva, Switzerland"}

@String{pub-JH = "Johns Hopkins University Press"}

@String{pub-JH:adr = "Baltimore, MD, USA"}

@String{pub-Kluwer = "Kluwer Academic Publishers"}

@String{pub-Kluwer:adr = "Dordrecht, The Netherlands"}

@String{pub-Kluwer:adr-NY = "New York"}

@String{pub-Longman-ST = "Longman Scientific and Technical"}

@String{pub-Longman-ST:adr = "Essex, UK"}

@String{pub-MAA = "Mathematical Association of America"}

@String{pub-MAA:adr = "Washington, D.C."}

@String{pub-MD = "Marcel Dekker"}

@String{pub-MD:adr = "New York"}

@String{pub-MH = "Mc{\-}Graw-Hill"}

@String{pub-MH:adr = "New York"}

@String{pub-MIT = "MIT Press"}

@String{pub-MIT:adr = "Cambridge, MA, USA"}

@String{pub-NH = "North-Hol{\-}land"}

@String{pub-NH:adr = "Amsterdam, The Netherlands"}

@String{pub-OUP = "Oxford University Press"}

@String{pub-OUP:adr-NY = "New York"}

@String{pub-Penguin = "Penguin"}

@String{pub-Penguin:adr-H = "Harmondsworth, UK"}

@String{pub-Penguin:adr-L = "London"}

@String{pub-Penguin:adr-NY = "New York"}

@String{pub-Peters = "A K Peters"}

@String{pub-Peters:adr = "Wellesley, Massachusetts"}

@String{pub-Plenum = "Plenum Press"}

@String{pub-Plenum:adr = "New York"}

@String{pub-PUP = "Princeton University Press"}

@String{pub-PUP:adr = "Princeton, NJ, USA"}

@String{pub-PH = "Pren{\-}tice-Hall"}

% @String{pub-PH:adr              = "Englewood Cliffs, NJ 07632, USA"}

@String{pub-PH:adr = "Englewood Cliffs, NJ, USA"}

@String{pub-PH2:adr = "Upper Saddle River, NJ, USA"}

@String{pub-PHI = "Pren{\-}tice-Hall International"}

@String{pub-PHI:adr = "Englewood Cliffs, NJ, USA"}

@String{pub-reidel = "D. Reidel"}

@String{pub-reidel:adr = "Dordrecht, Holland"}

@String{pub-SIAM = "Society for Industrial and Applied Mathematics"}

@String{pub-SIAM:adr = "Philadelphia, PA, USA"}

@String{pub-Springer = "Spring{\-}er-Ver{\-}lag"}

@String{pub-Springer:adr-B = "Berlin"}

@String{pub-Springer:adr-NY = "New York"}

@String{pub-Wellesley = "Wellesley-Cambridge Press"}

@String{pub-Wellesley:adr = "Wellesley, MA, USA"}

@String{pub-Wiley = "Wiley"}

@String{pub-Wiley:adr = "New York"}

@String{pub-Wiley:adr-C = "Chichester, UK"}

@String{pub-WS = "World Scientific"}

@String{pub-WS:adr = "Singapore"}

%=======================================================================



@Article{Aasen:1971:RSM,
  author =       "Jan Ole Aasen",
  title =        "On the Reduction of a Symmetric Matrix to Tridiagonal
                 Form",
  journal =      j-BIT,
  volume =       "11",
  pages =        "233--242",
  year =         "1971",
}

@Article{Alpert:1993:WLB,
  author =       "B. Alpert and G. Beylkin and R. Coifman and V.
                 Rokhlin",
  title =        "Wavelet-Like Bases for the Fast Solution of
                 Second-Kind Integral Equations",
  journal =      j-SISC,
  volume =       "14",
  number =       "1",
  pages =        "159--184",
  year =         "1993",
}

@Article{Anderson:1992:GQF,
  author =       "E. Anderson and Z. Bai and J. Dongarra",
  title =        "Generalized {QR} Factorization and Its Applications",
  journal =      j-LAA,
  volume =       "162--164",
  pages =        "243--271",
  year =         "1992",
}

@Article{Abdelmalek:1971:REA,
  author =       "Nabih N. Abdelmalek",
  title =        "Round Off Error Analysis for {Gram-Schmidt} Method and
                 Solution of Linear Least Squares Problems",
  journal =      j-BIT,
  volume =       "11",
  pages =        "345--368",
  year =         "1971",
}

@Article{Ahac:1988:SFM,
  author =       "Alan A. Ahac and John J. Buoni and D. D. Olesky",
  title =        "Stable {$LU$} Factorization of {$H$}-Matrices",
  journal =      j-LAA,
  volume =       "99",
  pages =        "97--110",
  year =         "1988",
}

@Book{acm87,
  key =          "ACM Press",
  title =        "{ACM Turing} Award Lectures: {The} First Twenty Years,
                 1966--1985",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  year =         "1987",
  ISBN =         "0-201-54885-2",
  pages =        "xviii+483",
}

@Book{Acton:1970:NMW,
  author =       "Forman S. Acton",
  title =        "Numerical Methods That Work",
  publisher =    "Harper and Row",
  address =      "New York",
  year =         "1970",
  pages =        "xviii+541",
  note =         "Reprinted by Mathematical Association of America,
                 Washington, D.C., with new preface and additional
                 problems, 1990",
  ISBN =         "0-88385-450-3",
}

@Book{Acton:1996:RCM,
  author =       "Forman S. Acton",
  title =        "Real Computing Made Real: {Preventing} Errors in
                 Scientific and Engineering Calculations",
  publisher =    pub-PUP,
  address =      pub-PUP:adr,
  year =         "1996",
  pages =        "xv+259",
  ISBN =         "0-691-03663-2",
}

@Article{Adams:1967:SCP,
  author =       "Duane A. Adams",
  title =        "A Stopping Criterion for Polynomial Root Finding",
  journal =      j-CACM,
  volume =       "10",
  numbewr =      "10",
  pages =        "655--658",
  year =         "1967",
}

@Article{Arioli:1989:SSL,
  author =       "M. Arioli and J. W. Demmel and I. S. Duff",
  title =        "Solving Sparse Linear Systems with Sparse Backward
                 Error",
  journal =      j-SIMAX,
  volume =       "10",
  number =       "2",
  pages =        "165--190",
  year =         "1989",
}

@Article{Arioli:1989:ASA,
  author =       "M. Arioli and I. S. Duff and P. P. M. de Rijk",
  title =        "On the Augmented System Approach to Sparse
                 Least-Squares Problems",
  journal =      j-NUM-MATH,
  volume =       "55",
  pages =        "667--684",
  year =         "1989",
}

@Article{Arioli:1992:SCI,
  author =       "Mario Arioli and Iain S. Duff and Daniel Ruiz",
  title =        "Stopping Criteria for Iterative Solvers",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "1",
  pages =        "138--144",
  year =         "1992",
}

@Article{Almacany:1984:DCA,
  author =       "M. Almacany and C. B. Dunham and J. Williams",
  title =        "Discrete {Chebyshev} Approximation by Interpolating
                 Rationals",
  journal =      j-IMAJNA,
  volume =       "4",
  pages =        "467--477",
  year =         "1984",
}

@Article{Aggarwal:1979:REM,
  author =       "Vijay B. Aggarwal and James W. Burgmeier",
  title =        "A Round-Off Error Model With Applications to
                 Arithmetic Expressions",
  journal =      j-SICOMP,
  volume =       "8",
  number =       "1",
  pages =        "60--72",
  year =         "1979",
}

@Article{Ashcraft:1998:ASI,
  author =       "Cleve Ashcraft and Roger G. Grimes and John G. Lewis",
  title =        "Accurate Symmetric Indefinite Linear Equation
                 Solvers",
  journal =      j-SIMAX,
  volume =       "20",
  number =       "2",
  pages =        "513--561",
  year =         "1998",
}

@Article{Alonso:1997:BEA,
  author =       "P. Alonso and M. Gasca and J. M. Pe{\~n}a",
  title =        "Backward Error Analysis of {Neville} Elimination",
  journal =      j-APP-NUM-MATH,
  volume =       "23",
  pages =        "193--204",
  year =         "1997",
}

@Article{Ahlberg:1963:CPS,
  author =       "J. H. Ahlberg and E. N. Nilson",
  title =        "Convergence Properties of the Spline Fit",
  journal =      j-SIAM,
  volume =       "11",
  number =       "1",
  pages =        "95--104",
  year =         "1963",
}

@InCollection{Ewing:1991:PHP,
  key =          "Albers, Donald J.",
  title =        "{Paul Halmos} By Parts (Interviews by {Donald J.
                 Albers})",
  editor =       "John H. Ewing and F. W. Gehring",
  booktitle =    "{Paul Halmos}: {Celebrating} 50 Years of Mathematics",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  pages =        "3--32",
  year =         "1991",
}

@Book{Alefeld:1983:IIC,
  author =       "G{\"o}ltz Alefeld and J{\"u}rgen Herzberger",
  title =        "Introduction to Interval Computations",
  publisher =    pub-AP,
  address =      pub-AP:adr-NY,
  year =         "1983",
  pages =        "xviii+333",
  ISBN =         "0-12-049820-0",
}

@Article{Althoen:1987:GJR,
  author =       "Steven C. Althoen and Renate Mclaughlin",
  title =        "{Gauss-Jordan} Reduction: {A} Brief History",
  journal =      j-AMM,
  volume =       "94",
  number =       "2",
  pages =        "130--142",
  year =         "1987",
}

@Article{Alt:1981:CBC,
  author =       "H. Alt and J. van Leeuwen",
  title =        "The Complexity of Basic Complex Operations",
  journal =      j-COMPUTING,
  volume =       "27",
  pages =        "205--215",
  year =         "1981",
}

@Article{Amodio:1994:BEA,
  author =       "Pierluigi Amodio and Francesca Mazzia",
  title =        "Backward Error Analysis of Cyclic Reduction for the
                 Solution of Tridiagonal Systems",
  journal =      j-MATH-COMP,
  volume =       "62",
  number =       "206",
  pages =        "601--617",
  year =         "1994",
}

@Book{Anderson:1971:SAT,
  author =       "T. W. Anderson",
  title =        "The Statistical Analysis of Time Series",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  year =         "1971",
  pages =        "xiv+704",
  ISBN =         "0-471-02900-9",
}

@TechReport{Anderson:1991:RTS,
  author =       "Edward Anderson",
  title =        "Robust Triangular Solves for Use in Condition
                 Estimation",
  institution =  inst-CS-U-Tenn,
  address =      inst-CS-U-Tenn:adr,
  type =         "Technical Report",
  number =       "CS-91-142",
  month =        aug,
  year =         "1991",
  pages =        "35",
  note =         "LAPACK Working Note 36",
}

@Article{Anderson:1999:DAF,
  author =       "I. J. Anderson",
  title =        "A Distillation Algorithm for Floating-Point
                 Summation",
  journal =      j-SISC,
  volume =       "20",
  number =       "5",
  pages =        "1797--1806",
  year =         "1999",
}

@Article{Ando:1987:TPM,
  author =       "T. Ando",
  title =        "Totally Positive Matrices",
  journal =      j-LAA,
  volume =       "90",
  pages =        "165--219",
  year =         "1987",
}

@Article{Andrew:1990:ESV,
  author =       "Alan L. Andrew",
  title =        "Eigenvalues and Singular Values of Certain Random
                 Matrices",
  journal =      j-JCAM,
  volume =       "30",
  pages =        "165--171",
  year =         "1990",
}

@Article{Anonymous:1922:CC,
  author =       "Anonymous",
  title =        "Le {Commandant Cholesky}",
  journal =      "Bulletin {G\'eod\'esique}",
  pages =        "159--161",
  year =         "1922",
  note =         "Translation by Richard W. Cottle (``Major
                 {Cholesky}'') appears in
                 \cite[Appendix]{Maindonald:1984:SC} and in NA Digest,
                 Volume 90, Issue 7, 1990",
}

@Article{Anda:1994:FPR,
  author =       "Andrew A. Anda and Haesun Park",
  title =        "Fast Plane Rotations with Dynamic Scaling",
  journal =      j-SIMAX,
  volume =       "15",
  number =       "1",
  pages =        "162--174",
  year =         "1994",
}

@Article{Anderson:1987:GRO,
  author =       "T. W. Anderson and I. Olkin and L. G. Underhill",
  title =        "Generation of Random Orthogonal Matrices",
  journal =      j-SISSC,
  volume =       "8",
  number =       "4",
  pages =        "625--629",
  year =         "1987",
}

@Book{Computer:1988:ANM,
  author =       "Apple Computer",
  title =        "Apple Numerics Manual",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Second",
  year =         "1988",
}

@Book{Computer:1994:IMP,
  author =       "Apple Computer",
  title =        "Inside {Macintosh}: {PowerPC} Numerics",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  year =         "1994",
  ISBN =         "0-201-40728-0",
}

@InCollection{Alvarado:1993:HPS,
  author =       "Fernando L. Alvarado and Alex Pothen and Robert S.
                 Schreiber",
  title =        "Highly Parallel Sparse Triangular Solution",
  booktitle =    "Graph Theory and Sparse Matrix Computations",
  editor =       "J. Alan George and John R. Gilbert and Joseph W. H.
                 Liu",
  series =       "IMA Volumes in Mathematics and Its Applications",
  volume =       "56",
  pages =        "141--158",
  publisher =    pub-Springer # ", " # pub-Springer:adr-NY,
  year =         "1993",
}

@TechReport{Arioli:2000:SCC,
  author =       "Mario Arioli",
  title =        "A Stopping Criterion for the Conjugate Gradient
                 Algorithm in a Finite Element Method Framework",
  institution =  "Istituto di Analisi Numerica - C.N.R.",
  address =      "Pavia, Italy",
  type =         "Technical Report",
  number =       "1179",
  year =         "2000",
  pages =        "12",
}

@Article{Arnold:1984:GEA,
  author =       "William F. Arnold and Alan J. Laub",
  title =        "Generalized Eigenproblem Algorithms and Software for
                 Algebraic {Riccati} Equations",
  journal =      "Proc. IEEE",
  volume =       "72",
  number =       "12",
  pages =        "1746--1754",
  year =         "1984",
}

@Article{Arioli:1985:EAA,
  author =       "M. Arioli and A. Laratta",
  title =        "Error Analysis of an Algorithm for Solving an
                 Underdetermined Linear System",
  journal =      j-NUM-MATH,
  volume =       "46",
  pages =        "255--268",
  year =         "1985",
}

@Article{Arioli:1986:EAA,
  author =       "M. Arioli and A. Laratta",
  title =        "Error Analysis of Algorithms for Computing the
                 Projection of a Point onto a Linear Manifold",
  journal =      j-LAA,
  volume =       "82",
  pages =        "1--26",
  year =         "1986",
}

@Article{Arioli:1992:SCC,
  author =       "Mario Arioli and Francesco Romani",
  title =        "Stability, Convergence, and Conditioning of Stationary
                 Iterative Methods of the Form {$x^{(i+1)} = P x^{(i)} +
                 q$} for the Solution of Linear Systems",
  journal =      j-IMAJNA,
  volume =       "12",
  pages =        "21--30",
  year =         "1992",
}

@Article{Ashenhurst:1965:EEC,
  author =       "R. L. Ashenhurst and N. Metropolis",
  title =        "Error Estimation in Computer Calculation",
  journal =      j-AMM,
  part =         "II",
  volume =       "72",
  number =       "2",
  pages =        "47--58",
  year =         "1965",
}

@Article{Asplund:1959:IMW,
  author =       "Edgar Asplund",
  title =        "Inverses of Matrices {$\{a_{ij}\}$} Which Satisfy
                 {$a_{ij}=0$} For {$j>i+p$}",
  journal =      "Math. Scand.",
  volume =       "7",
  pages =        "57--60",
  year =         "1959",
}

@Misc{Atanasoff:1940:CMS,
  author =       "John V. Atanasoff",
  title =        "Computing Machine for the Solution of Large Systems of
                 Linear Algebraic Equations",
  howpublished = "Unpublished manuscript, Iowa State College, Ames, IA,
                 USA",
  month =        aug,
  year =         "1940",
  note =         "Reprinted in \cite[pp.~315--335]{Randell:1975:ODC}",
}

@Book{Axelsson:1994:ISM,
  author =       "Owe Axelsson",
  title =        "Iterative Solution Methods",
  publisher =    pub-CUP,
  year =         "1994",
  pages =        "xiii+654",
  ISBN =         "0-521-44524-8",
}

@Article{Barlow:1985:RED,
  author =       "Jesse L. Barlow and E. H. Bareiss",
  title =        "On Roundoff Error Distributions in Floating Point and
                 Logarithmic Arithmetic",
  journal =      j-COMPUTING,
  volume =       "34",
  pages =        "325--347",
  year =         "1985",
}

@Article{Barlow:1985:PEA,
  author =       "Jesse L. Barlow and E. H. Bareiss",
  title =        "Probabilistic Error Analysis of {Gaussian} Elimination
                 in Floating Point and Logarithmic Arithmetic",
  journal =      j-COMPUTING,
  volume =       "34",
  pages =        "349--364",
  year =         "1985",
}

@InProceedings{Babuska:1969:NSM,
  author =       "Ivo Babu{\v{s}}ka",
  title =        "Numerical Stability in Mathematical Analysis",
  booktitle =    "Proc. IFIP Congress",
  series =       "Information Processing 68",
  publisher =    pub-NH # ", " # pub-NH:adr,
  pages =        "11--23",
  year =         "1969",
}

@Article{Bai:1993:SDB,
  author =       "Zhaojun Bai and James W. Demmel",
  title =        "On Swapping Diagonal Blocks in Real {Schur} Form",
  journal =      j-LAA,
  volume =       "186",
  pages =        "73--95",
  year =         "1993",
}

@Article{Bai:1993:CGS,
  author =       "Zhaojun Bai and James W. Demmel",
  title =        "Computing the Generalized Singular Value
                 Decomposition",
  journal =      j-SISC,
  volume =       "14",
  number =       "6",
  pages =        "1464--1486",
  year =         "1993",
}

@InProceedings{Bailey:1988:SNA,
  author =       "D. H. Bailey and H. R. P. Ferguson",
  title =        "A {Strassen--Newton} Algorithm for High-Speed
                 Parallelizable Matrix Inversion",
  booktitle =    "Proceedings of Supercomputing '88",
  publisher =    "IEEE Computer Society Press, New York",
  pages =        "419--424",
  year =         "1988",
}

@Article{Barwell:1976:CAS,
  author =       "Victor Barwell and Alan George",
  title =        "A Comparison of Algorithms for Solving Symmetric
                 Indefinite Systems of Linear Equations",
  journal =      j-TOMS,
  volume =       "2",
  number =       "3",
  pages =        "242--251",
  year =         "1976",
}

@Article{Bartels:1992:SSV,
  author =       "Sven G. Bartels and Desmond J. Higham",
  title =        "The Structured Sensitivity of {Vandermonde}-like
                 Systems",
  journal =      j-NUM-MATH,
  volume =       "62",
  pages =        "17--33",
  year =         "1992",
}

@Article{Bailey:1988:EHS,
  author =       "David H. Bailey",
  title =        "Extra High Speed Matrix Multiplication on the
                 {Cray}-2",
  journal =      j-SISSC,
  volume =       "9",
  number =       "3",
  pages =        "603--607",
  year =         "1988",
}

@Article{Bailey:1988:CDD,
  author =       "David H. Bailey",
  title =        "The Computation of {$\pi$} to 29,360,000 Decimal
                 Digits Using {Borweins'} Quartically Convergent
                 Algorithm",
  journal =      j-MATH-COMP,
  volume =       "50",
  number =       "181",
  pages =        "283--296",
  year =         "1988",
}

@Article{Bailey:1993:AMT,
  author =       "David H. Bailey",
  title =        "Algorithm 719: {Multiprecision} Translation and
                 Execution of {FORTRAN} Programs",
  journal =      j-TOMS,
  volume =       "19",
  number =       "3",
  pages =        "288--319",
  year =         "1993",
}

@Article{Bailey:1995:FBM,
  author =       "David H. Bailey",
  title =        "A {Fortran} 90-Based Multiprecision System",
  journal =      j-TOMS,
  volume =       "21",
  number =       "4",
  pages =        "379--387",
  year =         "1995",
}

@Article{Barlow:1987:SGR,
  author =       "Jesse L. Barlow and Ilse C. F. Ipsen",
  title =        "Scaled {Givens} Rotations for the Solution of Linear
                 Least Squares Problems on Systolic Arrays",
  journal =      j-SISSC,
  volume =       "8",
  number =       "5",
  pages =        "716--733",
  year =         "1987",
}

@Article{Baksalary:1979:ME,
  author =       "J. K. Baksalary and R. Kala",
  title =        "The Matrix Equation {$AX-YB=C$}",
  journal =      j-LAA,
  volume =       "25",
  pages =        "41--43",
  year =         "1979",
}

@Article{Baksalary:1980:ME,
  author =       "J. K. Baksalary and R. Kala",
  title =        "The Matrix Equation {$AXB + CYD = E$}",
  journal =      j-LAA,
  volume =       "30",
  pages =        "141--147",
  year =         "1980",
}

@Article{Ballester:1967:CDA,
  author =       "C. Ballester and V. Pereyra",
  title =        "On the Construction of Discrete Approximations to
                 Linear Differential Expressions",
  journal =      j-MATH-COMP,
  volume =       "21",
  pages =        "297--302",
  year =         "1967",
}

@Book{Bard:1974:NPE,
  author =       "Yonathan Bard",
  title =        "Nonlinear Parameter Estimation",
  publisher =    pub-AP,
  address =      pub-AP:adr-NY,
  year =         "1974",
}

@InCollection{Bauer:1971:IPD,
  author =       "F. L. Bauer and C. Reinsch",
  title =        "Inversion of Positive Definite Matrices by the
                 {Gauss-Jordan} Method",
  pages =        "45--49",
  editor =       "J. H. Wilkinson and C. Reinsch",
  booktitle =    "Linear Algebra",
  series =       "Handbook for Automatic Computation",
  volume =       "II",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  year =         "1971",
  note =         "Contribution I/3",
  mycrossref =   "Wilkinson:1971:LA",
}

@PhdThesis{Barlow:1981:PEA,
  author =       "Jesse L. Barlow",
  title =        "Probabilistic Error Analysis of Floating Point and
                 {CRD} Arithmetics",
  school =       "Northwestern University",
  address =      "Evanston, IL, USA",
  month =        jun,
  year =         "1981",
}

@InProceedings{Barlow:1981:DAR,
  author =       "Jesse L. Barlow",
  title =        "On the Distribution of Accumulated Roundoff Error in
                 Floating Point Arithmetic",
  booktitle =    "Proc. 5th IEEE Symposium on Computer Arithmetic, Ann
                 Arbor, Michigan",
  pages =        "100--105",
  year =         "1981",
}

@Article{barl86,
  author =       "Jesse L. Barlow",
  title =        "A Note on Monitoring the Stability of Triangular
                 Decomposition of Sparse Matrices",
  journal =      j-SISSC,
  volume =       "7",
  number =       "1",
  pages =        "166--168",
  year =         "1986",
}

@Article{Barlow:1988:EAI,
  author =       "Jesse L. Barlow",
  title =        "Error Analysis and Implementation Aspects of Deferred
                 Correction for Equality Constrained Least Squares
                 Problems",
  journal =      j-SINUM,
  volume =       "25",
  number =       "6",
  pages =        "1340--1358",
  year =         "1988",
}

@Article{Barlow:1991:EAP,
  author =       "Jesse L. Barlow",
  title =        "Error Analysis of a Pairwise Summation Algorithm to
                 Compute the Sample Variance",
  journal =      j-NUM-MATH,
  volume =       "58",
  pages =        "583--590",
  year =         "1991",
}

@Article{Bank:1977:MAE,
  author =       "Randolph E. Bank and Donald J. Rose",
  title =        "Marching Algorithms for Elliptic Boundary Value
                 Problems. {I}: The Constant Coefficient Case",
  journal =      j-SINUM,
  volume =       "14",
  number =       "5",
  pages =        "792--829",
  year =         "1977",
}

@Article{Barrett:1989:FMA,
  author =       "Geoff Barrett",
  title =        "Formal Methods Applied to a Floating-Point Number
                 System",
  journal =      j-IEEE-SE,
  volume =       "15",
  number =       "5",
  pages =        "611--621",
  year =         "1989",
}

@Article{Barrlund:1991:PBD,
  author =       "Anders Barrlund",
  title =        "Perturbation Bounds for the {$LDL^H$} and {$LU$}
                 Decompositions",
  journal =      j-BIT,
  volume =       "31",
  pages =        "358--363",
  year =         "1991",
}

@Article{Barrlund:1994:PBG,
  author =       "Anders Barrlund",
  title =        "Perturbation Bounds for the Generalized {$QR$}
                 Factorization",
  journal =      j-LAA,
  volume =       "207",
  pages =        "251--271",
  year =         "1994",
}

@MastersThesis{Bartels:1991:TTM,
  author =       "Sven G. Bartels",
  title =        "Two Topics in Matrix Analysis: {Structured}
                 Sensitivity for {Vandermonde}-Like Systems and a
                 Subgradient Method for Matrix Norm Estimation",
  school =       inst-U-Dundee,
  address =      inst-U-Dundee:adr,
  type =         "{M.Sc.} {Thesis}",
  month =        sep,
  year =         "1991",
}

@Article{Barnett:1968:SAL,
  author =       "S. Barnett and C. Storey",
  title =        "Some Applications of the {Lyapunov} Matrix Equation",
  journal =      j-JIMA,
  volume =       "4",
  pages =        "33--42",
  year =         "1968",
}

@Article{Bartels:1972:ASM,
  author =       "R. H. Bartels and G. W. Stewart",
  title =        "Algorithm 432: {Solution} of the Matrix Equation
                 {$AX+XB=C$}",
  journal =      j-CACM,
  volume =       "15",
  number =       "9",
  pages =        "820--826",
  year =         "1972",
}

@Article{Barron:1960:SSL,
  author =       "D. W. Barron and H. P. F. Swinnerton-Dyer",
  title =        "Solution of Simultaneous Linear Equations Using a
                 Magnetic-Tape Store",
  journal =      j-COMP-J,
  volume =       "3",
  number =       "1",
  pages =        "28--33",
  year =         "1960",
}

@Article{Bauer:1963:OSMa,
  author =       "F. L. Bauer",
  title =        "Optimally Scaled Matrices",
  journal =      j-NUM-MATH,
  volume =       "5",
  pages =        "73--87",
  year =         "1963",
}

@InProceedings{Bauer:1963:OSMb,
  author =       "F. L. Bauer",
  title =        "Optimal Scaling of Matrices and the Importance of the
                 Minimal Condition",
  booktitle =    "Proc. IFIP Congress 1962",
  editor =       "Cicely M. Popplewell",
  series =       "Information Processing 62",
  publisher =    pub-NH # ", " # pub-NH:adr,
  pages =        "198--201",
  year =         "1963",
}

@Article{Bauer:1966:GLL,
  author =       "F. L. Bauer",
  title =        "Genauigkeitsfragen bei der {L{\"o}sung} linearer
                 {Gleichungssysteme}",
  journal =      j-ZAMM,
  volume =       "46",
  number =       "7",
  pages =        "409--421",
  year =         "1966",
}

@Article{Bauer:1969:ROS,
  author =       "F. L. Bauer",
  title =        "Remarks on Optimally Scaled Matrices",
  journal =      j-NUM-MATH,
  volume =       "13",
  pages =        "1--3",
  year =         "1969",
}

@Article{Bauer:1974:CGR,
  author =       "F. L. Bauer",
  title =        "Computational Graphs and Rounding Errors",
  journal =      j-SINUM,
  volume =       "11",
  number =       "1",
  pages =        "87--96",
  year =         "1974",
}

@Article{Barlow:1992:RDM,
  author =       "Jesse L. Barlow and Udaya B. Vemulapati",
  title =        "Rank Detection Methods for Sparse Matrices",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "4",
  pages =        "1279--1297",
  year =         "1992",
}

@Article{Barlow:1992:NDC,
  author =       "Jesse L. Barlow and Udaya B. Vemulapati",
  title =        "A Note on Deferred Correction for Equality Constrained
                 Least Squares Problems",
  journal =      j-SINUM,
  volume =       "29",
  number =       "1",
  pages =        "249--256",
  year =         "1992",
}

@Article{Barlow:1998:GGE,
  author =       "Jesse L. Barlow and Hongyuan Zha",
  title =        "Growth in {Gaussian} Elimination, Orthogonal Matrices,
                 and the {$2$}-Norm",
  journal =      j-SIMAX,
  volume =       "19",
  number =       "3",
  pages =        "807--815",
  year =         "1998",
}

@Article{Borwein:1989:RME,
  author =       "J. M. Borwein and P. B. Borwein and D. H. Bailey",
  title =        "Ramanujan, Modular Equations, and Approximations to
                 {Pi} or How to Compute One Billion Digits of {Pi}",
  journal =      j-AMM,
  volume =       "96",
  number =       "3",
  pages =        "201--219",
  year =         "1989",
}

@InCollection{Bliss:1992:API,
  author =       "B. Bliss and M.-C. Brunet and E. Gallopoulos",
  title =        "Automatic Program Instrumentation with Applications in
                 Performance and Error Analysis",
  booktitle =    "Expert Systems for Scientific Computing",
  editor =       "E. N. Houstis and J. R. Rice and R. Vichnevetsky",
  publisher =    pub-NH # ", " # pub-NH:adr,
  pages =        "235--260",
  year =         "1992",
}

@Article{Blackford:1997:PEN,
  author =       "L. S. Blackford and A. Cleary and A. Petitet and R. C.
                 Whaley and J. Demmel and I. Dhillon and H. Ren and K.
                 Stanley and J. Dongarra and S. Hammarling",
  title =        "Practical Experience in the Numerical Dangers of
                 Heterogeneous Computing",
  journal =      j-TOMS,
  volume =       "23",
  number =       "2",
  pages =        "133--147",
  year =         "1997",
}

@Book{Burgisser:1997:ACT,
  author =       "Peter B{\"u}rgisser and Michael Clausen and M. Amin
                 Shokrollahi",
  title =        "Algebraic Complexity Theory",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  year =         "1997",
  ISBN =         "0-540-60582-7",
  pages =        "xxiii+618",
}

@Misc{Blackford:2001:USB,
  author =       "L. S. Blackford and J. Demmel and J. Dongarra and I.
                 Duff and S. Hammarling and G. Henry and M. Heroux and
                 L. Kaufman and A. Lumsdaine and A. Petitet and R. Pozo
                 and K. Remington and R. C. Whaley",
  title =        "An Updated Set of {Basic Linear Algebra Subprograms}
                 ({BLAS})",
  month =        feb,
  year =         "2001",
  pages =        "20",
  note =         "Submitted to " # j-TOMS,
}

@TechReport{Bai:1997:TMC,
  author =       "Zhaojun Bai and David Day and James Demmel and Jack
                 Dongarra",
  title =        "A Test Matrix Collection for Non-{Hermitian}
                 Eigenvalue Problems (Release 1.0)",
  institution =  inst-CS-U-Tenn,
  address =      inst-CS-U-Tenn:adr,
  type =         "Technical Report",
  number =       "CS-97-355",
  pages =        "45",
  month =        mar,
  year =         "1997",
  note =         "LAPACK Working Note 123",
}

@Article{Bai:1997:SDN,
  author =       "Zhaojun Bai and James W. Demmel and Jack J. Dongarra
                 and Antoine Petitet and Howard Robinson and K.
                 Stanley",
  title =        "The Spectral Decomposition of Nonsymmetric Matrices on
                 Distributed Memory Parallel Computers",
  journal =      j-SISC,
  volume =       "18",
  number =       "5",
  pages =        "1446--1461",
  year =         "1997",
}

@Article{Bai:1997:IFP,
  author =       "Zhaojun Bai and James W. Demmel and Ming Gu",
  title =        "Inverse Free Parallel Spectral Divide and Conquer
                 Algorithms for Nonsymmetric Eigenproblems",
  journal =      j-NUM-MATH,
  volume =       "76",
  pages =        "279--308",
  year =         "1997",
}

@TechReport{Browne:1994:NSR,
  author =       "Shirley V. Browne and Jack J. Dongarra and Stan C.
                 Green and Keith Moore and Thomas H. Rowan and Reed C.
                 Wade",
  title =        "Netlib Services and Resources",
  institution =  inst-ORNL,
  address =      inst-ORNL:adr,
  type =         "Report",
  number =       "ORNL/TM-12680",
  month =        apr,
  pages =        "42",
  year =         "1994",
}

@Article{Bai:1993:CCN,
  author =       "Zhaojun Bai and James W. Demmel and Alan McKenney",
  title =        "On Computing Condition Numbers for the Nonsymmetric
                 Eigenproblem",
  journal =      j-TOMS,
  volume =       "19",
  number =       "2",
  pages =        "202--223",
  year =         "1993",
}

@Article{Bunch:1989:SSA,
  author =       "James R. Bunch and James W. Demmel and Charles F. Van
                 Loan",
  title =        "The Strong Stability of Algorithms for Solving
                 Symmetric Linear Systems",
  journal =      j-SIMAX,
  volume =       "10",
  number =       "4",
  pages =        "494--499",
  year =         "1989",
}

@Article{Beckermann:2000:CNR,
  author =       "Bernhard Beckermann",
  title =        "The Condition Number of Real {Vandermonde}, {Krylov}
                 and Positive Definite {Hankel} Matrices",
  journal =      j-NUM-MATH,
  volume =       "85",
  pages =        "553--577",
  year =         "2000",
}

@Article{Bell:1931:RCH,
  author =       "E. T. Bell",
  title =        "Review of ``{Contributions to the History of
                 Determinants}, 1900-1920'', by {Sir Thomas Muir}",
  journal =      j-AMM,
  volume =       "38",
  pages =        "161--164",
  year =         "1931",
}

@Book{Bellman:1970:IMA,
  author =       "Richard Bellman",
  title =        "Introduction to Matrix Analysis",
  edition =      "Second",
  publisher =    pub-MH,
  address =      pub-MH:adr,
  year =         "1970",
  pages =        "xxiii+403",
  note =         "Reprinted by Society for Industrial and Applied
                 Mathematics, Philadelphia, PA, USA, 1997. ISBN
                 0-89871-399-4",
}

@Book{Bell:1971:CSR,
  author =       "C. Gordon Bell and Allen Newell",
  title =        "Computer Structures: {Readings} and Examples",
  publisher =    pub-MH,
  address =      pub-MH:adr,
  year =         "1971",
}

@Article{Benford:1938:LAN,
  author =       "Frank Benford",
  title =        "The Law of Anomalous Numbers",
  journal =      "Proceedings of the American Philosophical Society",
  volume =       "78",
  number =       "4",
  pages =        "551--572",
  year =         "1938",
}

@Article{Benoit:1924:NMR,
  author =       "Commandant Benoit",
  title =        "Note sur une m\'ethode de r\'esolution des \'equations
                 normales provenant de l'application de la m\'ethode des
                 moindres carr\'es \`a un syst\`eme d'\'equations
                 lin\'eaires en nombre inf\'erieur \`a celui des
                 inconnues. {Application} de la m\'ethode \`a la
                 r\'esolution d'un syst\`eme d\'efini d'\'equations
                 lin\'eaires \upshape{(}{Proc\'ed\'e du Commandant
                 Cholesky}\upshape{)}",
  journal =      "Bulletin G\'eod\'esique
                 \upshape{(}Toulouse\upshape{)}",
  volume =       "2",
  pages =        "67--77",
  year =         "1924",
  note =         "Cited in \cite[Cottle's
                 translation]{Anonymous:1922:CC}",
}

@Book{Berman:1994:NMM,
  author =       "Abraham Berman and Robert J. Plemmons",
  title =        "Nonnegative Matrices in the Mathematical Sciences",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "1994",
  pages =        "xx+340",
  ISBN =         "0-89871-321-8",
  note =         "Corrected republication, with supplement, of work
                 first published in 1979 by Academic Press",
}

@Article{Benschop:1971:MSE,
  author =       "N. F. Benschop and H. C. Ratz",
  title =        "A Mean Square Estimate of the Generated Roundoff Error
                 in Constant Matrix Iterative Processes",
  journal =      j-ACM,
  volume =       "18",
  number =       "1",
  pages =        "48--62",
  year =         "1971",
}

@Article{Berenbaum:1991:DSM,
  author =       "M. C. Berenbaum",
  title =        "Direct Search Methods in the Optimisation of Cancer
                 Chemotherapy",
  journal =      "Br. J. Cancer",
  volume =       "61",
  pages =        "101--109",
  year =         "1991",
}

@Article{Beam:1993:ASB,
  author =       "Richard M. Beam and Robert F. Warming",
  title =        "The Asymptotic Spectra of Banded {Toeplitz} and
                 Quasi-{Toeplitz} Matrices",
  journal =      j-SISC,
  volume =       "14",
  number =       "4",
  pages =        "971--1006",
  year =         "1993",
}

@Article{Boley:1994:FPF,
  author =       "Daniel Boley and Gene H. Golub and Samy Makar and
                 Nirmal Saxena and Edward J. McCluskey",
  title =        "Floating Point Fault Tolerance with Backward Error
                 Assertions",
  journal =      j-IEEE-C,
  volume =       "44",
  number =       "2",
  pages =        "302--311",
  year =         "1994",
}

@Article{Buzbee:1970:DMS,
  author =       "B. L. Buzbee and G. H. Golub and C. W. Nielson",
  title =        "On Direct Methods for Solving {Poisson's} Equations",
  journal =      j-SINUM,
  volume =       "7",
  number =       "4",
  pages =        "627--656",
  year =         "1970",
}

@Book{Bhatia:1997:MA,
  author =       "Rajendra Bhatia",
  title =        "Matrix Analysis",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-NY,
  pages =        "xi+347",
  year =         "1997",
  ISBN =         "0-387-94846-5",
}

@TechReport{Balle:1993:STM,
  author =       "Susanne M. Balle and Per Christian Hansen and Nicholas
                 J. Higham",
  title =        "A {Strassen}-Type Matrix Inversion Algorithm for the
                 {Connection Machine}",
  institution =  "Centre for Novel Computing, " # inst-U-Manchester,
  address =      inst-U-Manchester:adr,
  type =         "Technical Report",
  number =       "CNC/1993/028",
  pages =        "29",
  month =        oct,
  year =         "1993",
}

@Article{Bhatia:1994:VUP,
  author =       "Rajendra Bhatia and Kalyan Mukherjea",
  title =        "Variation of the Unitary Part of a Matrix",
  journal =      j-SIMAX,
  volume =       "15",
  number =       "3",
  pages =        "1007--1014",
  year =         "1994",
}

@Article{Bhatia:1997:HWS,
  author =       "Rajendra Bhatia and Peter Rosenthal",
  title =        "How and Why To Solve the Operator Equation {$AX - XB =
                 Y$}",
  journal =      "Bull. London Math. Soc.",
  volume =       "29",
  pages =        "1--21",
  year =         "1997",
}

@Article{Brent:1980:AIB,
  author =       "Richard P. Brent and Judith A. Hooper and J. Michael
                 Yohe",
  title =        "An {AUGMENT} Interface for {Brent's} Multiple
                 Precision Arithmetic Package",
  journal =      j-TOMS,
  volume =       "6",
  number =       "2",
  pages =        "146--149",
  year =         "1980",
}

@Article{Birkhoff:1979:IDT,
  author =       "Garrett Birkhoff and Surender Gulati",
  title =        "Isotropic Distributions of Test Matrices",
  journal =      "J. Appl. Math. Phys. \textup{(}ZAMP\textup{)}",
  volume =       "30",
  pages =        "148--158",
  year =         "1979",
}

@Article{Bini:1980:SFA,
  author =       "Dario Bini and Grazia Lotti",
  title =        "Stability of Fast Algorithms for Matrix
                 Multiplication",
  journal =      j-NUM-MATH,
  volume =       "36",
  pages =        "63--72",
  year =         "1980",
}

@Book{Birkhoff:1977:SMA,
  author =       "Garrett Birkhoff and Saunders Mac Lane",
  title =        "A Survey of Modern Algebra",
  edition =      "Fourth",
  publisher =    "Macmillan",
  address =      "New York",
  year =         "1977",
  pages =        "xi+500",
  ISBN =         "0-02-310070-2",
}

@Book{Bini:1994:PMC,
  author =       "Dario Bini and Victor Y. Pan",
  title =        "Polynomial and Matrix Computations. Volume 1:
                 {Fundamental} Algorithms",
  publisher =    pub-BH,
  address =      pub-BH:adr,
  year =         "1994",
  pages =        "xvi+415",
  ISBN =         "0-8176-3786-9",
}

@Article{Birkhoff:1975:THN,
  author =       "Garrett Birkhoff",
  title =        "Two {Hadamard} Numbers for Matrices",
  journal =      j-CACM,
  volume =       "18",
  number =       "1",
  pages =        "25--29",
  year =         "1975",
}

@Article{Bischof:1990:ICEa,
  author =       "Christian H. Bischof",
  title =        "Incremental Condition Estimation",
  journal =      j-SIMAX,
  volume =       "11",
  number =       "2",
  pages =        "312--322",
  year =         "1990",
}

@Article{Bischof:1987:WRP,
  author =       "Christian H. Bischof and Charles F. Van Loan",
  title =        "The {WY} Representation for Products of {Householder}
                 Matrices",
  journal =      j-SISSC,
  volume =       "8",
  number =       "1",
  pages =        "s2--s13",
  year =         "1987",
}

@Article{Bjorck:1973:ACV,
  author =       "{\AA}ke Bj{\"o}rck and Tommy Elfving",
  title =        "Algorithms for Confluent {Vandermonde} Systems",
  journal =      j-NUM-MATH,
  volume =       "21",
  pages =        "130--137",
  year =         "1973",
}

@Article{Bjorck:1967:IRLa,
  author =       "{\AA}ke Bj{\"o}rck and Gene H. Golub",
  title =        "Iterative Refinement of Linear Least Squares Solutions
                 by {Householder} Transformation",
  journal =      j-BIT,
  volume =       "7",
  pages =        "322--337",
  year =         "1967",
}

@Article{Bjorck:1967:IRLb,
  author =       "{\AA}ke Bj{\"o}rck",
  title =        "Iterative Refinement of Linear Least Squares Solutions
                 {I}",
  journal =      j-BIT,
  volume =       "7",
  pages =        "257--278",
  year =         "1967",
}

@Article{Bjorck:1967:SLL,
  author =       "{\AA}ke Bj{\"o}rck",
  title =        "Solving Linear Least Squares Problems by
                 {Gram-Schmidt} Orthogonalization",
  journal =      j-BIT,
  volume =       "7",
  pages =        "1--21",
  year =         "1967",
}

@Article{Bjorck:1968:IRL,
  author =       "{\AA}ke Bj{\"o}rck",
  title =        "Iterative Refinement of Linear Least Squares Solutions
                 {II}",
  journal =      j-BIT,
  volume =       "8",
  pages =        "8--30",
  year =         "1968",
}

@Article{Bjorck:1978:CIR,
  author =       "{\AA}ke Bj{\"o}rck",
  title =        "Comment on the Iterative Refinement of Least-Squares
                 Solutions",
  journal =      j-ASA,
  volume =       "73",
  number =       "361",
  pages =        "161--166",
  year =         "1978",
}

@Article{Bjorck:1987:SAM,
  author =       "{\AA}ke Bj{\"o}rck",
  title =        "Stability Analysis of the Method of Seminormal
                 Equations for Linear Least Squares Problems",
  journal =      j-LAA,
  volume =       "88/89",
  pages =        "31--48",
  year =         "1987",
}

@InProceedings{Bjorck:1990:LSM,
  author =       "{\AA}ke Bj{\"o}rck",
  title =        "Least Squares Methods",
  editor =       "P. G. Ciarlet and J. L. Lions",
  booktitle =    "Handbook of Numerical Analysis",
  volume =       "I: Finite Difference Methods---Solution of Equations
                 in {$R^n$}",
  publisher =    pub-ELSNH # ", " # pub-ELS:adr,
  year =         "1990",
}

@InProceedings{Bjorck:1990:IRR,
  author =       "{\AA}ke Bj{\"o}rck",
  title =        "Iterative Refinement and Reliable Computing",
  booktitle =    "Reliable Numerical Computation",
  editor =       "M. G. Cox and S. J. Hammarling",
  publisher =    pub-OUP,
  pages =        "249--266",
  year =         "1990",
  mycrossref =   "Cox:1990:RNC",
}

@Article{Bjorck:1991:CWP,
  author =       "{\AA}ke Bj{\"o}rck",
  title =        "Component-Wise Perturbation Analysis and Error Bounds
                 for Linear Least Squares Solutions",
  journal =      j-BIT,
  volume =       "31",
  pages =        "238--244",
  year =         "1991",
}

@InProceedings{Bjorck:1992:PSA,
  author =       "{\AA}ke Bj{\"o}rck",
  title =        "Pivoting and Stability in the Augmented System
                 Method",
  booktitle =    "Numerical Analysis \textup{1991}, Proceedings of the
                 \textup{14}th Dundee Conference",
  series =       "Pitman Research Notes in Mathematics",
  volume =       "260",
  editor =       "D. F. Griffiths and G. A. Watson",
  pages =        "1--16",
  publisher =    pub-Longman-ST # ", " # pub-Longman-ST:adr,
  year =         "1992",
}

@Article{Bjorck:1994:NGS,
  author =       "{\AA}ke Bj{\"o}rck",
  title =        "Numerics of {Gram-Schmidt} Orthogonalization",
  journal =      j-LAA,
  volume =       "197/198",
  pages =        "297--316",
  year =         "1994",
}

@Book{Bjorck:1996:NML,
  author =       "{\AA}ke Bj{\"o}rck",
  title =        "Numerical Methods for Least Squares Problems",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "1996",
  ISBN =         "0-89871-360-9",
  pages =        "xvii+408",
}

@Article{Bjorck:1992:LRO,
  author =       "{\AA}ke Bj{\"o}rck and C. C. Paige",
  title =        "Loss and Recapture of Orthogonality in the Modified
                 {Gram--Schmidt} Algorithm",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "1",
  pages =        "176--190",
  year =         "1992",
}

@Article{Bjorck:1994:SAL,
  author =       "{\AA}ke Bj{\"o}rck and C. C. Paige",
  title =        "Solution of Augmented Linear Systems Using Orthogonal
                 Factorizations",
  journal =      j-BIT,
  volume =       "34",
  pages =        "1--24",
  year =         "1994",
}

@Article{Bjorck:1970:SVS,
  author =       "{\AA}ke Bj{\"o}rck and Victor Pereyra",
  title =        "Solution of {Vandermonde} Systems of Equations",
  journal =      j-MATH-COMP,
  volume =       "24",
  number =       "112",
  pages =        "893--903",
  year =         "1970",
}

@Unpublished{Boros:1994:FAS,
  author =       "T. Boros and T. Kailath and V. Olshevsky",
  title =        "Fast Algorithms for Solving {Vandermonde} and
                 {Chebyshev--Vandermonde} Systems",
  year =         "1994",
  note =         "Manuscript",
  pages =        "22",
}

@Article{Bunch:1976:DSM,
  author =       "James R. Bunch and Linda Kaufman and Beresford N.
                 Parlett",
  title =        "Decomposition of a Symmetric Matrix",
  journal =      j-NUM-MATH,
  volume =       "27",
  pages =        "95--109",
  year =         "1976",
}

@InProceedings{Bailey:1993:MPM,
  author =       "David H. Bailey and Robert Krasny and Richard Pelz",
  title =        "Multiple Precision, Multiple Processor Vortex Sheet
                 Roll-Up Computation",
  editor =       "Richard F. Sincovec and David E. Keyes and Michael R.
                 Leuze and Linda R. Petzold and Daniel A. Reed",
  booktitle =    "Proceedings of the Sixth SIAM Conference on Parallel
                 Processing for Scientific Computing, {Volume I}",
  publisher =    pub-SIAM # ", " # pub-SIAM:adr,
  pages =        "52--56",
  year =         "1993",
}

@Article{Blanch:1964:NEC,
  author =       "G. Blanch",
  title =        "Numerical Evaluation of Continued Fractions",
  journal =      j-SIREV,
  volume =       "6",
  number =       "4",
  pages =        "383--421",
  year =         "1964",
}

@Article{BLAST,
  key =          "Basic Linear Algebra Subprograms Technical (BLAST)
                 Forum",
  title =        "{Basic Linear Algebra Subprograms Technical (BLAST)
                 Forum Standard}",
  journal =      "Int. J. High Performance Applications and
                 Supercomputing",
  year =         "2002",
  note =         "To appear",
}

@InProceedings{Bloch:1948:MC,
  author =       "Richard M. Bloch",
  title =        "Mark {I} Calculator",
  crossref =     "harv48",
  pages =        "23--30",
  year =         "1948",
}

@Article{Bischof:1990:ICEb,
  author =       "Christian H. Bischof and John G. Lewis and Daniel J.
                 Pierce",
  title =        "Incremental Condition Estimation for Sparse Matrices",
  journal =      j-SIMAX,
  volume =       "11",
  number =       "4",
  pages =        "644--659",
  year =         "1990",
}

@Article{Bailey:1991:USA,
  author =       "David H. Bailey and King Lee and Horst D. Simon",
  title =        "Using {Strassen's} Algorithm to Accelerate the
                 Solution of Linear Systems",
  journal =      "J. Supercomputing",
  volume =       "4",
  pages =        "357--371",
  year =         "1991",
}

@Article{Blue:1978:PFP,
  author =       "James L. Blue",
  title =        "A Portable {Fortran} Program to Find the {Euclidean}
                 Norm of a Vector",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "15--23",
  year =         "1978",
}

@Article{Bowdler:1966:SRC,
  author =       "H. J. Bowdler and R. S. Martin and G. Peters and J. H.
                 Wilkinson",
  title =        "Solution of Real and Complex Systems of Linear
                 Equations",
  journal =      j-NUM-MATH,
  volume =       "8",
  pages =        "217--234",
  year =         "1966",
  note =         "Also in \cite[pp.~93--110]{Wilkinson:1971:LA},
                 Contribution I/7",
}

@Article{Bjorstad:1992:EMM,
  author =       "P. Bj{\o}rstad and F. Manne and T. S{\o}revik and M.
                 Vajter\v{s}ic",
  title =        "Efficient Matrix Multiplication on {SIMD} Computers",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "1",
  pages =        "386--401",
  year =         "1992",
}

@TechReport{Bargmann:1946:SLS,
  author =       "V. Bargmann and D. Montgomery and J. von Neumann",
  title =        "Solution of Linear Systems of High Order",
  type =         "Report prepared for {Navy Bureau of Ordnance}",
  year =         "1946",
  note =         "Reprinted in \cite[pp.~421--477]{Taub:1963:JNC}",
}

@Article{Barlow:1988:IME,
  author =       "J. L. Barlow and N. K. Nichols and R. J. Plemmons",
  title =        "Iterative Methods for Equality-Constrained Least
                 Squares Problems",
  journal =      j-SISSC,
  volume =       "9",
  number =       "5",
  pages =        "892--906",
  year =         "1988",
}

@Article{Bodewig:1949:RRE,
  author =       "E. Bodewig",
  title =        "Review of ``{Rounding-Off Errors in Matrix
                 Processes}'' by {A. M. Turing}",
  journal =      "Math. Rev.",
  volume =       "10",
  pages =        "405",
  year =         "1949",
}

@Article{Bondeli:1994:CRS,
  author =       "S. Bondeli and W. Gander",
  title =        "Cyclic Reduction for Special Tridiagonal Systems",
  journal =      j-SIMAX,
  volume =       "15",
  number =       "1",
  pages =        "321--330",
  year =         "1994",
}

@Article{Bohlender:1977:FPC,
  author =       "Gerd Bohlender",
  title =        "Floating-point Computation of Functions with Maximum
                 Accuracy",
  journal =      j-IEEE-C,
  volume =       "C-26",
  number =       "7",
  pages =        "621--632",
  year =         "1977",
}

@Article{Bohte:1975:BRE,
  author =       "Z. Bohte",
  title =        "Bounds for Rounding Errors in the {Gaussian}
                 Elimination For Band Systems",
  journal =      j-JIMA,
  volume =       "16",
  pages =        "133--142",
  year =         "1975",
}

@Article{Bollen:1984:NSD,
  author =       "Jo A. M. Bollen",
  title =        "Numerical Stability of Descent Methods for Solving
                 Linear Equations",
  journal =      j-NUM-MATH,
  volume =       "43",
  pages =        "361--377",
  year =         "1984",
}

@InCollection{Bowden:1953:OTM,
  author =       "B. V. Bowden",
  title =        "The Organization of a Typical Machine",
  booktitle =    "Faster than Thought: {A} Symposium on Digital
                 Computing Machines",
  editor =       "B. V. Bowden",
  publisher =    "Pitman",
  address =      "London",
  pages =        "67--77",
  year =         "1953",
}

@Article{Boyd:1974:PMN,
  author =       "David W. Boyd",
  title =        "The Power Method for {$\ell^p$} Norms",
  journal =      j-LAA,
  volume =       "9",
  pages =        "95--101",
  year =         "1974",
}

@Book{Boyer:1989:HM,
  author =       "Carl B. Boyer",
  title =        "A History of Mathematics",
  edition =      "Second",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  year =         "1989",
  pages =        "xviii+762",
  note =         "Revised by Uta C. Merzbach",
  ISBN =         "0-471-50357-6",
}

@Article{Boyle:1994:AFS,
  author =       "Jeff Boyle",
  title =        "An Application of {Fourier} Series to the Most
                 Significant Digit Problem",
  journal =      j-AMM,
  volume =       "101",
  number =       "11",
  pages =        "879--886",
  year =         "1994",
}

@InProceedings{Boisvert:1997:MMW,
  author =       "Ronald F. Boisvert and Roldan Pozo and Karin Remington
                 and Richard F. Barrett and Jack J. Dongarra",
  title =        "{Matrix Market}: {A Web} Resource for Test Matrix
                 Collections",
  booktitle =    "Quality of Numerical Software: {Assessment} and
                 Enhancement",
  editor =       "Ronald F. Boisvert",
  publisher =    pub-CH # ", " # pub-CH:adr-L,
  pages =        "125--136",
  year =         "1997",
}

@Article{Beaton:1976:ARS,
  author =       "Albert E. Beaton and Donald B. Rubin and John L.
                 Barone",
  title =        "The Acceptability of Regression Solutions: {Another}
                 Look at Computational Accuracy",
  journal =      j-ASA,
  volume =       "71",
  number =       "353",
  pages =        "158--168",
  year =         "1976",
}

@Article{Brent:1970:EAA,
  author =       "R. P. Brent",
  title =        "Error Analysis of Algorithms for Matrix Multiplication
                 and Triangular Decomposition Using {Winograd's}
                 Identity",
  journal =      j-NUM-MATH,
  volume =       "16",
  pages =        "145--156",
  year =         "1970",
}

@TechReport{Brent:1970:AMM,
  author =       "R. P. Brent",
  title =        "Algorithms for Matrix Multiplication",
  type =         "Technical Report",
  number =       "CS 157",
  institution =  inst-CS-U-STANFORD,
  address =      inst-U-STANFORD:adr,
  pages =        "ii+52",
  month =        mar,
  year =         "1970",
}

@Article{Brent:1973:PAV,
  author =       "Richard P. Brent",
  title =        "On the Precision Attainable with Various
                 Floating-Point Number Systems",
  journal =      j-IEEE-C,
  volume =       "C-22",
  number =       "6",
  pages =        "601--607",
  year =         "1973",
}

@Article{Brent:19xx:FMP,
  author =       "Richard P. Brent",
  title =        "A {Fortran} Multiple-Precision Arithmetic Package",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "57--70",
  year =         "{\noopsort{a}}1978",
}

@Article{Brent:19xx:AMF,
  author =       "Richard P. Brent",
  title =        "{ALGORITHM 524} {MP}, {A} {Fortran} Multiple-Precision
                 Arithmetic Package",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "71--81",
  year =         "{\noopsort{b}}1978",
}

@InCollection{Brezinski:1996:ALC,
  author =       "Claude Brezinski",
  title =        "{Andr\'e Louis Cholesky}",
  booktitle =    "{A} Numerical Analysis Conference in Honour of {Jean
                 Meinguet}",
  pages =        "45--50",
  year =         "1996",
  note =         "Published as a supplement to the Bulletin of the
                 Belgian Mathematical Society. Also available as
                 Publication ANO-347, Laboratoire d'Analyse Num\'erique
                 et d'Optimisation, Universit\'e des Sciences et
                 Technologies de Lille, Nov. 1995,
                 \path|http://ano.univ-lille1.fr|",
}

@Book{Briggs:1995:DOM,
  author =       "William L. Briggs and Van Emden Henson",
  title =        "The {DFT}: {An} Owner's Manual for the Discrete
                 {Fourier} Transform",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "1995",
  pages =        "xv+434",
  ISBN =         "0-89871-342-0",
}

@Book{Britton:1992:CWM,
  editor =       "J. L. Britton",
  title =        "Collected Works of {A. M. Turing}: {Pure}
                 Mathematics",
  publisher =    pub-NH,
  address =      pub-NH:adr,
  year =         "1992",
  pages =        "xxii+287",
  ISBN =         "0-444-88059-3",
}

@Article{Bleher:1987:SFE,
  author =       "J. H. Bleher and S. M. Rump and U. Kulisch and M.
                 Metzger and Ch. Ullrich and W. Walter",
  title =        "A Study of a {FORTRAN} Extension for
                 Engineering/Scientific Computation with Access to
                 {ACRITH}",
  journal =      j-COMPUTING,
  volume =       "39",
  pages =        "93--110",
  year =         "1987",
}

@Article{Brown:1981:SRM,
  author =       "W. S. Brown",
  title =        "A Simple but Realistic Model of Floating-Point
                 Arithmetic",
  journal =      j-TOMS,
  volume =       "7",
  number =       "4",
  pages =        "445--480",
  year =         "1981",
}

@InProceedings{Bleher:1985:AHA,
  author =       "J. H. Bleher and A. E. Roeder and S. M. Rump",
  title =        "{ACRITH}: {High}-Accuracy Arithmetic. {An} Advanced
                 Tool for Numerical Computation",
  booktitle =    "Proceedings of the 7th Symposium on Computer
                 Arithmetic",
  editor =       "Kai Hwang",
  pages =        "318--321",
  publisher =    "IEEE Computer Society Press, Silver Spring, MD, USA",
  year =         "1985",
}

@PhdThesis{Brunet:1989:CFL,
  author =       "Marie-Christine Brunet",
  title =        "Contribution {\`a} la Fiabilit{\'e} de Logiciels
                 Num{\'e}riques et {\`a} {L}'analyse de Leur
                 Comportement: Une Approche Statistique",
  school =       "Universit\'e de Paris IX Dauphine, U.E.R.
                 Math\'ematiques de la D\'ecision",
  month =        jan,
  pages =        "viii+214",
  year =         "1989",
}

@Article{Bailey:1989:FPA,
  author =       "David H. Bailey and Horst D. Simon and John T. Barton
                 and Martin J. Fouts",
  title =        "Floating Point Arithmetic in Future Supercomputers",
  journal =      j-IJSA,
  volume =       "3",
  number =       "3",
  pages =        "86--90",
  year =         "1989",
}

@Article{Bauer:1961:AMN,
  author =       "F. L. Bauer and J. Stoer and C. Witzgall",
  title =        "Absolute and Monotonic Norms",
  journal =      j-NUM-MATH,
  volume =       "3",
  pages =        "257--264",
  year =         "1961",
}

@Article{Buchholz:1959:FFC,
  author =       "W. Buchholz",
  title =        "Fingers or Fists? ({The} Choice of Decimal or Binary
                 Representation)",
  journal =      j-CACM,
  volume =       "2",
  number =       "12",
  pages =        "3--11",
  year =         "1959",
}

@Article{Buchholz:1981:OWE,
  author =       "W. Buchholz",
  title =        "Origin of the Word {\emph{Byte}}",
  journal =      j-AHC,
  volume =       "3",
  number =       "1",
  pages =        "72",
  year =         "1981",
}

@Article{Bukhberger:1973:MIT,
  author =       "B. Bukhberger and G. A. Emel'yanenko",
  title =        "Methods of Inverting Tridiagonal Matrices",
  journal =      "U.S.S.R. Computational Math. and Math. Phys.",
  volume =       "13",
  pages =        "10--20",
  year =         "1973",
}

@Article{Businger:1965:LLS,
  author =       "P. Businger and G. H. Golub",
  title =        "Linear Least Squares Solutions by {Householder}
                 Transformations",
  journal =      j-NUM-MATH,
  volume =       "7",
  pages =        "269--276",
  year =         "1965",
  note =         "Also in \cite[pp.~111--118]{Wilkinson:1971:LA},
                 Contribution I/8",
}

@Article{Bunch:1977:SSM,
  author =       "James R. Bunch and Linda Kaufman",
  title =        "Some Stable Methods for Calculating Inertia and
                 Solving Symmetric Linear Systems",
  journal =      j-MATH-COMP,
  volume =       "31",
  number =       "137",
  pages =        "163--179",
  year =         "1977",
}

@Article{Bunch:1971:ESM,
  author =       "James R. Bunch",
  title =        "Equilibration of Symmetric Matrices in the Max-Norm",
  journal =      j-ACM,
  volume =       "18",
  number =       "4",
  pages =        "566--572",
  year =         "1971",
}

@Article{Bunch:1971:ADP,
  author =       "James R. Bunch",
  title =        "Analysis of the Diagonal Pivoting Method",
  journal =      j-SINUM,
  volume =       "8",
  number =       "4",
  pages =        "656--680",
  year =         "1971",
}

@Article{Bunch:1974:PPS,
  author =       "James R. Bunch",
  title =        "Partial Pivoting Strategies for Symmetric Matrices",
  journal =      j-SINUM,
  volume =       "11",
  number =       "3",
  pages =        "521--528",
  year =         "1974",
}

@Article{Bunch:1982:NSD,
  author =       "James R. Bunch",
  title =        "A Note on the Stable Decomposition of Skew-Symmetric
                 Matrices",
  journal =      j-MATH-COMP,
  volume =       "38",
  number =       "158",
  pages =        "475--479",
  year =         "1982",
}

@Article{Bunch:1987:WSS,
  author =       "James R. Bunch",
  title =        "The Weak and Strong Stability of Algorithms in
                 Numerical Linear Algebra",
  journal =      j-LAA,
  volume =       "88/89",
  pages =        "49--66",
  year =         "1987",
}

@Article{Bunch:1971:DMS,
  author =       "James R. Bunch and Beresford N. Parlett",
  title =        "Direct Methods for Solving Symmetric Indefinite
                 Systems of Linear Equations",
  journal =      j-SINUM,
  volume =       "8",
  number =       "4",
  pages =        "639--655",
  year =         "1971",
}

@Article{Burdakov:1997:GAO,
  author =       "Oleg Burdakov",
  title =        "A Greedy Algorithm for the Optimal Basis Problem",
  journal =      j-BIT,
  volume =       "37",
  number =       "3",
  pages =        "591--599",
  year =         "1997",
}

@Article{Businger:1968:MWC,
  author =       "P. A. Businger",
  title =        "Matrices Which Can Be Optimally Scaled",
  journal =      j-NUM-MATH,
  volume =       "12",
  pages =        "346--348",
  year =         "1968",
}

@Article{Businger:1971:MNS,
  author =       "P. A. Businger",
  title =        "Monitoring the numerical stability of {Gaussian}
                 elimination",
  journal =      j-NUM-MATH,
  volume =       "16",
  pages =        "360--361",
  year =         "1971",
}

@Book{Butcher:1987:NAO,
  author =       "J. C. Butcher",
  title =        "The Numerical Analysis of Ordinary Differential
                 Equations: {Runge--Kutta} and General Linear Methods",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr-C,
  year =         "1987",
  pages =        "xv+512",
  ISBN =         "0-471-91046-5",
}

@Book{Buchanan:1992:NMA,
  author =       "James L. Buchanan and Peter R. Turner",
  title =        "Numerical Methods and Analysis",
  publisher =    pub-MH,
  address =      pub-MH:adr,
  year =         "1992",
  pages =        "xv+751",
  ISBN =         "0-07-008717-2, 0-07-112922-7 (international \pbk\
                 edition)",
}

@Article{Byers:1984:LSC,
  author =       "Ralph Byers",
  title =        "A {LINPACK}-Style Condition Estimator for the Equation
                 {$AX-XB^T=C$}",
  journal =      j-IEEE-AC,
  volume =       "AC-29",
  number =       "10",
  pages =        "926--928",
  year =         "1984",
}

@InProceedings{Byers:1985:NCA,
  author =       "Ralph Byers",
  title =        "Numerical Condition of the Algebraic {Riccati}
                 Equation",
  editor =       "B. N. Datta",
  booktitle =    "Linear Algebra and Its Role in Systems Theory",
  series =       "Contemporary Math.",
  volume =       "47",
  publisher =    pub-AMS # ", " # pub-AMS:adr,
  pages =        "35--49",
  year =         "1985",
}

@Article{Byers:1987:SAR,
  author =       "Ralph Byers",
  title =        "Solving the Algebraic {Riccati} Equation with the
                 Matrix Sign Function",
  journal =      j-LAA,
  volume =       "85",
  pages =        "267--279",
  year =         "1987",
}

@Article{Byers:1988:BMM,
  author =       "Ralph Byers",
  title =        "A Bisection Method for Measuring the Distance of a
                 Stable Matrix to the Unstable Matrices",
  journal =      j-SISSC,
  volume =       "9",
  number =       "5",
  pages =        "875--881",
  year =         "1988",
}

@Article{Byers:1987:SVL,
  author =       "Ralph Byers and Stephen Nash",
  title =        "On the Singular ``Vectors'' of the {Lyapunov}
                 Operator",
  journal =      j-SIAD,
  volume =       "8",
  number =       "1",
  pages =        "59--66",
  year =         "1987",
}

@Book{Carpenter:1986:MTA,
  editor =       "B. E. Carpenter and R. W. Doran",
  title =        "{A. M. Turing's} {ACE} Report of 1946 and Other
                 Papers",
  series =       "Charles Babbage Institute Reprint Series for the
                 History of Computing",
  volume =       "10",
  publisher =    pub-MIT,
  address =      pub-MIT:adr,
  year =         "1986",
  pages =        "vii+141",
  ISBN =         "0-262-03114-0",
}

@Article{Caffney:1963:ATM,
  author =       "John Caffney",
  title =        "Another Test Matrix for Determinants and Inverses",
  journal =      j-CACM,
  volume =       "6",
  number =       "6",
  pages =        "310",
  year =         "1963",
}

@Book{Campbell:1979:GIL,
  author =       "S. L. Campbell and C. D. {Meyer, Jr.}",
  title =        "Generalized Inverses of Linear Transformations",
  publisher =    "Pitman",
  address =      "London",
  year =         "1979",
  note =         "Reprinted by Dover, New York, 1991",
  pages =        "xi+272",
  ISBN =         "0-486-66693-X",
}

@Article{Campbell-Kelly:1981:PPA,
  author =       "Martin Campbell-Kelly",
  title =        "Programming the {Pilot ACE}: {Early} Programming
                 Activity at the {National Physical Laboratory}",
  journal =      j-AHC,
  volume =       "3",
  number =       "2",
  pages =        "133--162",
  year =         "1981",
}

@Article{Campbell-Kelly:1984:RAT,
  author =       "Martin Campbell-Kelly",
  title =        "Review of {``Alan Turing: The Enigma'', by Andrew
                 Hodges}",
  journal =      j-AHC,
  volume =       "6",
  number =       "2",
  pages =        "176--178",
  year =         "1984",
}

@Article{Caprani:1971:ILR,
  author =       "Ole Caprani",
  title =        "Implementation of a Low Round-Off Summation Method",
  journal =      j-BIT,
  volume =       "11",
  pages =        "271--275",
  year =         "1971",
}

@Article{Calvetti:1992:CVS,
  author =       "D. Calvetti and L. Reichel",
  title =        "A {Chebychev-Vandermonde} Solver",
  journal =      j-LAA,
  volume =       "172",
  pages =        "219--229",
  year =         "1992",
}

@Article{Calvetti:1993:FIV,
  author =       "D. Calvetti and L. Reichel",
  title =        "Fast Inversion of {Vandermonde}-Like Matrices
                 Involving Orthogonal Polynomials",
  journal =      j-BIT,
  volume =       "33",
  pages =        "473--484",
  year =         "1993",
}

@Article{Carr:1959:EAF,
  author =       "John W. {Carr III}",
  title =        "Error Analysis in Floating Point Arithmetic",
  journal =      j-CACM,
  volume =       "2",
  number =       "5",
  pages =        "10--15",
  year =         "1959",
}

@Article{Carter:1991:MFP,
  author =       "Russell Carter",
  title =        "{Y-MP} Floating Point and {Cholesky} Factorization",
  journal =      "Int. J. High Speed Computing",
  volume =       "3",
  number =       "3/4",
  pages =        "215--222",
  year =         "1991",
}

@Article{Cao:1986:NIH,
  author =       "Wei-Lu Cao and William J. Stewart",
  title =        "A Note on Inverses of {Hessenberg}-Like Matrices",
  journal =      j-LAA,
  volume =       "76",
  pages =        "233--240",
  year =         "1986",
}

@Book{Cauchy:1841:EAP,
  author =       "A. Cauchy",
  title =        "Exercices d'Analyse et de Phys. Math.",
  volume =       "2",
  address =      "Paris",
  year =         "1841",
  note =         "Cited in \cite{Savage:1954:TIF}",
}

@Article{Cody:1984:PRW,
  author =       "W. J. Cody and J. T. Coonen and D. M. Gay and K.
                 Hanson and D. Hough and W. Kahan and R. Karpinski and
                 J. Palmer and F. N. Ris and D. Stevenson",
  title =        "A Proposed Radix- and Word-Length-Independent Standard
                 for Floating-Point Arithmetic",
  journal =      "IEEE Micro",
  volume =       "4",
  number =       "4",
  pages =        "86--100",
  year =         "1984",
}

@InProceedings{Cline:1982:GLC,
  author =       "Alan K. Cline and Andrew R. Conn and Charles F. Van
                 Loan",
  title =        "Generalizing the {LINPACK} Condition Estimator",
  booktitle =    "Numerical Analysis, Mexico 1981",
  editor =       "J. P. Hennart",
  series =       "Lecture Notes in Mathematics",
  volume =       "909",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  pages =        "73--83",
  year =         "1982",
}

@Article{Chan:1983:ACS,
  author =       "Tony F. Chan and Gene H. Golub and Randall J.
                 LeVeque",
  title =        "Algorithms for Computing the Sample Variance:
                 {Analysis} and Recommendations",
  journal =      "The American Statistician",
  volume =       "37",
  number =       "3",
  pages =        "242--247",
  year =         "1983",
}

@Article{Concus:1985:BPC,
  author =       "P. Concus and G. H. Golub and G. Meurant",
  title =        "Block Preconditioning for the Conjugate Gradient
                 Method",
  journal =      j-SISSC,
  volume =       "6",
  number =       "1",
  pages =        "220--252",
  year =         "1985",
}

@Book{Conn:1992:LFP,
  author =       "Andrew R. Conn and Nicholas I. M. Gould and Philippe
                 L. Toint",
  title =        "{LANCELOT}: {A Fortran} Package for Large-Scale
                 Nonlinear Optimization (Release {A})",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  year =         "1992",
  ISBN =         "0-387-55470-X",
  pages =        "xviii+330",
}

@Book{Chatelin:1993:EM,
  author =       "Fran{\c{c}}oise Chatelin",
  title =        "Eigenvalues of Matrices",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr-C,
  year =         "1993",
}

@InProceedings{Brunet:1986:CTS,
  author =       "Marie-Christine Brunet and Fran{\c{c}}oise Chatelin",
  title =        "{CESTAC}, a Tool for a Stochastic Round-off Error
                 Analysis in Scientific Computing",
  booktitle =    "Numerical Mathematics and Applications",
  editor =       "R. Vichnevetsky and J. Vignes",
  pages =        "11--20",
  publisher =    "Elsevier Science Publishers B.V. (North-Holland), " #
                 pub-NH:adr,
  year =         "1986",
}

@InProceedings{Chatelin:1990:PRE,
  author =       "Fran{\c{c}}oise Chatelin and Marie-Christine Brunet",
  title =        "A Probabilistic Round-off Error Propagation Model.
                 {Application} to the Eigenvalue Problem.",
  booktitle =    "Reliable Numerical Computation",
  editor =       "M. G. Cox and S. J. Hammarling",
  pages =        "139--160",
  publisher =    pub-OUP,
  year =         "1990",
}

@PhdThesis{Cheng:1998:SIM,
  author =       "Sheung Hun Cheng",
  title =        "Symmetric Indefinite Matrices: Linear System Solvers
                 and Modified Inertia Problems",
  school =       inst-U-Manchester,
  address =      inst-U-Manchester:adr,
  year =         "1998",
  month =        jan,
  pages =        "150",
}

@Article{Chan:1988:EWC,
  author =       "Tony F. Chan and David E. Foulser",
  title =        "Effectively Well-Conditioned Linear Systems",
  journal =      j-SISSC,
  volume =       "9",
  number =       "6",
  pages =        "963--969",
  year =         "1988",
}

@InProceedings{Chatelin:1992:ECT,
  author =       "Fran{\c{c}}oise Chatelin and Val{\'e}rie Frayss{\'e}",
  title =        "Elements of a Condition Theory for the Computational
                 Analysis of Algorithms",
  booktitle =    "Iterative Methods in Linear Algebra",
  editor =       "R. Beauwens and P. de Groen",
  pages =        "15--25",
  publisher =    "Elsevier Science Publishers B.V. (North-Holland), " #
                 pub-NH:adr,
  year =         "1992",
}

@Book{Chaitin-Chatelin:1996:LFP,
  author =       "Fran{\c{c}}oise Chaitin-Chatelin and Val{\'e}rie
                 Frayss{\'e}",
  title =        "Lectures on Finite Precision Computations",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "1996",
  pages =        "xv+235",
  ISBN =         "0-89871-358-7",
}

@Article{Chartres:1967:CEB,
  author =       "Bruce A. Chartres and James C. Geuder",
  title =        "Computable Error Bounds for Direct Solution of Linear
                 Equations",
  journal =      j-ACM,
  volume =       "14",
  number =       "1",
  pages =        "63--71",
  year =         "1967",
}

@Article{Chu:1985:NEE,
  author =       "Eleanor Chu and Alan George",
  title =        "A Note on Estimating the Error in {Gaussian}
                 Elimination Without Pivoting",
  journal =      j-SIGNUM,
  volume =       "20",
  number =       "2",
  pages =        "2--7",
  year =         "1985",
}

@Article{Cohen:1983:CCP,
  author =       "Marty S. Cohen and T. E. Hull and V. Carl Hamacher",
  title =        "{CADAC}: {A} Controlled-Precision Decimal Arithmetic
                 Unit",
  journal =      j-IEEE-C,
  volume =       "C-32",
  number =       "4",
  pages =        "370--377",
  year =         "1983",
}

@Article{Chan:1992:SAR,
  author =       "T. F. Chan and P. C. Hansen",
  title =        "Some Applications of the Rank Revealing {QR}
                 Factorization",
  journal =      j-SISSC,
  volume =       "13",
  number =       "3",
  pages =        "727--741",
  year =         "1992",
}

@Article{Christiansen:1994:ECN,
  author =       "S{\o}ren Christiansen and Per Christian Hansen",
  title =        "The Effective Condition Number Applied to Error
                 Analysis of Certain Boundary Collocation Methods",
  journal =      j-JCAM,
  volume =       "54",
  pages =        "15--36",
  year =         "1994",
}

@InProceedings{Cheng:2001:PIB,
  author =       "Sheung Hun Cheng and Nicholas J. Higham",
  title =        "Parallel Implementation of a Block Algorithm for
                 Matrix 1-Norm Estimation",
  booktitle =    "Euro-Par \textup{2001}, Parallel Processing",
  editor =       "Rizos Sakellariou and John Keane and John Gurd and Len
                 Freeman",
  series =       "Lecture Notes in Computer Science",
  volume =       "2150",
  pages =        "568--577",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  year =         "2001",
}

@TechReport{Cheng:2001:ILB,
  author =       "Sheung Hun Cheng and Nicholas J. Higham",
  title =        "Implementation for {LAPACK} of a Block Algorithm for
                 Matrix 1-Norm Estimation",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  type =         t-NAREP,
  number =       "No. 393",
  pages =        "19",
  month =        aug,
  year =         "2001",
  note =         "LAPACK Working Note 152",
}

@Article{Cheng:1998:MCA,
  author =       "Sheung Hun Cheng and Nicholas J. Higham",
  title =        "A Modified {Cholesky} Algorithm Based on a Symmetric
                 Indefinite Factorization",
  journal =      j-SIMAX,
  volume =       "19",
  number =       "4",
  pages =        "1097--1110",
  month =        oct,
  year =         "1998",
}

@Article{Chandrasekaran:1994:BEE,
  author =       "Shivkumar Chandrasekaran and Ilse C. F. Ipsen",
  title =        "Backward Errors for Eigenvalue and Singular Value
                 Decompositions",
  journal =      j-NUM-MATH,
  volume =       "68",
  pages =        "215--223",
  year =         "1994",
}

@Article{Chandrasekaran:1995:SSC,
  author =       "Shivkumar Chandrasekaran and Ilse C. F. Ipsen",
  title =        "On the Sensitivity of Solution Components in Linear
                 Systems of Equations",
  journal =      j-SIMAX,
  volume =       "16",
  number =       "1",
  pages =        "93--112",
  year =         "1995",
}

@Article{Cheng:2001:ALM,
  author =       "Sheung Hun Cheng and Nicholas J. Higham and Charles S.
                 Kenney and Alan J. Laub",
  title =        "Approximating the Logarithm of a Matrix to Specified
                 Accuracy",
  journal =      j-SIMAX,
  volume =       "22",
  number =       "4",
  pages =        "1112--1125",
  year =         "2001",
}

@Article{Chan:1979:CSD,
  author =       "Tony F. Chan and John Gregg Lewis",
  title =        "Computing Standard Deivations: {Accuracy}",
  journal =      j-CACM,
  volume =       "22",
  number =       "9",
  pages =        "526--531",
  year =         "1979",
}

@Article{Chan:1983:DEE,
  author =       "N. N. Chan and Kim-Hung Li",
  title =        "Diagonal Elements and Eigenvalues of a Real Symmetric
                 Matrix",
  journal =      "J. Math. Anal. Appl.",
  volume =       "91",
  pages =        "562--566",
  year =         "1983",
}

@Article{Chan:1983:AFS,
  author =       "N. N. Chan and Kim-Hung Li",
  title =        "{Algorithm 115}: {A} {FORTRAN} Subroutine for Finding
                 a Real Symmetric Matrix with Prescribed Diagonal
                 Elements and Eigenvalues",
  journal =      j-COMP-J,
  volume =       "26",
  number =       "2",
  pages =        "184--186",
  year =         "1983",
}

@Article{Chan:1996:CGM,
  author =       "Raymond H. Chan and Michael K. Ng",
  title =        "Conjugate Gradient Methods for {Toeplitz} Systems",
  journal =      j-SIREV,
  volume =       "38",
  number =       "3",
  pages =        "427--482",
  year =         "1996",
}

@Article{Cho:1968:TDC,
  author =       "Choong Yun Cho",
  title =        "On the Triangular Decomposition of {Cauchy} Matrices",
  journal =      j-MATH-COMP,
  volume =       "2",
  number =       "104",
  pages =        "819--825",
  year =         "1968",
}

@Article{Choi:1983:TTH,
  author =       "Man-Duen Choi",
  title =        "Tricks or Treats with the {Hilbert} Matrix",
  journal =      j-AMM,
  volume =       "90",
  pages =        "301--312",
  year =         "1983",
}

@Article{Chang:2001:CPA,
  author =       "{Xiao-Wen} Chang and Christopher C. Paige",
  title =        "Componentwise Perturbation Analyses for the {QR}
                 Factorization",
  journal =      j-NUM-MATH,
  volume =       "88",
  pages =        "319--345",
  year =         "2001",
}

@Article{Chang:1998:SLF,
  author =       "{Xiao-Wen} Chang and Christopher C. Paige",
  title =        "On the Sensitivity of the {LU} Factorization",
  journal =      j-BIT,
  volume =       "38",
  number =       "3",
  pages =        "486--501",
  year =         "1998",
}

@Article{Chu:2000:FRA,
  author =       "Moody T. Chu",
  title =        "A Fast Recursive Algorithm for Constructing Matrices
                 with Prescribed Eigenvalues and Singular Values",
  journal =      j-SINUM,
  volume =       "37",
  number =       "3",
  pages =        "1004--1020",
  year =         "2000",
}

@Article{Chu:1987:SME,
  author =       "{King-wah} Eric Chu",
  title =        "The Solution of the Matrix Equations {$AXB - CXD = E$}
                 and {$(YA - DZ, YC - BZ) = (E,F)$}",
  journal =      j-LAA,
  volume =       "93",
  pages =        "93--105",
  year =         "1987",
}

@Article{Chu:1999:CMP,
  author =       "Moody T. Chu",
  title =        "On Constructing Matrices with Prescribed Singular
                 Values and Diagonal Elements",
  journal =      j-LAA,
  volume =       "288",
  pages =        "11--22",
  year =         "1999",
}

@Article{OCinneide:1993:EPT,
  author =       "Colm Art O'Cinneide",
  title =        "Entrywise Perturbation Theory and Error Analysis for
                 {Markov} Chains",
  journal =      j-NUM-MATH,
  volume =       "65",
  pages =        "109--120",
  year =         "1993",
}

@Article{Coomes:1995:RCS,
  author =       "Brian A. Coomes and H{\"u}seyin Ko{\c{c}}ak and
                 Kenneth J. Palmer",
  title =        "Rigorous Computational Shadowing of Orbits of Ordinary
                 Differential Equations",
  journal =      j-NUM-MATH,
  volume =       "69",
  number =       "4",
  pages =        "401--421",
  year =         "1995",
}

@Article{Clenshaw:1955:NSC,
  author =       "C. W. Clenshaw",
  title =        "A Note on the Summation of {Chebyshev} Series",
  journal =      j-MTAC,
  volume =       "9",
  number =       "51",
  pages =        "118--120",
  year =         "1955",
}

@Article{Cline:1973:EMS,
  author =       "A. K. Cline",
  title =        "An Elimination Method for the Solution of Linear Least
                 Squares Problems",
  journal =      j-SINUM,
  volume =       "10",
  number =       "2",
  pages =        "283--289",
  year =         "1973",
}

@Article{Clinger:1990:HRF,
  author =       "William D. Clinger",
  title =        "How to Read Floating Point Numbers Accurately",
  journal =      "SIGPLAN Notices",
  volume =       "25",
  number =       "6",
  pages =        "92--101",
  year =         "1990",
}

@Article{Clenshaw:1984:BFP,
  author =       "C. W. Clenshaw and F. W. J. Olver",
  title =        "Beyond Floating Point",
  journal =      j-ACM,
  volume =       "31",
  number =       "2",
  pages =        "319--328",
  year =         "1984",
}

@Article{Codenotti:2001:RAF,
  author =       "B. Codenotti and M. Leoncini and F. P. Preparata",
  title =        "The Role of Arithmetic in Fast Parallel Matrix
                 Inversion",
  journal =      "Algorithmica",
  volume =       "30",
  number =       "4",
  pages =        "685--707",
  year =         "2001",
}

@Article{Cline:1976:SUL,
  author =       "R. E. Cline and R. J. Plemmons",
  title =        "{$l_2$}-Solutions to Underdetermined Linear Systems",
  journal =      j-SIREV,
  volume =       "18",
  number =       "1",
  pages =        "92--106",
  year =         "1976",
}

@Article{Cline:1983:SCE,
  author =       "A. K. Cline and R. K. Rew",
  title =        "A Set of Counter-Examples to Three Condition Number
                 Estimators",
  journal =      j-SISSC,
  volume =       "4",
  number =       "4",
  pages =        "602--611",
  year =         "1983",
}

@Article{Cline:1979:ECN,
  author =       "A. K. Cline and C. B. Moler and G. W. Stewart and J.
                 H. Wilkinson",
  title =        "An Estimate for the Condition Number of a Matrix",
  journal =      j-SINUM,
  volume =       "16",
  number =       "2",
  pages =        "368--375",
  year =         "1979",
}

@Article{Cody:1993:AFS,
  author =       "W. J. Cody and Jerome T. Coonen",
  title =        "{ALGORITHM 722}: {Functions} to Support the {IEEE}
                 Standard for Binary Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "19",
  number =       "4",
  pages =        "443--451",
  year =         "1993",
}

@Book{Conte:1980:ENA,
  author =       "Samuel D. Conte and Carl de Boor",
  title =        "Elementary Numerical Analysis: {An} Algorithmic
                 Approach",
  edition =      "Third",
  publisher =    pub-MH,
  address =      "Tokyo",
  year =         "1980",
  pages =        "xii+432",
  ISBN =         "0-07-066228-2",
}

@Article{Cody:1973:SDN,
  author =       "William J. {Cody, Jr.}",
  title =        "Static and Dynamic Numerical Characteristics of
                 Floating-Point Arithmetic",
  journal =      j-IEEE-C,
  volume =       "C-22",
  number =       "6",
  pages =        "598--601",
  year =         "1973",
}

@InProceedings{Cody:1982:ITF,
  author =       "W. J. Cody",
  title =        "Implementation and Testing of Function Software",
  booktitle =    "Problems and Methodologies in Mathematical Software
                 Production",
  editor =       "Paul C. Messina and Almerico Murli",
  series =       "Lecture Notes in Computer Science",
  volume =       "142",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  year =         "1982",
  pages =        "24--47",
}

@Article{Cody:1988:AMS,
  author =       "W. J. Cody",
  title =        "{ALGORITHM 665 MACHAR}: {A} Subroutine to Dynamically
                 Determine Machine Parameters",
  journal =      j-TOMS,
  volume =       "14",
  number =       "4",
  pages =        "303--311",
  year =         "1988",
}

@InProceedings{Cody:1988:FPS,
  author =       "W. J. Cody",
  title =        "Floating-Point Standards---{Theory} and Practice",
  editor =       "Ramon E. Moore",
  booktitle =    "Reliability in Computing: {The} Role of Interval
                 Methods in Scientific Computing",
  publisher =    pub-AP # ", " # pub-AP:adr-B,
  pages =        "99--107",
  year =         "1988",
}

@Article{Cody:1993:ACP,
  author =       "W. J. Cody",
  title =        "Algorithm 714. {CELEFUNT}: {A} Portable Test Package
                 for Complex Elementary Functions",
  journal =      j-TOMS,
  volume =       "19",
  number =       "1",
  pages =        "121",
  year =         "1993",
}

@Article{Cohen:1974:NPS,
  author =       "A. M. Cohen",
  title =        "A Note on Pivot Size in {Gaussian} Elimination",
  journal =      j-LAA,
  volume =       "8",
  pages =        "361--368",
  year =         "1974",
}

@Article{Cohen:1975:IPM,
  author =       "A. M. Cohen",
  title =        "The Inverse of a {Pascal} Matrix",
  journal =      j-MATH-GAZ,
  volume =       "59",
  number =       "408",
  pages =        "111--112",
  year =         "1975",
}

@InProceedings{Cox:1998:SHQ,
  author =       "Anthony J. Cox and Nicholas J. Higham",
  title =        "Stability of {Householder QR} Factorization for
                 Weighted Least Squares Problems",
  booktitle =    "Numerical Analysis \textup{1997}, Proceedings of the
                 \textup{17}th Dundee Biennial Conference",
  series =       "Pitman Research Notes in Mathematics",
  volume =       "380",
  editor =       "D. F. Griffiths and D. J. Higham and G. A. Watson",
  pages =        "57--73",
  publisher =    pub-AWLongman # ", " # pub-AWLongman:adr,
  year =         "1998",
}

@Article{Cox:1999:ASN,
  author =       "Anthony J. Cox and Nicholas J. Higham",
  title =        "Accuracy and Stability of the Null Space Method for
                 Solving the Equality Constrained Least Squares
                 Problem",
  journal =      j-BIT,
  volume =       "39",
  number =       "1",
  pages =        "34--50",
  year =         "1999",
}

@Article{Cox:1999:BEB,
  author =       "Anthony J. Cox and Nicholas J. Higham",
  title =        "Backward Error Bounds for Constrained Least Squares
                 Problems",
  journal =      j-BIT,
  volume =       "39",
  number =       "2",
  pages =        "210--227",
  year =         "1999",
}

@Article{Cox:1999:RWB,
  author =       "Anthony J. Cox and Nicholas J. Higham",
  title =        "Row-Wise Backward Stable Elimination Methods for the
                 Equality Constrained Least Squares Problem",
  journal =      j-SIMAX,
  volume =       "21",
  number =       "1",
  pages =        "313--326",
  year =         "1999",
}

@Article{Cornea-Hasegan:1999:IFP,
  author =       "Marius Cornea-Hasegan and Bob Norin",
  title =        "{IA-64} Floating-Point Operations and the {IEEE}
                 Standard for Binary Floating-Point Arithmetic",
  journal =      j-INTEL-TECH-J,
  volume =       "Q4",
  year =         "1999",
  note =         "\path|http://developer.intel.com/technology/itj/|",
}

@InProceedings{cool90,
  author =       "James W. Cooley",
  title =        "How the {FFT} Gained Acceptance",
  editor =       "Stephen G. Nash",
  booktitle =    "A History of Scientific Computing",
  publisher =    pub-AW # ", " # pub-AW:adr,
  pages =        "133--140",
  year =         "1990",
}

@InProceedings{Cooley:1994:LFD,
  author =       "James W. Cooley",
  title =        "{Lanczos} and the {FFT}: {A} Discovery Before Its
                 Time",
  editor =       "J. David Brown and Moody T. Chu and Donald C. Ellison
                 and Robert J. Plemmons",
  booktitle =    "Proceedings of the {Cornelius Lanczos} International
                 Centenary Conference",
  publisher =    pub-SIAM # ", " # pub-SIAM:adr,
  year =         "1994",
  pages =        "3--9",
}

@Article{Coonen:1981:UDN,
  author =       "Jerome T. Coonen",
  title =        "Underflow and the Denormalized Numbers",
  journal =      "Computer",
  volume =       "14",
  pages =        "75--87",
  year =         "1981",
}

@Article{Cope:1979:BSL,
  author =       "J. E. Cope and B. W. Rust",
  title =        "Bounds on Solutions of Linear Systems with Inaccurate
                 Data",
  journal =      j-SINUM,
  volume =       "16",
  number =       "6",
  pages =        "950--963",
  year =         "1979",
}

@InProceedings{Clenshaw:1989:LIA,
  author =       "C. W. Clenshaw and F. W. J. Olver and P. R. Turner",
  title =        "Level-Index Arithmetic: {An} Introductory Survey",
  editor =       "Peter R. Turner",
  booktitle =    "Numerical Analysis and Parallel Processing, Lancaster
                 1987",
  series =       "Lecture Notes in Mathematics",
  volume =       "1397",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  pages =        "95--168",
  year =         "1989",
}

@Article{Cottle:1974:MSC,
  author =       "Richard W. Cottle",
  title =        "Manifestations of the {Schur} Complement",
  journal =      j-LAA,
  volume =       "8",
  pages =        "189--211",
  year =         "1974",
}

@Article{Cooley:1965:AMC,
  author =       "James W. Cooley and John W. Tukey",
  title =        "An Algorithm for the Machine Calculation of Complex
                 {Fourier} Series",
  journal =      j-MATH-COMP,
  volume =       "19",
  number =       "90",
  pages =        "297--301",
  year =         "1965",
}

@Article{Cooley:1993:OPF,
  author =       "James W. Cooley and John W. Tukey",
  title =        "On the Origin and Publication of the {FFT} Paper",
  journal =      "Current Contents",
  number =       "51--52",
  pages =        "8--9",
  year =         "1993",
}

@Book{Cody:1980:SME,
  author =       "William J. {Cody, Jr.} and William Waite",
  title =        "Software Manual for the Elementary Functions",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  year =         "1980",
  pages =        "x+269",
  ISBN =         "0-13-822064-6",
}

@InProceedings{Coppersmith:1987:MMA,
  author =       "Don Coppersmith and Shmuel Winograd",
  title =        "Matrix Multiplication via Arithmetic Progressions",
  booktitle =    "Proceedings of the Nineteenth Annual ACM Symposium on
                 Theory of Computing",
  pages =        "1--6",
  publisher =    "ACM Press, New York",
  year =         "1987",
}

@Article{Chang:1996:NPA,
  author =       "{Xiao-Wen} Chang and Christopher C. Paige and G. W.
                 Stewart",
  title =        "New Perturbation Analyses for the {Cholesky}
                 Factorization",
  journal =      j-IMAJNA,
  volume =       "16",
  number =       "4",
  pages =        "457--484",
  year =         "1996",
}

@Article{Chang:1997:PAQ,
  author =       "{Xiao-Wen} Chang and Christopher C. Paige and G. W.
                 Stewart",
  title =        "Perturbation Analyses for the {QR} Factorization",
  journal =      j-SIMAX,
  volume =       "18",
  number =       "3",
  pages =        "775--791",
  year =         "1997",
}

@Article{Crary:1979:VPN,
  author =       "Fred D. Crary",
  title =        "A Versatile Precompiler for Nonstandard Arithmetics",
  journal =      j-TOMS,
  volume =       "5",
  number =       "2",
  pages =        "204--217",
  year =         "1979",
}

@Book{Inc:1989:UMS,
  key =          "Cray",
  author =       "Cray Research Inc.",
  title =        "{UNICOS} Math and Scientific Library Reference
                 Manual",
  publisher =    "Number SR-2081, Version 5.0",
  address =      "Eagan, MN, USA",
  year =         "1989",
}

@Article{Crout:1941:SME,
  author =       "Prescott D. Crout",
  title =        "A Short Method for Evaluating Determinants and Solving
                 Systems of Linear Equations with Real or Complex
                 Coefficients",
  journal =      "Trans. Amer. Inst. Elec. Eng.",
  volume =       "60",
  pages =        "1235--1241",
  year =         "1941",
}

@Article{Cryer:1968:PSG,
  author =       "Colin W. Cryer",
  title =        "Pivot Size in {Gaussian} Elimination",
  journal =      j-NUM-MATH,
  volume =       "12",
  pages =        "335--345",
  year =         "1968",
}

@Article{Cryer:1973:FTP,
  author =       "Colin W. Cryer",
  title =        "The {$LU$}-Factorization of Totally Positive
                 Matrices",
  journal =      j-LAA,
  volume =       "7",
  pages =        "83--92",
  year =         "1973",
}

@Article{Cryer:1976:SPT,
  author =       "Colin W. Cryer",
  title =        "Some Properties of Totally Positive Matrices",
  journal =      j-LAA,
  volume =       "15",
  pages =        "1--25",
  year =         "1976",
}

@Article{Csanky:1976:FPM,
  author =       "L. Csanky",
  title =        "Fast Parallel Matrix Inversion Algorithms",
  journal =      j-SICOMP,
  volume =       "5",
  number =       "4",
  pages =        "618--623",
  year =         "1976",
}

@Article{Curtis:1972:ASM,
  author =       "A. R. Curtis and J. K. Reid",
  title =        "On the Automatic Scaling of Matrices for {Gaussian}
                 Elimination",
  journal =      j-JIMA,
  volume =       "10",
  pages =        "118--124",
  year =         "1972",
}

@Article{Cybenko:1986:CME,
  author =       "George Cybenko and Charles F. Van Loan",
  title =        "Computing the Minimum Eigenvalue of a Symmetric
                 Positive Definite {Toeplitz} matrix",
  journal =      j-SISSC,
  volume =       "7",
  number =       "1",
  pages =        "123--131",
  year =         "1986",
}

@Book{Dahlquist:1974:NM,
  author =       "Germund Dahlquist and {\AA}ke Bj{\"o}rck",
  title =        "Numerical Methods",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  year =         "1974",
  pages =        "xviii+573",
  ISBN =         "0-13-627315-7",
  note =         "Translated by Ned Anderson",
}

@Article{Davies:2000:NSG,
  author =       "Philip I. Davies and Nicholas J. Higham",
  title =        "Numerically Stable Generation of Correlation Matrices
                 and their Factors",
  journal =      j-BIT,
  volume =       "40",
  number =       "4",
  pages =        "640--651",
  year =         "2000",
}

@Article{Dahlquist:1983:MMM,
  author =       "G. Dahlquist",
  title =        "On matrix majorants and minorants, with applications
                 to differential equations",
  journal =      j-LAA,
  volume =       "52/53",
  pages =        "199--216",
  year =         "1983",
}

@Article{Dax:1977:PTS,
  author =       "Achiya Dax and S. Kaniel",
  title =        "Pivoting Techniques for Symmetric {Gaussian}
                 Elimination",
  journal =      j-NUM-MATH,
  volume =       "28",
  pages =        "221--241",
  year =         "1977",
}

@Article{Danloy:1976:CSH,
  author =       "B. Danloy",
  title =        "On the Choice of Signs for {Householder's} Matrices",
  journal =      j-JCAM,
  volume =       "2",
  number =       "1",
  pages =        "67--69",
  year =         "1976",
}

@Article{Day:1988:GGE,
  author =       "Jane M. Day and Brian Peterson",
  title =        "Growth in {Gaussian} Elimination",
  journal =      j-AMM,
  volume =       "95",
  number =       "6",
  pages =        "489--513",
  year =         "1988",
}

@Book{Davis:1984:MNI,
  author =       "Philip J. Davis and Philip Rabinowitz",
  title =        "Methods of Numerical Integration",
  edition =      "Second",
  publisher =    pub-AP,
  address =      pub-AP:adr-L,
  year =         "1984",
  pages =        "xiv+612",
  ISBN =         "0-12-206360-0",
}

@Article{Datta:1988:MEA,
  author =       "Karabi Datta",
  title =        "The Matrix Equation {$XA-BX=R$} and Its Applications",
  journal =      j-LAA,
  volume =       "109",
  pages =        "91--105",
  year =         "1988",
}

@Book{Davis:1979:CM,
  author =       "Philip J. Davis",
  title =        "Circulant Matrices",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  year =         "1979",
  ISBN =         "0-471-05771-1",
  pages =        "xv+250",
}

@Article{Dax:1982:PPS,
  author =       "Achiya Dax",
  title =        "Partial Pivoting Strategies for Symmetric {Gaussian}
                 Elimination",
  journal =      j-MATH-PROG,
  volume =       "22",
  pages =        "288--303",
  year =         "1982",
}

@Article{Dax:1990:CLS,
  author =       "Achiya Dax",
  title =        "The Convergence of Linear Stationary Iterative
                 Processes for Solving Singular Unstructured Systems of
                 Linear Equations",
  journal =      j-SIREV,
  volume =       "32",
  number =       "4",
  pages =        "611--635",
  year =         "1990",
}

@Book{Dongarra:1979:LUG,
  author =       "J. J. Dongarra and J. R. Bunch and C. B. Moler and G.
                 W. Stewart",
  title =        "{LINPACK} Users' Guide",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "1979",
  ISBN =         "0-89871-172-X",
}

@Article{Boor:1977:BEA,
  author =       "Carl de Boor and Allan Pinkus",
  title =        "Backward Error Analysis for Totally Positive Linear
                 Systems",
  journal =      j-NUM-MATH,
  volume =       "27",
  pages =        "485--490",
  year =         "1977",
}

@Article{Dongarra:19xx:SLB,
  author =       "J. J. Dongarra and J. J. Du Croz and I. S. Duff and S.
                 J. Hammarling",
  title =        "A Set of {Level 3} Basic Linear Algebra Subprograms",
  journal =      j-TOMS,
  volume =       "16",
  pages =        "1--17",
  year =         "{\noopsort{a}}1990",
}

@Article{Dongarra:19xx:ASL,
  author =       "J. J. Dongarra and J. J. Du Croz and I. S. Duff and S.
                 J. Hammarling",
  title =        "Algorithm 679. {A} set of {Level 3} Basic Linear
                 Algebra Subprograms: {Model} Implementation and Test
                 Programs",
  journal =      j-TOMS,
  volume =       "16",
  pages =        "18--28",
  year =         "{\noopsort{b}}1990",
}

@Article{Dongarra:19xx:ESF,
  author =       "Jack J. Dongarra and Jeremy J. Du Croz and Sven J.
                 Hammarling and Richard J. Hanson",
  title =        "An Extended Set of {Fortran} Basic Linear Algebra
                 Subprograms",
  journal =      j-TOMS,
  volume =       "14",
  number =       "1",
  pages =        "1--17",
  year =         "{\noopsort{a}}1988",
}

@Article{Dongarra:19xx:AES,
  author =       "Jack J. Dongarra and Jeremy J. Du Croz and Sven J.
                 Hammarling and Richard J. Hanson",
  title =        "Algorithm 656. {An} Extended Set of {Fortran} Basic
                 Linear Algebra Subprograms: {Model} Implementation and
                 Test Programs",
  journal =      j-TOMS,
  volume =       "14",
  number =       "1",
  pages =        "18--32",
  year =         "{\noopsort{b}}1988",
}

@InProceedings{Demmel:1992:DPH,
  author =       "James W. Demmel and J. J. Dongarra and W. Kahan",
  title =        "On Designing Portable High Performance Numerical
                 Libraries",
  booktitle =    "Numerical Analysis \textup{1991}, Proceedings of the
                 \textup{14}th Dundee Conference",
  series =       "Pitman Research Notes in Mathematics",
  volume =       "260",
  editor =       "D. F. Griffiths and G. A. Watson",
  pages =        "69--84",
  publisher =    pub-Longman-ST # ", " # pub-Longman-ST:adr,
  year =         "1992",
}

@Article{Demmel:2001:CCE,
  author =       "James W. Demmel and Benjamin Diament and Gregorio
                 Malajovich",
  title =        "On the Complexity of Computing Error Bounds",
  journal =      j-FOCM,
  volume =       "1",
  number =       "1",
  pages =        "101--125",
  year =         "2001",
}

@Article{Demmel:1995:CSB,
  author =       "James W. Demmel and Inderjit Dhillon and Huan Ren",
  title =        "On the Correctness of Some Bisection-Like Parallel
                 Eigenvalue Algorithms in Floating Point Arithmetic",
  journal =      j-ETNA,
  volume =       "3",
  pages =        "116--149",
  year =         "1995",
}

@Book{Dongarra:1998:NLA,
  author =       "Jack J. Dongarra and Iain S. Duff and Danny C.
                 Sorensen and Henk A. {van der Vorst}",
  title =        "Numerical Linear Algebra for High-Performance
                 Computers",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "1998",
  pages =        "xviii+342",
  ISBN =         "0-89871-428-1",
}

@Article{Demmel:1992:SBA,
  author =       "James W. Demmel and Nicholas J. Higham",
  title =        "Stability of Block Algorithms with Fast Level-3
                 {BLAS}",
  journal =      j-TOMS,
  volume =       "18",
  number =       "3",
  pages =        "274--291",
  month =        sep,
  year =         "1992",
}

@Article{Demmel:1993:IEB,
  author =       "James W. Demmel and Nicholas J. Higham",
  title =        "Improved Error Bounds for Underdetermined System
                 Solvers",
  journal =      j-SIMAX,
  volume =       "14",
  number =       "1",
  pages =        "1--14",
  month =        jan,
  year =         "1993",
}

@Article{Dekker:1989:RGJ,
  author =       "T. J. Dekker and W. Hoffmann",
  title =        "Rehabilitation of the {Gauss-Jordan} Algorithm",
  journal =      j-NUM-MATH,
  volume =       "54",
  pages =        "591--599",
  year =         "1989",
}

@Article{Demmel:1987:CSE,
  author =       "James W. Demmel and Bo K{\aa}gstr{\"o}m",
  title =        "Computing Stable Eigendecompositions of Matrix
                 Pencils",
  journal =      j-LAA,
  volume =       "88/89",
  pages =        "139--186",
  year =         "1987",
}

@Article{Demmel:1988:ASI,
  author =       "James W. Demmel and Bo K{\aa}gstr{\"o}m",
  title =        "Accurate Solutions of Ill-Posed Problems in Control
                 Theory",
  journal =      j-SIMAX,
  volume =       "9",
  number =       "1",
  pages =        "126--145",
  year =         "1988",
}

@Article{Demmel:1990:ASV,
  author =       "James W. Demmel and W. Kahan",
  title =        "Accurate Singular Values of Bidiagonal Matrices",
  journal =      j-SISSC,
  volume =       "11",
  number =       "5",
  pages =        "873--912",
  year =         "1990",
}

@Article{Dekker:1971:FPT,
  author =       "T. J. Dekker",
  title =        "A Floating-Point Technique for Extending the Available
                 Precision",
  journal =      j-NUM-MATH,
  volume =       "18",
  pages =        "224--242",
  year =         "1971",
}

@Article{Demmel:1985:IAS,
  author =       "James W. Demmel and F. Kr{\"u}ckeberg",
  title =        "An Interval Algorithm for Solving Systems of Linear
                 Equations to Prespecified Accuracy",
  journal =      j-COMPUTING,
  volume =       "34",
  pages =        "117--129",
  year =         "1985",
}

@InProceedings{Dongarra:2000:RAS,
  author =       "Jack Dongarra and Victor Eijkhout and Piotr Luszczek",
  title =        "Recursive Approach in Sparse Matrix {LU}
                 Factorization",
  booktitle =    "Proceedings of the 1st SGI Users Conference",
  address =      "Cracow, Poland",
  organization = "ACC Cyfronet UMM",
  month =        oct,
  year =         "2000",
  pages =        "409--418",
}

@Article{Demmel:1994:FNA,
  author =       "James W. Demmel and Xiaoye Li",
  title =        "Faster Numerical Algorithms via Exception Handling",
  journal =      j-IEEE-C,
  volume =       "43",
  number =       "8",
  pages =        "983--992",
  year =         "1994",
}

@TechReport{Demmel:1989:TMG,
  author =       "James W. Demmel and A. McKenney",
  title =        "A Test Matrix Generation Suite",
  institution =  inst-MCS-Argonne,
  address =      inst-MCS-Argonne:adr,
  type =         "Preprint",
  number =       "MCS-P69-0389",
  note =         "LAPACK Working Note 9",
  year =         "1989",
  month =        mar,
  pages =        "16",
}

@Article{Demeure:1989:FFV,
  author =       "C{\'e}dric J. Demeure",
  title =        "Fast {$QR$} Factorization of {Vandermonde} Matrices",
  journal =      j-LAA,
  volume =       "122/3/4",
  pages =        "165--194",
  year =         "1989",
}

@Article{Demeure:1990:FCV,
  author =       "C{\'e}dric J. Demeure",
  title =        "{$QR$} Factorization of Confluent {Vandermonde}
                 Matrices",
  journal =      j-IEEE-ASSP,
  volume =       "38",
  number =       "10",
  pages =        "1799--1802",
  year =         "1990",
}

@Unpublished{Demmel:2001:NAF,
  author =       "James W. Demmel",
  title =        "A Note on Accurate Floating Point Summation",
  note =         "Manuscript",
  pages =        "5",
  year =         "2001",
}

@Article{Demmel:1983:CNE,
  author =       "James W. Demmel",
  title =        "The Condition Number of Equivalence Transformations
                 that Block Diagonalize Matrix Pencils",
  journal =      j-SINUM,
  volume =       "20",
  number =       "3",
  pages =        "599--610",
  year =         "1983",
}

@Article{Demmel:1984:URN,
  author =       "James W. Demmel",
  title =        "Underflow and the Reliability of Numerical Software",
  journal =      j-SISSC,
  volume =       "5",
  number =       "4",
  pages =        "887--919",
  year =         "1984",
}

@Article{Demmel:1987:CND,
  author =       "James W. Demmel",
  title =        "On Condition Numbers and the Distance to the Nearest
                 Ill-Posed Problem",
  journal =      j-NUM-MATH,
  volume =       "51",
  pages =        "251--289",
  year =         "1987",
}

@InProceedings{Demmel:1987:EAA,
  author =       "James W. Demmel",
  title =        "On Error Analysis in Arithmetic With Varying Relative
                 Precision",
  booktitle =    "Proceedings of the Eighth Symposium on Computer
                 Arithmetic, Como, Italy",
  editor =       "Mary Jane Irwin and Renato Stefanelli",
  pages =        "148--152",
  publisher =    "IEEE Computer Society, Washington, D.C.",
  year =         "1987",
}

@TechReport{Demmel:1989:FPE,
  author =       "James W. Demmel",
  title =        "On Floating Point Errors in {Cholesky}",
  institution =  inst-CS-U-Tenn,
  address =      inst-CS-U-Tenn:adr,
  type =         "Technical Report",
  number =       "CS-89-87",
  month =        oct,
  pages =        "6",
  year =         "1989",
  note =         "LAPACK Working Note 14",
}

@Article{Demmel:1991:OIA,
  author =       "James W. Demmel",
  title =        "On the Odor of {IEEE} Arithmetic",
  journal =      "NA Digest",
  volume =       "Volume 91, Issue 39",
  year =         "1991",
  note =         "(Response to a message ``IEEE Arithmetic Stinks'' in
                 Volume 91, Issue 33)",
}

@Article{demm92,
  author =       "James W. Demmel",
  title =        "The Componentwise Distance to the Nearest Singular
                 Matrix",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "1",
  pages =        "10--19",
  year =         "1992",
}

@TechReport{Demmel:1992:OPN,
  author =       "James W. Demmel",
  title =        "Open Problems in Numerical Linear Algebra",
  institution =  inst-IMA,
  address =      inst-IMA:adr,
  type =         "IMA Preprint Series",
  number =       "\#961",
  month =        apr,
  pages =        "21",
  year =         "1992",
  note =         "LAPACK Working Note 47",
}

@TechReport{Demmel:1992:SFP,
  author =       "James W. Demmel",
  title =        "A Specification for Floating Point Parallel Prefix",
  institution =  inst-CS-U-Tenn,
  address =      inst-CS-U-Tenn:adr,
  type =         "Technical Report",
  number =       "CS-92-167",
  month =        jul,
  year =         "1992",
  pages =        "8",
  note =         "LAPACK Working Note 49",
}

@InProceedings{Demmel:1993:TPN,
  author =       "James W. Demmel",
  title =        "Trading Off Parallelism and Numerical Stability",
  booktitle =    "Linear Algebra for Large Scale and Real-Time
                 Applications",
  series =       "NATO ASI Series E",
  volume =       "232",
  editor =       "Marc S. Moonen and Gene H. Golub and Bart L. De Moor",
  pages =        "49--68",
  publisher =    pub-Kluwer # ", " # pub-Kluwer:adr,
  year =         "1993",
}

@Book{Demmel:1997:ANL,
  author =       "James W. Demmel",
  title =        "Applied Numerical Linear Algebra",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "1997",
  pages =        "xi+419",
  ISBN =         "0-89871-389-7",
}

@Article{Demmel:1999:ASV,
  author =       "James W. Demmel",
  title =        "Accurate Singular Value Decompositions of Structured
                 Matrices",
  journal =      j-SIMAX,
  volume =       "21",
  number =       "2",
  pages =        "562--580",
  year =         "1999",
}

@Book{Duff:1986:DMS,
  author =       "I. S. Duff and A. M. Erisman and J. K. Reid",
  title =        "Direct Methods for Sparse Matrices",
  publisher =    pub-OUP,
  year =         "1986",
  pages =        "xiii+341",
  ISBN =         "0-19-853408-6",
}

@Article{Dembo:1982:INM,
  author =       "Ron S. Dembo and Stanley C. Eisenstat and Trond
                 Steihaug",
  title =        "Inexact {Newton} Methods",
  journal =      j-SINUM,
  volume =       "19",
  number =       "2",
  pages =        "400--408",
  year =         "1982",
}

@Article{Descloux:1963:NRE,
  author =       "J. Descloux",
  title =        "Note on the Round-Off Errors in Iterative Processes",
  journal =      j-MATH-COMP,
  volume =       "17",
  pages =        "18--27",
  year =         "1963",
}

@Book{Dennis:1983:NMU,
  author =       "John E. {Dennis, Jr.} and Robert B. Schnabel",
  title =        "Numerical Methods for Unconstrained Optimization and
                 Nonlinear Equations",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xiii+378",
  year =         "1983",
  ISBN =         "0-13-627216-9 (original), 0-89871-364-1 (reprint)",
  note =         "Reprinted by " # pub-SIAM # ", " # pub-SIAM:adr # ",
                 1996",
}

@Article{Dennis:1991:DSM,
  author =       "John E. {Dennis, Jr.} and Virginia Torczon",
  title =        "Direct Search Methods on Parallel Machines",
  journal =      j-SIOPT,
  volume =       "1",
  number =       "4",
  pages =        "448--474",
  year =         "1991",
}

@Article{Dennis:1984:IQN,
  author =       "John E. {Dennis, Jr.} and Homer F. Walker",
  title =        "Inaccuracy in Quasi-{Newton} Methods: {Local}
                 Improvement Theorems",
  journal =      "Math. Prog. Study",
  volume =       "22",
  pages =        "70--85",
  year =         "1984",
}

@Article{Dennis:1993:SLC,
  author =       "John E. {Dennis, Jr.} and Henry Wolkowicz",
  title =        "Sizing and Least-Change Secant Methods",
  journal =      j-SINUM,
  volume =       "30",
  number =       "5",
  pages =        "1291--1314",
  year =         "1993",
}

@Article{Demmel:1999:CSV,
  author =       "James W. Demmel and Ming Gu and Stanley Eisenstat and
                 Ivan Slapni\v{c}ar and Kre\v{s}imir Veseli{\'c} and
                 Zlatko Drma\v{c}",
  title =        "Computing the Singular Value Decomposition with High
                 Relative Accuracy",
  journal =      j-LAA,
  volume =       "299",
  pages =        "21--80",
  year =         "1999",
}

@Article{Dongarra:1984:ILA,
  author =       "J. J. Dongarra and F. G. Gustavson and A. Karp",
  title =        "Implementing Linear Algebra Algorithms for Dense
                 Matrices on a Vector Pipeline Machine",
  journal =      j-SIREV,
  volume =       "26",
  number =       "1",
  pages =        "91--112",
  year =         "1984",
}

@Article{Daniel:1976:RSA,
  author =       "J. W. Daniel and W. B. Gragg and L. Kaufman and G. W.
                 Stewart",
  title =        "Reorthogonalization and Stable Algorithms for Updating
                 the {Gram-Schmidt} {QR} Factorization",
  journal =      j-MATH-COMP,
  volume =       "30",
  number =       "136",
  pages =        "772--795",
  year =         "1976",
}

@Article{Duff:1989:SMT,
  author =       "Iain S. Duff and Roger G. Grimes and John G. Lewis",
  title =        "Sparse Matrix Test Problems",
  journal =      j-TOMS,
  volume =       "15",
  number =       "1",
  pages =        "1--14",
  year =         "1989",
}

@TechReport{Duff:1992:UGH,
  author =       "Iain S. Duff and Roger G. Grimes and John G. Lewis",
  title =        "Users' Guide for the {Harwell--Boeing} Sparse Matrix
                 Collection (Release 1)",
  institution =  inst-RAL,
  address =      inst-RAL:adr,
  type =         "Report",
  number =       "RAL-92-086",
  pages =        "84",
  month =        dec,
  year =         "1992",
}

@Article{Duff:1991:FSS,
  author =       "I. S. Duff and N. I. M. Gould and J. K. Reid and J. A.
                 Scott and K. Turner",
  title =        "The Factorization of Sparse Symmetric Indefinite
                 Matrices",
  journal =      j-IMAJNA,
  volume =       "11",
  pages =        "181--204",
  year =         "1991",
}

@Article{Drkosova:1995:NSG,
  author =       "J. Drko{\v{s}}ov{\'a} and A. Greenbaum and M.
                 Rozlo{\v{z}}n{\'\i}k and Z. Strako{\u{s}}",
  title =        "Numerical Stability of {GMRES}",
  journal =      j-BIT,
  volume =       "35",
  pages =        "309--330",
  year =         "1995",
}

@Article{Dhillon:1998:RCC,
  author =       "Inderjit Dhillon",
  title =        "Reliable Computation of the Condition Number of a
                 Tridiagonal Matrix in {$O(n)$} Time",
  journal =      j-SIMAX,
  volume =       "19",
  number =       "3",
  pages =        "776--796",
  year =         "1998",
}

@Article{Demmel:1995:SBF,
  author =       "James W. Demmel and Nicholas J. Higham and Robert S.
                 Schreiber",
  title =        "Stability of Block {$LU$} Factorization",
  journal =      j-NLAA,
  volume =       "2",
  number =       "2",
  pages =        "173--190",
  year =         "1995",
}

@Article{Douglas:1994:GPL,
  author =       "Craig C. Douglas and Michael Heroux and Gordon
                 Slishman and Roger M. Smith",
  title =        "{GEMMW}: {A} Portable Level 3 {BLAS Winograd} Variant
                 of {Strassen's} Matrix--Matrix Multiply Algorithm",
  journal =      j-JCOMP-PHYS,
  volume =       "110",
  pages =        "1--10",
  year =         "1994",
}

@Article{Diamond:1978:SRI,
  author =       "Harold G. Diamond",
  title =        "Stability of Rounded Off Inverses Under Iteration",
  journal =      j-MATH-COMP,
  volume =       "32",
  number =       "141",
  pages =        "227--232",
  year =         "1978",
}

@Article{Dixon:1983:EEE,
  author =       "John D. Dixon",
  title =        "Estimating Extremal Eigenvalues and Condition Numbers
                 of Matrices",
  journal =      j-SINUM,
  volume =       "20",
  number =       "4",
  pages =        "812--814",
  year =         "1983",
}

@Article{Dongarra:1987:DMS,
  author =       "Jack J. Dongarra and Eric Grosse",
  title =        "Distribution of Mathematical Software Via Electronic
                 Mail",
  journal =      j-CACM,
  volume =       "30",
  number =       "5",
  pages =        "403--407",
  year =         "1987",
}

@TechReport{Dongarra:2001:PVC,
  author =       "Jack J. Dongarra",
  title =        "Performance of Various Computers Using Standard Linear
                 Equations Software",
  institution =  inst-CS-U-Tenn,
  address =      inst-CS-U-Tenn:adr,
  type =         "Technical Report",
  number =       "CS-89-85",
  pages =        "58",
  year =         "2001",
  month =        aug,
}

@Article{Douglas:1994:VMM,
  author =       "Craig C. Douglas and Gordon Slishman",
  title =        "Variants of Matrix-Matrix Multiplication for
                 {Fortran}-90",
  journal =      j-SIGNUM,
  volume =       "29",
  pages =        "4--6",
  year =         "1994",
}

@Article{Douglas:1959:REN,
  author =       "Jim {Douglas, Jr.}",
  title =        "Round-Off Error in the Numerical Solution of the Heat
                 Equation",
  journal =      j-ACM,
  volume =       "6",
  pages =        "48--58",
  year =         "1959",
}

@Article{Drmac:1994:PCF,
  author =       "Zlatko Drma\v{c} and Matja\v{z} Omladi\v{c} and
                 Kre\v{s}imir Veseli{\'c}",
  title =        "On the Perturbation of the {Cholesky} Factorization",
  journal =      j-SIMAX,
  volume =       "15",
  number =       "4",
  pages =        "1319--1332",
  year =         "1994",
}

@Article{Doyle:1957:ISC,
  author =       "Thomas C. Doyle",
  title =        "Inversion of Symmetric Coefficient Matrix of
                 Positive-Definite Quadratic Form",
  journal =      j-MTAC,
  volume =       "11",
  pages =        "55--58",
  year =         "1957",
}

@Article{Duff:1979:DSS,
  author =       "Iain S. Duff and John K. Reid and Neils Munskgaard and
                 Hans B. Nielsen",
  title =        "Direct Solution of Sets of Linear Equations Whose
                 Matrix is Sparse, Symmetric and Indefinite",
  journal =      j-JIMA,
  volume =       "23",
  pages =        "235--250",
  year =         "1979",
}

@Article{Dubrulle:1983:CNM,
  author =       "Augustin A. Dubrulle",
  title =        "A Class of Numerical Methods for the Computation of
                 {Pythagorean} Sums",
  journal =      "IBM J. Res. Develop.",
  volume =       "27",
  number =       "6",
  pages =        "582--589",
  year =         "1983",
}

@Article{Dubrulle:1994:MQI,
  author =       "Augustin A. Dubrulle and Gene H. Golub",
  title =        "A Multishift {QR} Iteration Without Computation of the
                 Shifts",
  journal =      j-NUM-ALG,
  volume =       "7",
  pages =        "173--181",
  year =         "1994",
}

@Article{Croz:1992:SMM,
  author =       "Jeremy J. Du Croz and Nicholas J. Higham",
  title =        "Stability of Methods for Matrix Inversion",
  journal =      j-IMAJNA,
  volume =       "12",
  pages =        "1--19",
  year =         "1992",
}

@Article{Dumitrescu:1998:IEA,
  author =       "Bogdan Dumitrescu",
  title =        "Improving and Estimating the Accuracy of {Strassen's}
                 Algorithm",
  journal =      j-NUM-MATH,
  volume =       "79",
  pages =        "485--499",
  year =         "1998",
}

@Book{Dunham:1990:JTG,
  author =       "William Dunham",
  title =        "Journey Through Genius: {The} Great Theorems of
                 Mathematics",
  publisher =    pub-Penguin,
  address =      pub-Penguin:adr-NY,
  pages =        "xiii+300",
  year =         "1990",
  ISBN =         "0-14-014739-X",
}

@TechReport{Duff:1982:MSF,
  author =       "Iain S. Duff and John K. Reid",
  title =        "{MA27}---{A} Set of {Fortran} Subroutines for Solving
                 Sparse Symmetric Sets of Linear Equations",
  number =       "AERE R10533",
  institution =  inst-HARWELL,
  year =         "1982",
  month =        jul,
  ISBN =         "0-7058-0985-4",
  note =         "Published by " # pub-HMSO # ", " # pub-HMSO:adr,
}

@TechReport{dure95,
  author =       "Iain S. Duff and John K. Reid",
  title =        "{MA47}, a {Fortran} Code for Direct Solution of
                 Indefinite Sparse Symmetric Linear Systems",
  institution =  inst-RAL,
  address =      inst-RAL:adr,
  type =         "Report",
  number =       "RAL-95-001",
  pages =        "63",
  month =        jan,
  year =         "1995",
}

@Book{Dwyer:1951:LC,
  author =       "Paul S. Dwyer",
  title =        "Linear Computations",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  year =         "1951",
  pages =        "xi+344",
}

@Article{Eckart:1936:AOM,
  author =       "Carl Eckart and Gale Young",
  title =        "The Approximation of One Matrix by Another of Lower
                 Rank",
  journal =      j-PSYCHO,
  volume =       "1",
  number =       "3",
  pages =        "211--218",
  year =         "1936",
}

@Article{Edelman:1988:ECN,
  author =       "Alan Edelman",
  title =        "Eigenvalues and Condition Numbers of Random Matrices",
  journal =      j-SIMAX,
  volume =       "9",
  number =       "4",
  pages =        "543--560",
  year =         "1988",
}

@Article{Edelman:1991:FAL,
  author =       "Alan Edelman",
  title =        "The First Annual Large Dense Linear System Survey",
  journal =      j-SIGNUM,
  volume =       "26",
  pages =        "6--12",
  month =        oct,
  year =         "1991",
}

@Article{edel91a,
  key =          "Editor",
  title =        "Editor's Note",
  journal =      j-SIMAX,
  volume =       "12",
  number =       "3",
  year =         "1991",
}

@Article{Edelman:1991:DMS,
  author =       "Alan Edelman",
  title =        "The Distribution and Moments of the Smallest
                 Eigenvalue of a Random Matrix of {Wishart} Type",
  journal =      j-LAA,
  volume =       "159",
  pages =        "55--80",
  year =         "1991",
}

@Article{Edelman:1992:CPC,
  author =       "Alan Edelman",
  title =        "The Complete Pivoting Conjecture for {Gaussian}
                 Elimination is False",
  journal =      "The Mathematica Journal",
  volume =       "2",
  pages =        "58--61",
  year =         "1992",
}

@Article{Edelman:1992:DSC,
  author =       "Alan Edelman",
  title =        "On the Distribution of a Scaled Condition Number",
  journal =      j-MATH-COMP,
  volume =       "58",
  number =       "197",
  pages =        "185--190",
  year =         "1992",
}

@InProceedings{Edelman:1993:ERR,
  author =       "Alan Edelman",
  title =        "Eigenvalue Roulette and Random Test Matrices",
  booktitle =    "Linear Algebra for Large Scale and Real-Time
                 Applications",
  series =       "NATO ASI Series E",
  volume =       "232",
  editor =       "Marc S. Moonen and Gene H. Golub and Bart L. De Moor",
  pages =        "365--368",
  publisher =    pub-Kluwer # ", " # pub-Kluwer:adr,
  year =         "1993",
}

@Article{Edelman:1993:LDN,
  author =       "Alan Edelman",
  title =        "Large Dense Numerical Linear Algebra in 1993: {The}
                 Parallel Computing Influence.",
  journal =      j-IJSA,
  volume =       "7",
  number =       "2",
  pages =        "113--128",
  year =         "1993",
}

@InProceedings{Edelman:1994:SDN,
  author =       "Alan Edelman",
  title =        "Scalable Dense Numerical Linear Algebra in 1994: {The}
                 Multicomputer Influence",
  editor =       "John G. Lewis",
  booktitle =    "Proceedings of the Fifth SIAM Conference on Applied
                 Linear Algebra",
  publisher =    pub-SIAM # ", " # pub-SIAM:adr,
  pages =        "344--348",
  year =         "1994",
}

@Unpublished{Edelman:1994:W,
  author =       "Alan Edelman",
  title =        "When is {$x*(1/x) \ne 1$}?",
  note =         "Manuscript",
  year =         "1994",
}

@Article{Edelman:1997:MPD,
  author =       "Alan Edelman",
  title =        "The Mathematics of the {Pentium} Division Bug",
  journal =      j-SIREV,
  volume =       "39",
  number =       "1",
  pages =        "54--67",
  year =         "1997",
}

@Article{Edelman:1995:CPC,
  author =       "Alan Edelman and Walter Mascarenhas",
  title =        "On the Complete Pivoting Conjecture for a {Hadamard}
                 Matrix of Order 12",
  journal =      j-LMA,
  volume =       "38",
  number =       "3",
  pages =        "181--188",
  year =         "1995",
}

@Article{Edelman:1995:PRC,
  author =       "Alan Edelman and H. Murakami",
  title =        "Polynomial Roots from Companion Matrix Eigenvalues",
  journal =      j-MATH-COMP,
  volume =       "64",
  number =       "210",
  pages =        "763--776",
  year =         "1995",
}

@Article{Edelman:1993:SO,
  author =       "Alan Edelman and G. W. Stewart",
  title =        "Scaling for Orthogonality",
  journal =      j-IEEE-SP,
  volume =       "41",
  number =       "4",
  pages =        "1676--1677",
  year =         "1993",
}

@Article{Egecioglu:1990:PMF,
  author =       "{\"O}mer E\v{g}ecio\u{g}lu and E. Gallopoulos and
                 {\c{C}}. K. Ko{\c{c}}",
  title =        "A Parallel Method for Fast and Practical High-Order
                 {Newton} Interpolation",
  journal =      j-BIT,
  volume =       "30",
  pages =        "268--288",
  year =         "1990",
}

@Article{Erisman:1987:EOU,
  author =       "A. M. Erisman and R. G. Grimes and J. G. Lewis and W.
                 G. Poole and H. D. Simon",
  title =        "Evaluation of Orderings for Unsymmetric Sparse
                 Matrices",
  journal =      j-SISSC,
  volume =       "8",
  number =       "4",
  pages =        "600--624",
  year =         "1987",
}

@Article{Eirola:1993:ABE,
  author =       "Timo Eirola",
  title =        "Aspects of Backward Error Analysis of Numerical
                 {ODE}s",
  journal =      j-JCAM,
  volume =       "45",
  number =       "1-2",
  pages =        "65--73",
  year =         "1993",
}

@Article{Edelman:1994:HME,
  author =       "Alan Edelman and Eric Kostlan and Michael Shub",
  title =        "How Many Eigenvalues of a Random Matrix are Real?",
  journal =      j-JAMS,
  volume =       "7",
  number =       "1",
  pages =        "247--267",
  year =         "1994",
}

@Article{Elden:1980:PTL,
  author =       "Lars Eld{\'e}n",
  title =        "Perturbation Theory for the Least Squares Problem with
                 Linear Equality Constraints",
  journal =      j-SINUM,
  volume =       "17",
  number =       "3",
  pages =        "338--350",
  year =         "1980",
}

@Article{Eldersveld:1992:BUL,
  author =       "Samuel K. Eldersveld and Michael A. Saunders",
  title =        "A Block-{$LU$} Update for Large-Scale Linear
                 Programming",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "1",
  pages =        "191--201",
  year =         "1992",
}

@Article{Enright:1989:NEC,
  author =       "W. H. Enright",
  title =        "A New Error-Control for Initial Value Solvers",
  journal =      j-APP-MATH-COMP,
  volume =       "31",
  pages =        "288--301",
  year =         "1989",
}

@Article{Epton:1980:MSA,
  author =       "Michael A. Epton",
  title =        "Methods for the Solution of {$AXD-BXC=E$} and its
                 Application in the Numerical Solution of Implicit
                 Ordinary Differential Equations",
  journal =      j-BIT,
  volume =       "20",
  pages =        "341--345",
  year =         "1980",
}

@Article{Erisman:1974:MST,
  author =       "A. M. Erisman and J. K. Reid",
  title =        "Monitoring the Stability of the Triangular
                 Factorization of a Sparse Matrix",
  journal =      j-NUM-MATH,
  volume =       "22",
  pages =        "183--186",
  year =         "1974",
}

@Article{Espelid:1995:FPS,
  author =       "Terje O. Espelid",
  title =        "On Floating-Point Summation",
  journal =      j-SIREV,
  volume =       "37",
  number =       "4",
  pages =        "603--607",
  year =         "1995",
}

@Book{Ewing:1991:PHC,
  editor =       "John H. Ewing and F. W. Gehring",
  title =        "{Paul Halmos}: {Celebrating} 50 Years of Mathematics",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-NY,
  year =         "1991",
  pages =        "viii+320",
  ISBN =         "3-540-97509-8",
}

@Book{Ewing:1994:CMT,
  editor =       "John Ewing",
  title =        "A Century of Mathematics Through the Eyes of the
                 {Monthly}",
  publisher =    "Mathematical Association of America",
  address =      "Washington, D.C.",
  year =         "1994",
  pages =        "xi+323",
  ISBN =         "0-88385-459-7",
}

@Book{Faddeeva:1959:CML,
  author =       "V. N. Faddeeva",
  title =        "Computational Methods of Linear Algebra",
  publisher =    pub-Dover,
  address =      pub-Dover:adr,
  year =         "1959",
  pages =        "x+252",
  ISBN =         "0-486-60424-1",
}

@Article{Fan:1955:SMI,
  author =       "Ky Fan and A. J. Hoffman",
  title =        "Some Metric Inequalities in the Space of Matrices",
  journal =      j-PROC-AMS,
  volume =       "6",
  pages =        "111--116",
  year =         "1955",
}

@Article{Fallat:2001:BFT,
  author =       "Shaun M. Fallat",
  title =        "Bidiagonal Factorizations of Totally Nonnegative
                 Matrices",
  journal =      j-AMM,
  volume =       "108",
  number =       "8",
  pages =        "697--712",
  year =         "2001",
}

@Article{Farebrother:1987:MLM,
  author =       "R. W. Farebrother",
  title =        "A Memoir of the Life of {M. H. Doolittle}",
  journal =      j-IMA-BULL,
  volume =       "23",
  number =       "6/7",
  pages =        "102",
  year =         "1987",
}

@Book{Farebrother:1988:LLS,
  author =       "R. W. Farebrother",
  title =        "Linear Least Squares Computations",
  publisher =    "Marcel Dekker",
  address =      "New York",
  year =         "1988",
  pages =        "xiii+293",
  ISBN =         "0-8247-7661-5",
}

@Article{Farnum:1988:CSF,
  author =       "Charles Farnum",
  title =        "Compiler Support for Floating-Point Computation",
  journal =      "Software---Practice and Experience",
  volume =       "18",
  number =       "7",
  pages =        "701--709",
  year =         "1988",
}

@Article{Fateman:1982:HLL,
  author =       "Richard J. Fateman",
  title =        "High-Level Language Implications of the Proposed
                 {IEEE} Floating-Point Standard",
  journal =      "ACM Trans. Program. Lang. Syst.",
  volume =       "4",
  number =       "2",
  pages =        "239--257",
  year =         "1982",
}

@InProceedings{Ferguson:1991:AMA,
  author =       "Warren E. {Ferguson, Jr.} and Tom Brightman",
  title =        "Accurate and Monotone Approximations of Some
                 Transcendental Functions",
  editor =       "Peter Kornerup and David W. Matula",
  booktitle =    "Proc. 10th IEEE Symposium on Computer Arithmetic",
  publisher =    "IEEE Computer Society Press, Los Alamitos, CA, USA",
  pages =        "237--244",
  year =         "1991",
}

@Article{Feldstein:1982:LSF,
  author =       "Alan Feldstein and Richard Goodman",
  title =        "Loss of Significance in Floating Point Subtraction and
                 Addition",
  journal =      j-IEEE-C,
  volume =       "C-31",
  number =       "4",
  pages =        "328--335",
  year =         "1982",
}

@InProceedings{Ferguson:1995:ECS,
  author =       "Warren E. {Ferguson, Jr.}",
  title =        "Exact Computation of a Sum or Difference with
                 Applications to Argument Reduction",
  editor =       "Simon Knowles and William H. McAllister",
  booktitle =    "Proc. 12th IEEE Symposium on Computer Arithmetic,
                 Bath, England",
  publisher =    "IEEE Computer Society Press, Los Alamitos, CA, USA",
  pages =        "216--221",
  year =         "1995",
}

@Article{Feldstein:1986:OUS,
  author =       "Alan Feldstein and Peter Turner",
  title =        "Overflow, Underflow, and Severe Loss of Significance
                 in Floating-Point Addition and Subtraction",
  journal =      j-IMAJNA,
  volume =       "6",
  pages =        "241--251",
  year =         "1986",
}

@Article{Feingold:1962:BDD,
  author =       "David G. Feingold and Richard S. Varga",
  title =        "Block Diagonally Dominant Matrices and Generalizations
                 of the {Gerschgorin} Circle Theorem",
  journal =      "Pacific J. Math.",
  volume =       "12",
  pages =        "1241--1250",
  year =         "1962",
}

@Article{Forsgren:1995:CMN,
  author =       "Anders Forsgren and Philip E. Gill and Walter Murray",
  title =        "Computing Modified {Newton} Directions Using a Partial
                 {Cholesky} Factorization",
  journal =      j-SISC,
  volume =       "16",
  number =       "1",
  pages =        "139--150",
  year =         "1995",
}

@Article{Ferng:1991:ALM,
  author =       "William R. Ferng and Gene H. Golub and Robert J.
                 Plemmons",
  title =        "Adaptive {Lanczos} Methods for Recursive Condition
                 Estimation",
  journal =      j-NUM-ALG,
  volume =       "1",
  number =       "1",
  pages =        "1--19",
  year =         "1991",
}

@Article{Forsgren:1996:SSI,
  author =       "Anders Forsgren and Philip E. Gill and Joseph R.
                 Shinnerl",
  title =        "Stability of Symmetric Ill-Conditioned Systems Arising
                 in Interior Methods for Constrained Optimization",
  journal =      j-SIMAX,
  volume =       "17",
  number =       "1",
  pages =        "187--211",
  year =         "1996",
}

@Article{Fox:1978:PMS,
  author =       "P. A. Fox and A. D. Hall and N. L. Schryer",
  title =        "The {PORT} Mathematical Subroutine Library",
  journal =      j-TOMS,
  volume =       "4",
  number =       "2",
  pages =        "104--126",
  year =         "1978",
}

@Article{Fox:1948:NSA,
  author =       "L. Fox and H. D. Huskey and J. H. Wilkinson",
  title =        "Notes on the Solution of Algebraic Linear Simultaneous
                 Equations",
  journal =      j-QJMAM,
  volume =       "1",
  pages =        "149--173",
  year =         "1948",
}

@Article{Fike:1967:MEP,
  author =       "C. T. Fike",
  title =        "Methods of Evaluating Polynomial Approximations in
                 Function Evaluation Routines",
  journal =      j-CACM,
  volume =       "10",
  number =       "3",
  pages =        "175--178",
  year =         "1967",
}

@Book{Fike:1968:CEM,
  author =       "C. T. Fike",
  title =        "Computer Evaluation of Mathematical Functions",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  year =         "1968",
  pages =        "xii+227",
}

@InProceedings{Fischer:1974:FSC,
  author =       "Patrick C. Fischer",
  title =        "Further Schemes for Combining Matrix Algorithms",
  editor =       "Jacques Loeckx",
  booktitle =    "Automata, Languages and Programming",
  series =       "Lecture Notes in Computer Science",
  volume =       "14",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  pages =        "428--436",
  year =         "1974",
}

@Article{Fletcher:1976:FSI,
  author =       "R. Fletcher",
  title =        "Factorizing Symmetric Indefinite Matrices",
  journal =      j-LAA,
  volume =       "14",
  pages =        "257--272",
  year =         "1976",
}

@Article{Fletcher:1985:EC,
  author =       "R. Fletcher",
  title =        "Expected Conditioning",
  journal =      j-IMAJNA,
  volume =       "5",
  pages =        "247--273",
  year =         "1985",
}

@Book{Fletcher:1987:PMO,
  author =       "R. Fletcher",
  title =        "Practical Methods of Optimization",
  edition =      "Second",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr-C,
  year =         "1987",
  pages =        "xiv+436",
  ISBN =         "0-471-91547-5",
}

@Article{Fletcher:1974:MF,
  author =       "R. Fletcher and M. J. D. Powell",
  title =        "On the Modification of {$LDL^T$} Factorizations",
  journal =      j-MATH-COMP,
  volume =       "28",
  number =       "128",
  pages =        "1067--1087",
  year =         "1974",
}

@Book{Forsythe:1977:CMM,
  author =       "George E. Forsythe and Michael A. Malcolm and Cleve B.
                 Moler",
  title =        "Computer Methods for Mathematical Computations",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  year =         "1977",
  pages =        "xi+259",
  ISBN =         "0-13-165332-6",
}

@Article{Funderlic:1982:DGD,
  author =       "R. E. Funderlic and M. Neumann and R. J. Plemmons",
  title =        "{$LU$} Decompositions of Generalized Diagonally
                 Dominant Matrices",
  journal =      j-NUM-MATH,
  volume =       "40",
  pages =        "57--69",
  year =         "1982",
}

@Book{Forsythe:1967:CSL,
  author =       "George E. Forsythe and Cleve B. Moler",
  title =        "Computer Solution of Linear Algebraic Systems",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  year =         "1967",
  pages =        "xi+148",
}

@Article{Ford:1978:PET,
  author =       "Brian Ford",
  title =        "Parameterization of the Environment for Transportable
                 Numerical Software",
  journal =      j-TOMS,
  volume =       "4",
  number =       "2",
  pages =        "100--103",
  year =         "1978",
}

@Article{Forsythe:1951:GGR,
  author =       "George E. Forsythe",
  title =        "Gauss to {Gerling} on Relaxation",
  journal =      "Mathematical Tables and Other Aids to Computation",
  volume =       "5",
  pages =        "255--258",
  year =         "1951",
}

@Article{Forsythe:1953:SLA,
  author =       "George E. Forsythe",
  title =        "Solving Linear Algebraic Equations Can Be
                 Interesting",
  journal =      j-BAMS,
  volume =       "59",
  number =       "4",
  pages =        "299--329",
  year =         "1953",
}

@Article{Forsythe:1959:RNR,
  author =       "George E. Forsythe",
  title =        "Reprint of a Note on Rounding-Off Errors",
  journal =      j-SIREV,
  volume =       "1",
  number =       "1",
  pages =        "66--67",
  year =         "1959",
}

@Article{Forsythe:1960:ACP,
  author =       "George E. Forsythe",
  title =        "Algorithm 16: {Crout} With Pivoting",
  journal =      j-CACM,
  volume =       "3",
  number =       "9",
  pages =        "507--508",
  year =         "1960",
}

@Article{Forsythe:1967:TCM,
  author =       "George E. Forsythe",
  title =        "Today's Computational Methods of Linear Algebra",
  journal =      j-SIREV,
  volume =       "9",
  nuber =        "3",
  pages =        "489--515",
  year =         "1967",
}

@InCollection{Forsythe:1969:WSQ,
  author =       "George E. Forsythe",
  title =        "What is a Satisfactory Quadratic Equation Solver?",
  booktitle =    "Constructive Aspects of the Fundamental Theorem of
                 Algebra",
  editor =       "Bruno Dejon and Peter Henrici",
  publisher =    "Wiley-Interscience",
  address =      "London",
  pages =        "53--61",
  year =         "1969",
}

@InCollection{Forsythe:1969:SQE,
  author =       "George E. Forsythe",
  title =        "Solving a Quadratic Equation on a Computer",
  booktitle =    "The Mathematical Sciences: {A} Collection of Essays",
  editor =       "National Research Council's Committee on Support of
                 Research in the Mathematical Sciences",
  publisher =    pub-MIT,
  address =      pub-MIT:adr,
  pages =        "138--152",
  year =         "1969",
}

@Article{Forsythe:1970:PCW,
  author =       "George E. Forsythe",
  title =        "Pitfalls in Computation, or Why a Math Book Isn't
                 Enough",
  journal =      j-AMM,
  volume =       "77",
  pages =        "931--956",
  year =         "1970",
}

@Article{Forsythe:1955:BCM,
  author =       "George E. Forsythe and E. G. Straus",
  title =        "On Best Conditioned Matrices",
  journal =      j-PROC-AMS,
  volume =       "6",
  pages =        "340--345",
  year =         "1955",
}

@InProceedings{Foster:1991:MNE,
  author =       "Leslie Foster",
  title =        "Modifications of the Normal Equations Method That Are
                 Numerically Stable",
  booktitle =    "Numerical Linear Algebra, Digital Signal Processing
                 and Parallel Algorithms",
  editor =       "G. H. Golub and P. M. Van Dooren",
  series =       "NATO ASI Series",
  volume =       "F70",
  pages =        "501--512",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  year =         "1991",
}

@Article{Foster:1994:GEP,
  author =       "Leslie V. Foster",
  title =        "Gaussian Elimination with Partial Pivoting Can Fail in
                 Practice",
  journal =      j-SIMAX,
  volume =       "15",
  number =       "4",
  pages =        "1354--1362",
  year =         "1994",
}

@Article{Foster:1997:GFE,
  author =       "Leslie V. Foster",
  title =        "The Growth Factor and Efficiency of {Gaussian}
                 Elimination with Rook Pivoting",
  journal =      j-JCAM,
  volume =       "86",
  pages =        "177--194",
  year =         "1997",
  note =         "Corrigendum in " # j-JCAM # ", 98:177, 1998",
}

@Book{Fox:1964:INL,
  author =       "L. Fox",
  title =        "An Introduction to Numerical Linear Algebra",
  publisher =    pub-OUP,
  year =         "1964",
  pages =        "xi+328",
}

@Article{Fox:1971:HGM,
  author =       "L. Fox",
  title =        "How to Get Meaningless Answers in Scientific
                 Computation (and What to Do About It)",
  journal =      j-IMA-BULL,
  volume =       "7",
  number =       "10",
  pages =        "296--302",
  year =         "1971",
}

@InProceedings{Fox:1978:AAJ,
  author =       "L. Fox",
  title =        "All About {Jim Wilkinson}, with a Commemorative
                 Snippet on Backward Error Analysis",
  pages =        "1--20",
  booktitle =    "The Contribution of {Dr. J. H. Wilkinson} to Numerical
                 Analysis",
  series =       "Symposium Proceedings Series No. 19",
  publisher =    inst-IMA-UK # ", " # inst-IMA-UK:adr,
  year =         "1978",
}

@Article{Fox:1987:JHW,
  author =       "L. Fox",
  title =        "{James Hardy Wilkinson}, 1919--1986",
  journal =      "Biographical Memoirs of Fellows of the Royal Society",
  volume =       "33",
  pages =        "671--708",
  year =         "1987",
}

@TechReport{fpv86,
  key =          "NAG",
  title =        "{FPV}: {A} Floating-Point Validation Package. {Release
                 I}. {User's} Guide.",
  institution =  "NAG Ltd.",
  address =      "Oxford",
  type =         "Technical Report",
  number =       "NP 1201",
  month =        may,
  year =         "1986",
}

@Article{Frank:1958:CEC,
  author =       "Werner L. Frank",
  title =        "Computing Eigenvalues of Complex Matrices by
                 Determinant Evaluation and by Methods of {Danilewski}
                 and {Wielandt}",
  journal =      j-SIAM,
  volume =       "6",
  numbre =       "4",
  pages =        "378--392",
  year =         "1958",
}

@PhdThesis{Fraysse:1992:RCS,
  author =       "V. Frayss{\'e}",
  title =        "Reliability of Computer Solutions",
  school =       "L'Institut National Polytechnique de Toulouse",
  address =      "Toulouse, France",
  month =        jul,
  year =         "1992",
  note =         "CERFACS Report TH/PA/92/11",
}

@Article{Friedland:1991:RMS,
  author =       "Shmuel Friedland",
  title =        "Revisiting Matrix Squaring",
  journal =      j-LAA,
  volume =       "154--156",
  pages =        "59--63",
  year =         "1991",
}

@InProceedings{Frigo:1998:FAS,
  author =       "Matteo Frigo and Steven G. Johnson",
  title =        "{FFTW}: {An} Adaptive Software Architecture for the
                 {FFT}",
  booktitle =    "Proceedings of International Conference on Acoustics,
                 Speech and Signal Processing, Volume 3",
  pages =        "1381+",
  year =         "1998",
}

@InProceedings{Francois:1991:SPM,
  author =       "Philippe Francois and Jean-Michel Muller",
  title =        "The {SCALP} Perturbation Method",
  booktitle =    "Proceedings of IMACS '91, 13th World Congress on
                 Computation and Applied Mathematics, Dublin, Volume 1",
  pages =        "59--60",
  year =         "1991",
}

@InCollection{Frommer:2001:PCU,
  author =       "Andreas Frommer",
  title =        "Proving Conjectures by Use of Interval Arithmetic",
  booktitle =    "Perspectives on Enclosure Methods",
  editor =       "A. Facius and U. Kulisch and R. Lohner",
  pages =        "1--13",
  publisher =    pub-Springer # ", " # pub-Springer:adr-NY,
  year =         "2001",
}

@Article{Friedland:1980:GPN,
  author =       "Shmuel Friedland and Hans Schneider",
  title =        "The Growth of Powers of a Nonnegative Matrix",
  journal =      j-SIAD,
  volume =       "1",
  number =       "2",
  pages =        "185--200",
  year =         "1980",
}

@Article{Gal:1991:AEM,
  author =       "Shmuel Gal and Boris Bachelis",
  title =        "An Accurate Elementary Mathematical Library for the
                 {IEEE} Floating Point Standard",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "26--45",
  year =         "1991",
}

@Book{Godunov:1993:GAN,
  author =       "S. K. Godunov and A. G. Antonov and O. P. Kiriljuk and
                 V. I. Kostin",
  title =        "Guaranteed Accuracy in Numerical Linear Algebra",
  publisher =    pub-Kluwer,
  address =      pub-Kluwer:adr,
  year =         "1993",
  pages =        "xi+535",
  ISBN =         "0-7923-2352-1",
}

@Article{Gardiner:1991:PAA,
  author =       "Judith D. Gardiner and Alan J. Laub",
  title =        "Parallel Algorithms for Algebraic {Riccati}
                 Equations",
  journal =      j-IJC,
  volume =       "54",
  number =       "6",
  pages =        "1317--1333",
  year =         "1991",
}

@Book{Gantmacher:1959:TMa,
  author =       "F. R. Gantmacher",
  title =        "The Theory of Matrices",
  volume =       "one",
  publisher =    "Chelsea",
  address =      "New York",
  year =         "1959",
  pages =        "x+374",
  ISBN =         "0-8284-0131-4",
}

@Book{Gantmacher:1959:TMb,
  author =       "F. R. Gantmacher",
  title =        "The Theory of Matrices",
  volume =       "two",
  publisher =    "Chelsea",
  address =      "New York",
  year =         "1959",
  pages =        "ix+276",
  ISBN =         "0-8284-0133-0",
}

@Article{Gasca:1992:TPN,
  author =       "M. Gasca and J. M. Pe{\~n}a",
  title =        "Total Positivity and {Neville} Elimination",
  journal =      j-LAA,
  volume =       "165",
  pages =        "25--44",
  year =         "1992",
}

@Book{Gardner:1961:MMP,
  author =       "Martin Gardner",
  title =        "More Mathematical Puzzles and Diversions",
  publisher =    pub-Penguin,
  address =      pub-Penguin:adr-NY,
  year =         "1961",
  pages =        "187",
  ISBN =         "0-14-020748-1",
}

@Article{Garner:1976:SSR,
  author =       "Harvey L. Garner",
  title =        "A Survey of Some Recent Contributions to Computer
                 Arithmetic",
  journal =      j-IEEE-C,
  volume =       "C-25",
  number =       "12",
  pages =        "1277--1282",
  year =         "1976",
}

@Book{Gastinel:1983:LNA,
  author =       "Noel Gastinel",
  title =        "Linear Numerical Analysis",
  publisher =    "Kershaw Publishing",
  address =      "London",
  year =         "1983",
  pages =        "ix+341",
  note =         "First published in English by Academic Press, London,
                 1970",
  ISBN =         "0-901665-16-9",
}

@Article{Gautschi:1953:ABP,
  author =       "Werner Gautschi",
  title =        "The Asymptotic Behaviour of Powers of Matrices",
  journal =      "Duke Math. J.",
  volume =       "20",
  pages =        "127--140",
  year =         "1953",
}

@Article{Gautschi:1962:IVC,
  author =       "Walter Gautschi",
  title =        "On Inverses of {Vandermonde} and Confluent
                 {Vandermonde} Matrices",
  journal =      j-NUM-MATH,
  volume =       "4",
  pages =        "117--123",
  year =         "1962",
}

@Article{Gautschi:1975:NEI,
  author =       "Walter Gautschi",
  title =        "Norm Estimates for Inverses of {Vandermonde}
                 Matrices",
  journal =      j-NUM-MATH,
  volume =       "23",
  pages =        "337--347",
  year =         "1975",
}

@Article{Gautschi:1978:IVC,
  author =       "Walter Gautschi",
  title =        "On Inverses of {Vandermonde} and Confluent
                 {Vandermonde} Matrices {III}",
  journal =      j-NUM-MATH,
  volume =       "29",
  pages =        "445--450",
  year =         "1978",
}

@Article{Gautschi:1983:CVL,
  author =       "Walter Gautschi",
  title =        "The Condition of {Vandermonde}-Like Matrices Involving
                 Orthogonal Polynomials",
  journal =      j-LAA,
  volume =       "52/53",
  pages =        "293--300",
  year =         "1983",
}

@InProceedings{Gautschi:1990:HSV,
  author =       "Walter Gautschi",
  title =        "How (Un)stable are {Vandermonde} Systems?",
}

@TechReport{Gay:1990:CRB,
  author =       "David M. Gay",
  title =        "Correctly Rounded Binary-Decimal and Decimal-Binary
                 Conversions",
  institution =  inst-ATT,
  address =      inst-ATT:adr,
  type =         "Numerical Analysis Manuscript",
  number =       "90-10",
  month =        nov,
  year =         "1990",
  pages =        "16",
}

@Article{gaze24,
  key =          "Mathematical Gazette",
  title =        "Gleanings Far and Near",
  journal =      j-MATH-GAZ,
  volume =       "22",
  number =       "170",
  pages =        "95",
  year =         "1924",
}

@Book{Garbow:1977:MER,
  author =       "B. S. Garbow and J. M. Boyle and J. J. Dongarra and C.
                 B. Moler",
  title =        "Matrix Eigensystem Routines---{EISPACK} Guide
                 Extension",
  series =       "Lecture Notes in Computer Science",
  volume =       "51",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  pages =        "viii+343",
  ISBN =         "3-540-08254-9",
  year =         "1977",
}

@TechReport{Gu:1994:ECS,
  author =       "Ming Gu and James W. Demmel and Inderjit Dhillon",
  title =        "Efficient Computation of the Singular Value
                 Decomposition with Applications to Least Squares
                 Problems",
  institution =  inst-CS-U-Tenn,
  address =      inst-CS-U-Tenn:adr,
  type =         "Technical Report",
  number =       "CS-94-257",
  month =        oct,
  year =         "1994",
  pages =        "19",
  note =         "LAPACK Working Note 88",
}

@Article{Guggenheimer:1995:SEC,
  author =       "Heinrich W. Guggenheimer and Alan S. Edelman and
                 Charles R. Johnson",
  title =        "A Simple Estimate of the Condition Number of a Linear
                 System",
  journal =      j-CMJ,
  volume =       "26",
  number =       "1",
  pages =        "2--5",
  year =         "1995",
}

@Book{George:1981:CSL,
  author =       "Alan George and Joseph W-H Liu",
  title =        "Computer Solution of Large Sparse Positive Definite
                 Systems",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  year =         "1981",
  pages =        "xii+324",
  ISBN =         "0-13-165274-5",
}

@Article{Gentleman:1974:MAR,
  author =       "W. Morven Gentleman and Scott B. Marovich",
  title =        "More on Algorithms that Reveal Properties of Floating
                 Point Arithmetic Units",
  journal =      j-CACM,
  volume =       "17",
  number =       "5",
  pages =        "276--277",
  year =         "1974",
}

@Article{Geman:1986:SRL,
  author =       "Stuart Geman",
  title =        "The Spectral Radius of Large Random Matrices",
  journal =      "Ann. Probab.",
  volume =       "14",
  number =       "4",
  pages =        "1318--1328",
  year =         "1986",
}

@Article{Gentleman:1969:EAG,
  author =       "W. M. Gentleman",
  title =        "An Error Analysis of {Goertzel's (Watt's)} Method for
                 Computing {Fourier} Coefficients",
  journal =      j-COMP-J,
  volume =       "12",
  pages =        "160--165",
  year =         "1969",
}

@Article{Gentleman:1973:LSC,
  author =       "W. Morven Gentleman",
  title =        "Least Squares Computations by {Givens} Transformations
                 Without Square Roots",
  journal =      j-JIMA,
  volume =       "12",
  pages =        "329--336",
  year =         "1973",
}

@Article{Gentleman:1975:EAD,
  author =       "W. Morven Gentleman",
  title =        "Error Analysis of {$QR$} Decompositions by {Givens}
                 Transformations",
  journal =      j-LAA,
  volume =       "10",
  pages =        "189--197",
  year =         "1975",
}

@InProceedings{Gentleman:1966:FFT,
  author =       "W. M. Gentleman and G. Sande",
  title =        "Fast {Fourier} Transforms---For Fun and Profit",
  booktitle =    "Fall Joint Computer Conference",
  series =       "AFIPS Conference Proceedings",
  volume =       "29",
  pages =        "563--578",
  publisher =    "Spartan Books, Washington, D.C.",
  year =         "1966",
}

@Article{Geurts:1982:CTC,
  author =       "A. J. Geurts",
  title =        "A Contribution to the Theory of Condition",
  journal =      j-NUM-MATH,
  volume =       "39",
  pages =        "85--96",
  year =         "1982",
}

@Article{Goodman:1985:REF,
  author =       "R. H. Goodman and A. Feldstein and J. Bustoz",
  title =        "Relative Error in Floating-Point Multiplication",
  journal =      j-COMPUTING,
  volume =       "35",
  pages =        "127--139",
  year =         "1985",
}

@Article{Ghavimi:1995:BES,
  author =       "Ali R. Ghavimi and Alan J. Laub",
  title =        "Backward Error, Sensitivity, and Refinement of
                 Computed Solutions of Algebraic {Riccati} Equations",
  journal =      "Numerical Linear Algebra with Applications",
  volume =       "2",
  number =       "1",
  pages =        "29--49",
  year =         "1995",
}

@Article{Ghavimi:1995:RBD,
  author =       "Ali R. Ghavimi and Alan J. Laub",
  title =        "Residual Bounds for Discrete-Time {Lyapunov}
                 Equations",
  journal =      j-IEEE-AC,
  volume =       "40",
  number =       "7",
  pages =        "1244--1249",
  year =         "1995",
}

@Article{George:2002:GFG,
  author =       "Alan George and Khakim D. Ikramov and Andrey B.
                 Kucherov",
  title =        "On the Growth Factor in {Gaussian} Elimination for
                 Generalized {Higham} Matrices",
  journal =      j-NLAA,
  volume =       "9",
  pages =        "107--114",
  year =         "2002",
}

@Article{Gill:1951:PSS,
  author =       "S. Gill",
  title =        "A Process for the Step-By-Step Integration of
                 Differential Equations in an Automatic Digital
                 Computing Machine",
  journal =      "Proc. Cambridge Phil. Soc.",
  volume =       "47",
  pages =        "96--108",
  year =         "1951",
}

@InCollection{Gillespie:1991:NVT,
  author =       "T. A. Gillespie",
  title =        "Noncommutative Variations on Theorems of {Marcel
                 Riesz} and Others",
  editor =       "John H. Ewing and F. W. Gehring",
  booktitle =    "{Paul Halmos}: {Celebrating} 50 Years of Mathematics",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  pages =        "221--236",
  year =         "1991",
}

@Article{Gill:1973:NSF,
  author =       "P. E. Gill and W. Murray",
  title =        "A Numerically Stable Form of the Simplex Algorithm",
  journal =      j-LAA,
  volume =       "7",
  pages =        "99--138",
  year =         "1973",
}

@TechReport{Givens:1954:NCC,
  author =       "Wallace J. Givens",
  title =        "Numerical Computation of the Characteristic Values of
                 a Real Symmetric Matrix",
  institution =  inst-ORNL,
  address =      inst-ORNL:adr,
  number =       "ORNL-1574",
  year =         "1954",
  pages =        "107",
}

@Article{Gudmundsson:1995:SSS,
  author =       "Thorkell Gudmundsson and Charles S. Kenney and Alan J.
                 Laub",
  title =        "Small-Sample Statistical Estimates for Matrix Norms",
  journal =      j-SIMAX,
  volume =       "16",
  number =       "3",
  pages =        "776--792",
  year =         "1995",
}

@Book{Graham:1994:CMF,
  author =       "Ronald L. Graham and Donald E. Knuth and Oren
                 Patashnik",
  title =        "Concrete Mathematics: {A} Foundation for Computer
                 Science",
  edition =      "Second",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  year =         "1994",
  pages =        "xiii+657",
  ISBN =         "0-201-55802-5",
}

@Article{Gardiner:1992:SSM,
  author =       "Judith D. Gardiner and Alan J. Laub and James J. Amato
                 and Cleve B. Moler",
  title =        "Solution of the {Sylvester} Matrix Equation
                 {$AXB^T+CXD^T=E$}",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "223--231",
  year =         "1992",
}

@Article{Gardiner:1992:AFS,
  author =       "Judith D. Gardiner and Matthew R. Wette and Alan J.
                 Laub and James J. Amato and Cleve B. Moler",
  title =        "Algorithm 705: {A} {FORTRAN}-77 Software Package for
                 Solving the {Sylvester} Matrix Equation
                 {$AXB^T+CXD^T=E$}",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "232--238",
  year =         "1992",
}

@Article{Glanz:1995:MLF,
  author =       "James Glanz",
  title =        "Mathematical Logic Flushes Out the Bugs in Chip
                 Designs",
  journal =      j-SCIENCE,
  volume =       "267",
  pages =        "332--333",
  year =         "1995",
  note =         "20 " # jan,
}

@Article{Gahinet:1990:SSD,
  author =       "Pascal M. Gahinet and Alan J. Laub and Charles S.
                 Kenney and Gary A. Hewer",
  title =        "Sensitivity of the Stable Discrete-Time {Lyapunov}
                 Equation",
  journal =      j-IEEE-AC,
  volume =       "AC-35",
  number =       "11",
  pages =        "1209--1217",
  year =         "1990",
}

@Article{Gluchowska:1990:SLL,
  author =       "J. Gluchowska and A. Smoktunowicz",
  title =        "Solving the Linear Least Squares Problem with Very
                 High Relative Accuracy",
  journal =      j-COMPUTING,
  volume =       "45",
  pages =        "345--354",
  year =         "1990",
}

@Article{Gill:1992:PIS,
  author =       "Philip E. Gill and Walter Murray and Dulce B.
                 Poncele{\'o}n and Michael A. Saunders",
  title =        "Preconditioners For Indefinite Systems Arising in
                 Optimization",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "1",
  pages =        "292--311",
  year =         "1992",
}

@TechReport{Gill:1986:UGN,
  author =       "Philip E. Gill and Walter Murray and Michael A.
                 Saunders and Margaret H. Wright",
  title =        "User's Guide for {NPSOL} (Version 4.0): {A} {Fortran}
                 Package for Nonlinear Programming",
  type =         "Technical Report",
  number =       "SOL 86-2",
  institution =  inst-OR-U-STANFORD,
  address =      inst-U-STANFORD:adr,
  month =        jan,
  year =         "1986",
  pages =        "53",
}

@Article{Gill:1991:ICM,
  author =       "Philip E. Gill and Walter Murray and Michael A.
                 Saunders and Margaret H. Wright",
  title =        "Inertia-Controlling Methods for General Quadratic
                 Programming",
  journal =      j-SIREV,
  volume =       "33",
  number =       "1",
  pages =        "1--36",
  year =         "1991",
}

@Book{Gill:1981:PO,
  author =       "Philip E. Gill and Walter Murray and Margaret H.
                 Wright",
  title =        "Practical Optimization",
  publisher =    pub-AP,
  address =      pub-AP:adr-L,
  year =         "1981",
  pages =        "xvi+401",
  ISBN =         "0-12-283952-8",
}

@Article{Golub:1979:HSM,
  author =       "G. H. Golub and S. Nash and C. F. Van Loan",
  title =        "A {Hessenberg--Schur} Method for the Problem
                 {$AX+XB=C$}",
  journal =      j-IEEE-AC,
  volume =       "AC-24",
  number =       "6",
  pages =        "909--913",
  year =         "1979",
}

@Article{Goodman:1975:REP,
  author =       "R. Goodman and A. Feldstein",
  title =        "Round-Off Error in Products",
  journal =      j-COMPUTING,
  volume =       "15",
  pages =        "263--273",
  year =         "1975",
}

@Article{Gohberg:1993:MCS,
  author =       "I. Gohberg and I. Koltracht",
  title =        "Mixed, Componentwise, and Structured Condition
                 Numbers",
  journal =      j-SIMAX,
  volume =       "14",
  number =       "3",
  pages =        "688--704",
  year =         "1993",
}

@Article{Goldberg:1967:BED,
  author =       "I. Bennett Goldberg",
  title =        "27 Bits Are Not Enough For 8-Digit Accuracy",
  journal =      j-CACM,
  volume =       "10",
  number =       "2",
  pages =        "105--106",
  year =         "1967",
}

@Book{Goldstine:1972:CPN,
  author =       "Herman H. Goldstine",
  title =        "The Computer: {From Pascal} to {von Neumann}",
  publisher =    pub-PUP,
  address =      pub-PUP:adr,
  year =         "1972",
  ISBN =         "0-691-02367-0",
  pages =        "xii+378",
  note =         "1993 printing with new preface",
}

@Book{Goldstine:1977:HNA,
  author =       "Herman H. Goldstine",
  title =        "A History of Numerical Analysis from the 16th through
                 the 19th Century",
  publisher =    "Springer-Verlag",
  address =      "New York",
  year =         "1977",
  ISBN =         "0-387-90277-5",
  pages =        "xiv+348",
}

@Article{Goldberg:1991:WEC,
  author =       "David Goldberg",
  title =        "What Every Computer Scientist Should Know About
                 Floating-Point Arithmetic",
  journal =      "ACM Computing Surveys",
  volume =       "23",
  number =       "1",
  pages =        "5--48",
  year =         "1991",
}

@Article{Golub:1962:BRE,
  author =       "Gene H. Golub",
  title =        "Bounds for the Round-Off Errors in the {Richardson}
                 Second Order Method",
  journal =      j-BIT,
  volume =       "2",
  pages =        "212--223",
  year =         "1962",
}

@Article{Golub:1965:NMS,
  author =       "G. H. Golub",
  title =        "Numerical Methods for Solving Linear Least Squares
                 Problems",
  journal =      j-NUM-MATH,
  volume =       "7",
  pages =        "206--216",
  year =         "1965",
}

@Article{Goodnight:1979:TSO,
  author =       "James H. Goodnight",
  title =        "A Tutorial on the {SWEEP} Operator",
  journal =      "The American Statistician",
  volume =       "33",
  number =       "3",
  pages =        "149--158",
  year =         "1979",
}

@Article{Gohberg:1994:FIC,
  author =       "I. Gohberg and V. Olshevsky",
  title =        "Fast Inversion of {Chebyshev--Vandermonde} Matrices",
  journal =      j-NUM-MATH,
  volume =       "67",
  number =       "1",
  pages =        "71--92",
  year =         "1994",
}

@Article{Govaerts:1990:BEO,
  author =       "W. Govaerts and J. D. Pryce",
  title =        "Block elimination with one iterative refinement solves
                 bordered linear systems accurately",
  journal =      j-BIT,
  volume =       "30",
  pages =        "490--507",
  year =         "1990",
}

@Article{Goldberg:1983:MNM,
  author =       "Moshe Goldberg and E. G. Straus",
  title =        "Multiplicativity of {$l_p$} Norms for Matrices",
  journal =      j-LAA,
  volume =       "52/53",
  pages =        "351--360",
  year =         "1983",
}

@Article{Gould:1991:GGE,
  author =       "N. I. M. Gould",
  title =        "On Growth in {Gaussian} Elimination with Complete
                 Pivoting",
  journal =      j-SIMAX,
  volume =       "12",
  number =       "2",
  pages =        "354--361",
  year =         "1991",
}

@Book{Govaerts:2000:NMB,
  author =       "Willy J. F. Govaerts",
  title =        "Numerical Methods for Bifurcations of Dynamical
                 Equiilibria",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "2000",
  pages =        "xxii+362",
  ISBN =         "0-89871-442-7",
}

@Article{Golub:1974:CBS,
  author =       "G. H. Golub and J. M. Varah",
  title =        "On a Characterization of the Best {$\ell_2$}-Scaling
                 of a Matrix",
  journal =      j-SINUM,
  volume =       "11",
  number =       "3",
  pages =        "472--479",
  year =         "1974",
}

@Article{Golub:1979:UPD,
  author =       "Gene H. Golub and Charles F. Van Loan",
  title =        "Unsymmetric Positive Definite Linear Systems",
  journal =      j-LAA,
  volume =       "28",
  pages =        "85--97",
  year =         "1979",
}

@Book{Golub:1996:MC,
  author =       "Gene H. Golub and Charles F. Van Loan",
  title =        "Matrix Computations",
  edition =      "Third",
  publisher =    pub-JH,
  address =      pub-JH:adr,
  year =         "1996",
  pages =        "xxvii+694",
  ISBN =         "0-8018-5413-X (\hbk), 0-8018-5414-8 (\pbk)",
}

@Article{Goldstine:1951:NIM,
  author =       "Herman H. Goldstine and John von Neumann",
  title =        "Numerical Inverting of Matrices of High Order {II}",
  journal =      j-PROC-AMS,
  volume =       "2",
  pages =        "188--202",
  year =         "1951",
  note =         "Reprinted in \cite[pp.~558--572]{Taub:1963:JNC}",
}

@Article{Golub:1966:NIR,
  author =       "G. H. Golub and J. H. Wilkinson",
  title =        "Note on the iterative refinement of least squares
                 solution",
  journal =      j-NUM-MATH,
  volume =       "9",
  pages =        "139--148",
  year =         "1966",
}

@Article{Golub:1976:ICE,
  author =       "G. H. Golub and J. H. Wilkinson",
  title =        "Ill-Conditioned Eigensystems and the Computation of
                 the {Jordan} Canonical Form",
  journal =      j-SIREV,
  volume =       "18",
  number =       "4",
  pages =        "578--619",
  year =         "1976",
}

@Article{Gallivan:1990:PAD,
  author =       "K. A. Gallivan and R. J. Plemmons and A. H. Sameh",
  title =        "Parallel Algorithms for Dense Linear Algebra
                 Computations",
  journal =      j-SIREV,
  volume =       "32",
  number =       "1",
  pages =        "54--135",
  year =         "1990",
}

@Article{Granville:1992:ZBB,
  author =       "Andrew Granville",
  title =        "{Zaphod Beeblebrox's} Brain and the Fifty-Ninth Row of
                 {Pascal's} Triangle",
  journal =      j-AMM,
  volume =       "99",
  pages =        "318--331",
  year =         "1992",
}

@Article{Greenbaum:1989:BSP,
  author =       "Anne Greenbaum",
  title =        "Behavior of Slightly Perturbed {Lanczos} and
                 Conjugate-Gradient Recurrences",
  journal =      j-LAA,
  volume =       "113",
  pages =        "7--63",
  year =         "1989",
}

@InProceedings{Greenbaum:1994:LCG,
  author =       "Anne Greenbaum",
  title =        "The {Lanczos} and Conjugate Gradient Algorithms in
                 Finite Precision Arithmetic",
  editor =       "J. David Brown and Moody T. Chu and Donald C. Ellison
                 and Robert J. Plemmons",
  booktitle =    "Proceedings of the {Cornelius Lanczos} International
                 Centenary Conference",
  publisher =    pub-SIAM # ", " # pub-SIAM:adr,
  year =         "1994",
  pages =        "49--60",
}

@Book{Greenbaum:1997:IMS,
  author =       "Anne Greenbaum",
  title =        "Iterative Methods for Solving Linear Systems",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "1997",
  pages =        "xiii+220",
  ISBN =         "0-89871-396-X",
}

@Article{Greenbaum:1997:EAA,
  author =       "Anne Greenbaum",
  title =        "Estimating the Attainable Accuracy of Recursively
                 Computed Residual Methods",
  journal =      j-SIMAX,
  volume =       "18",
  number =       "3",
  pages =        "535--551",
  year =         "1997",
}

@Article{Griewank:1985:SNE,
  author =       "Andreas Griewank",
  title =        "On Solving Nonlinear Equations with Simple
                 Singularities or Nearly Singular Solutions",
  journal =      j-SIREV,
  volume =       "27",
  number =       "4",
  pages =        "537--563",
  year =         "1985",
}

@Book{Gregory:1969:CMT,
  author =       "Robert T. Gregory and David L. Karney",
  title =        "A Collection of Matrices for Testing Computational
                 Algorithms",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  year =         "1969",
  pages =        "ix+154",
  note =         "Reprinted with corrections by Robert E. Krieger,
                 Huntington, New York, 1978",
  ISBN =         "0-88275-649-4",
}

@Article{Grimes:1981:CNE,
  author =       "Roger G. Grimes and John G. Lewis",
  title =        "Condition Number Estimation for Sparse Matrices",
  journal =      j-SISSC,
  volume =       "2",
  number =       "4",
  pages =        "384--388",
  year =         "1981",
}

@Article{Gragg:1976:SVS,
  author =       "W. B. Gragg and G. W. Stewart",
  title =        "A Stable Variant of the Secant Method for Solving
                 Nonlinear Equations",
  journal =      j-SINUM,
  volume =       "13",
  number =       "6",
  pages =        "889--903",
  year =         "1976",
}

@Article{Greenbaum:1992:PBF,
  author =       "Anne Greenbaum and Zden{\u{e}}k Strako{\u{s}}",
  title =        "Predicting the Behavior of Finite Precision {Lanczos}
                 and Conjugate Gradient Computations",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "1",
  pages =        "121--137",
  year =         "1992",
}

@Article{Gill:1996:SCF,
  author =       "Philip E. Gill and Michael A. Saunders and Joseph R.
                 Shinnerl",
  title =        "On the Stability of {Cholesky} Factorization for
                 Symmetric Quasidefinite Systems",
  journal =      j-SIMAX,
  volume =       "17",
  number =       "1",
  year =         "1996",
  pages =        "35--46",
}

@Article{Gu:1998:BPB,
  author =       "Ming Gu",
  title =        "Backward Perturbation Bounds for Linear Least Squares
                 Problems",
  journal =      j-SIMAX,
  volume =       "20",
  number =       "2",
  pages =        "363--372",
  year =         "1998",
}

@Article{Gustafson:1996:MPS,
  author =       "John L. Gustafson and Srinivas Aluru",
  title =        "Massively Parallel Searching for Better Algorithms or,
                 How to Do a Cross Product with Five Multiplications",
  journal =      "Scientific Programming",
  pages =        "203--213",
  year =         "1996",
}

@Article{Gulliksson:1994:IRC,
  author =       "M{\aa}rten Gulliksson",
  title =        "Iterative Refinement for Constrained and Weighted
                 Linear Least Squares",
  journal =      j-BIT,
  volume =       "34",
  pages =        "239--253",
  year =         "1994",
}

@Article{Gulliksson:1995:BEA,
  author =       "M{\aa}rten Gulliksson",
  title =        "Backward Error Analysis for the Constrained and
                 Weighted Linear Least Squares Problem When Using the
                 Weighted {$QR$} Factorization",
  journal =      j-SIMAX,
  volume =       "16",
  number =       "2",
  pages =        "675--687",
  year =         "1995",
}

@Article{Gustavson:1997:RLA,
  author =       "F. G. Gustavson",
  title =        "Recursion Leads to Automatic Variable Blocking for
                 Dense Linear-Algebra Algorithms",
  journal =      "IBM Journal of Research and Development",
  volume =       "41",
  number =       "6",
  pages =        "737--755",
  month =        nov,
  year =         "1997",
}

@Article{Gulliksson:1992:MQD,
  author =       "M{\aa}rten Gulliksson and Per-{\AA}ke Wedin",
  title =        "Modifying the {QR}-Decomposition to Constrained and
                 Weighted Linear Least Squares",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "4",
  pages =        "1298--1313",
  year =         "1992",
}

@Article{Hull:1985:NT,
  author =       "T. E. Hull and A. Abraham and M. S. Cohen and A. F. X.
                 Curley and C. B. Hall and D. A. Penny and J. T. M.
                 Sawchuk",
  title =        "Numerical {TURING}",
  journal =      j-SIGNUM,
  volume =       "20",
  number =       "3",
  pages =        "26--34",
  year =         "1985",
}

@Article{Hager:1984:CE,
  author =       "William W. Hager",
  title =        "Condition Estimates",
  journal =      j-SISSC,
  volume =       "5",
  number =       "2",
  pages =        "311--316",
  year =         "1984",
}

@Book{Hall:1967:CT,
  author =       "Marshall {Hall, Jr.}",
  title =        "Combinatorial Theory",
  publisher =    pub-Blaisdell,
  address =      pub-Blaisdell:adr-MA,
  year =         "1967",
  pages =        "x+310",
}

@InProceedings{Hamada:1987:NRN,
  author =       "Hozumi Hamada",
  title =        "A New Real Number Representation and its Operation",
  booktitle =    "Proceedings of the Eighth Symposium on Computer
                 Arithmetic, Como, Italy",
  editor =       "Mary Jane Irwin and Renato Stefanelli",
  pages =        "153--157",
  publisher =    "IEEE Computer Society, Washington, D.C.",
  year =         "1987",
}

@Book{Hamming:1973:NMS,
  author =       "R. W. Hamming",
  title =        "Numerical Methods for Scientists and Engineers",
  edition =      "Second",
  publisher =    pub-MH,
  address =      pub-MH:adr,
  year =         "1973",
  pages =        "ix+721",
  ISBN =         "0-07-025887-2",
}

@Article{Hammarling:1974:NMG,
  author =       "Sven Hammarling",
  title =        "A Note on Modifications to the {Givens} Plane
                 Rotation",
  journal =      j-JIMA,
  volume =       "13",
  pages =        "215--218",
  year =         "1974",
}

@Article{Hammarling:1982:NSS,
  author =       "S. J. Hammarling",
  title =        "Numerical Solution of the Stable, Non-Negative
                 Definite {Lyapunov} Equation",
  journal =      j-IMAJNA,
  volume =       "2",
  pages =        "303--323",
  year =         "1982",
}

@InProceedings{Hammarling:1987:NSG,
  author =       "Sven J. Hammarling",
  title =        "The Numerical Solution of the General {Gauss--Markov}
                 Linear Model",
  editor =       "T. S. Durrani and J. B. Abbiss and J. E. Hudson",
  booktitle =    "Mathematics in Signal Processing",
  publisher =    pub-OUP,
  pages =        "451--456",
  year =         "1987",
}

@Unpublished{Hanson:1997:AML,
  author =       "Richard J. Hanson",
  title =        "{Aasen's} Method for Linear Systems with Self-Adjoint
                 Matrices",
  note =         "Visual Numerics, Inc.,
                 \path|http://www.vni.com/books/whitepapers/Aasen.html|",
  month =        jul,
  year =         "1997",
}

@Book{Hardy:1967:CPM,
  author =       "G. H. Hardy",
  title =        "A Course of Pure Mathematics",
  edition =      "Tenth",
  publisher =    pub-CUP,
  pages =        "xii+509",
  year =         "1967",
  ISBN =         "0-521-09227-2",
}

@Article{Harter:1972:OWF,
  author =       "Richard Harter",
  title =        "The Optimality of {Winograd's} Formula",
  journal =      j-CACM,
  volume =       "15",
  number =       "5",
  pages =        "352",
  year =         "1972",
}

@Article{Hartfiel:1980:CSS,
  author =       "D. J. Hartfiel",
  title =        "Concerning the Solution Set of {$Ax = b$} where {$P
                 \le A \le Q$} and {$p \le b \le q$}",
  journal =      j-NUM-MATH,
  volume =       "35",
  pages =        "355--359",
  year =         "1980",
}

@Article{Hauser:1996:HFP,
  author =       "John R. Hauser",
  title =        "Handling Floating-Point Exceptions in Numeric
                 Programs",
  journal =      j-TPLS,
  volume =       "18",
  number =       "2",
  pages =        "139--174",
  year =         "1996",
}

@Book{Hairer:1991:SOD,
  author =       "E. Hairer and G. Wanner",
  title =        "Solving Ordinary Differential Equations {II}",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  year =         "1991",
  pages =        "xv+601",
  ISBN =         "3-540-53775-9",
}

@TechReport{Hammarling:1976:PBL,
  author =       "S. J. Hammarling and J. H. Wilkinson",
  title =        "The Practical Behaviour of Linear Iterative Methods
                 with Particular Reference to {S.O.R.}",
  institution =  inst-NPL,
  address =      inst-NPL:adr,
  type =         "Report",
  number =       "NAC 69",
  pages =        "19",
  month =        sep,
  year =         "1976",
}

@Article{Hearon:1977:NS,
  author =       "John Z. Hearon",
  title =        "Nonsingular Solutions of {$TA-BT=C$}",
  journal =      j-LAA,
  volume =       "16",
  pages =        "57--63",
  year =         "1977",
}

@Article{Heath:1984:NML,
  author =       "Michael T. Heath",
  title =        "Numerical Methods for Large Sparse Linear Least
                 Squares Problems",
  journal =      j-SISSC,
  volume =       "5",
  number =       "3",
  pages =        "497--513",
  year =         "1984",
}

@Book{Hein:1992:G,
  author =       "Piet Hein",
  title =        "Grooks",
  edition =      "Second",
  series =       "Borgens Pocketbooks",
  number =       "85",
  publisher =    "Borgens Forlag",
  address =      "Copenhagen, Denmark",
  year =         "1992",
  pages =        "53",
  ISBN =         "87-418-1079-1",
}

@Article{Hewer:1988:SSL,
  author =       "Gary Hewer and Charles Kenney",
  title =        "The Sensitivity of the Stable {Lyapunov} Equation",
  journal =      j-SICOPT,
  volume =       "26",
  number =       "2",
  pages =        "321--344",
  year =         "1988",
}

@Article{Henrici:1962:BII,
  author =       "Peter Henrici",
  title =        "Bounds for Iterates, Inverses, Spectral Variation and
                 Fields of Values of Non-Normal Matrices",
  journal =      j-NUM-MATH,
  volume =       "4",
  pages =        "24--40",
  year =         "1962",
}

@Book{Henrici:1962:DVM,
  author =       "Peter Henrici",
  title =        "Discrete Variable Methods in Ordinary Differential
                 Equations",
  publisher =    "John Wiley",
  address =      "New York",
  pages =        "xi+407",
  year =         "1962",
}

@Book{Henrici:1963:EPD,
  author =       "Peter Henrici",
  title =        "Error Propagation for Difference Methods",
  publisher =    "John Wiley",
  address =      "New York",
  year =         "1963",
  pages =        "vi+73",
}

@Book{Henrici:1964:ENA,
  author =       "Peter Henrici",
  title =        "Elements of Numerical Analysis",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  year =         "1964",
  pages =        "xv+328",
}

@Article{Henrici:1966:TPM,
  author =       "Peter Henrici",
  title =        "Test of Probabilistic Models for the Propagation of
                 Roundoff Errors",
  journal =      j-CACM,
  volume =       "9",
  number =       "6",
  pages =        "409--410",
  year =         "1966",
}

@InProceedings{Henrici:1980:MPR,
  author =       "Peter Henrici",
  title =        "A Model for the Propagation of Rounding Error in
                 Floating Arithmetic",
  editor =       "Karl L. E. Nickel",
  booktitle =    "Interval Mathematics 1980",
  publisher =    pub-AP # ", " # pub-AP:adr-NY,
  pages =        "49--73",
  year =         "1980",
}

@Book{Hennessy:1996:CAQ,
  author =       "John L. Hennessy and David A. Patterson",
  title =        "Computer Architecture: {A} Quantitative Approach",
  edition =      "Second",
  publisher =    "Morgan Kaufmann",
  address =      "San Francisco, CA, USA",
  year =         "1996",
  ISBN =         "1-55860-329-8",
  pages =        "xxiii+760+appendices",
}

@Article{Henderson:1981:DIS,
  author =       "H. V. Henderson and S. R. Searle",
  title =        "On Deriving the Inverse of a Sum of Matrices",
  journal =      j-SIREV,
  volume =       "23",
  number =       "1",
  pages =        "53--60",
  year =         "1981",
}

@Article{Henderson:1981:VPM,
  author =       "Harold V. Henderson and S. R. Searle",
  title =        "The Vec-Permutation Matrix, the Vec Operator and
                 {Kronecker} Products: {A} Review",
  journal =      j-LMA,
  volume =       "9",
  pages =        "271--288",
  year =         "1981",
}

@Article{Hull:1994:ICE,
  author =       "T. E. Hull and Thomas F. Fairgrieve and Ping Tak Peter
                 Tang",
  title =        "Implementing Complex Elementary Functions Using
                 Exception Handling",
  journal =      j-TOMS,
  volume =       "20",
  number =       "2",
  pages =        "215--244",
  year =         "1994",
}

@TechReport{Heath:1990:EEI,
  author =       "M. T. Heath and G. A. Geist and J. B. Drake",
  title =        "Early Experience with the {Intel iPSC/860} at {Oak
                 Ridge National Laboratory}",
  institution =  inst-ORNL,
  address =      inst-ORNL:adr,
  type =         "Report",
  number =       "ORNL/TM-11655",
  pages =        "26",
  month =        sep,
  year =         "1990",
}

@Book{Hammer:1993:NTV,
  author =       "Rolf Hammer and Matthias Hocks and Ulrich Kulisch and
                 Dietmar Ratz",
  title =        "Numerical Toolbox for Verified Computing {I}. {Basic}
                 Numerical Problems: Theory, Algorithms, and
                 {Pascal-XSC} Programs",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  year =         "1993",
  pages =        "xiii+337",
  ISBN =         "3-540-57118-3",
}

@Article{Higham:2000:QFC,
  author =       "Nicholas J. Higham",
  title =        "{QR} Factorization with Complete Pivoting and Accurate
                 Computation of the {SVD}",
  journal =      j-LAA,
  volume =       "309",
  pages =        "153--174",
  year =         "2000",
}

@Article{Higham:2001:EPA,
  author =       "Nicholas J. Higham",
  title =        "Evaluating {Pad\'e} Approximants of the Matrix
                 Logarithm",
  journal =      j-SIMAX,
  volume =       "22",
  number =       "4",
  pages =        "1126--1135",
  year =         "2001",
}

@Article{Higham:1986:CPD,
  author =       "Nicholas J. Higham",
  title =        "Computing the Polar Decomposition---with
                 Applications",
  journal =      j-SISSC,
  volume =       "7",
  number =       "4",
  month =        oct,
  pages =        "1160--1174",
  year =         "1986",
}

@Article{Higham:1986:EAC,
  author =       "Nicholas J. Higham",
  title =        "Efficient Algorithms for Computing the Condition
                 Number of a Tridiagonal Matrix",
  journal =      j-SISSC,
  volume =       "7",
  number =       "1",
  pages =        "150--165",
  year =         "1986",
}

@Article{Higham:1987:CRS,
  author =       "Nicholas J. Higham",
  title =        "Computing Real Square Roots of a Real Matrix",
  journal =      j-LAA,
  volume =       "88/89",
  pages =        "405--430",
  year =         "1987",
}

@Article{Higham:1987:SCN,
  author =       "Nicholas J. Higham",
  title =        "A Survey of Condition Number Estimation for Triangular
                 Matrices",
  journal =      j-SIREV,
  volume =       "29",
  number =       "4",
  month =        dec,
  pages =        "575--596",
  year =         "1987",
}

@Article{Higham:1987:EAB,
  author =       "Nicholas J. Higham",
  title =        "Error Analysis of the {Bj\"orck}-{Pereyra} Algorithms
                 for Solving {Vandermonde} Systems",
  journal =      j-NUM-MATH,
  volume =       "50",
  number =       "5",
  pages =        "613--632",
  year =         "1987",
}

@Article{Higham:1988:CNS,
  author =       "Nicholas J. Higham",
  title =        "Computing a Nearest Symmetric Positive Semidefinite
                 Matrix",
  journal =      j-LAA,
  volume =       "103",
  pages =        "103--118",
  year =         "1988",
}

@Article{Higham:1988:FCE,
  author =       "Nicholas J. Higham",
  title =        "{FORTRAN} Codes for Estimating the One-norm of a Real
                 or Complex Matrix, with Applications to Condition
                 Estimation ({Algorithm} 674)",
  journal =      j-TOMS,
  volume =       "14",
  number =       "4",
  month =        dec,
  pages =        "381--396",
  year =         "1988",
}

@Article{Higham:1988:FSV,
  author =       "Nicholas J. Higham",
  title =        "Fast Solution of {Vandermonde}-like Systems Involving
                 Orthogonal Polynomials",
  journal =      j-IMAJNA,
  volume =       "8",
  pages =        "473--486",
  year =         "1988",
}

@InProceedings{Higham:1989:MNP,
  author =       "Nicholas J. Higham",
  title =        "Matrix Nearness Problems and Applications",
  booktitle =    "Applications of Matrix Theory",
  editor =       "M. J. C. Gover and S. Barnett",
  pages =        "1--27",
  publisher =    pub-OUP,
  year =         "1989",
}

@Article{Higham:1989:AST,
  author =       "Nicholas J. Higham",
  title =        "The Accuracy of Solutions to Triangular Systems",
  journal =      j-SINUM,
  volume =       "26",
  number =       "5",
  month =        oct,
  pages =        "1252--1265",
  year =         "1989",
}

@InProceedings{Higham:1990:ACD,
  author =       "Nicholas J. Higham",
  title =        "Analysis of the {Cholesky} Decomposition of a
                 Semi-definite Matrix",
  booktitle =    "Reliable Numerical Computation",
  editor =       "M. G. Cox and S. J. Hammarling",
  pages =        "161--185",
  publisher =    pub-OUP,
  year =         "1990",
}

@Article{Higham:1990:EMN,
  author =       "Nicholas J. Higham",
  title =        "Experience with a Matrix Norm Estimator",
  journal =      j-SISSC,
  volume =       "11",
  number =       "4",
  pages =        "804--809",
  month =        jul,
  year =         "1990",
}

@InProceedings{Higham:1990:HAG,
  author =       "Nicholas J. Higham",
  title =        "How Accurate is {Gaussian} Elimination?",
  booktitle =    "Numerical Analysis \textup{1989}, Proceedings of the
                 \textup{13}th Dundee Conference",
  series =       "Pitman Research Notes in Mathematics",
  volume =       "228",
  editor =       "D. F. Griffiths and G. A. Watson",
  pages =        "137--154",
  publisher =    pub-Longman-ST # ", " # pub-Longman-ST:adr,
  year =         "1990",
}

@TechReport{Higham:1990:IRE,
  author =       "Nicholas J. Higham",
  title =        "Iterative Refinement Enhances the Stability of {$QR$}
                 Factorization Methods for Solving Linear Equations",
  institution =  inst-U-MANCHESTER,
  address =      inst-U-MANCHESTER:adr,
  type =         t-NAREP,
  number =       "No. 182",
  month =        apr,
  year =         "1990",
}

@InProceedings{Higham:1990:CEB,
  author =       "Nicholas J. Higham",
  title =        "Computing Error Bounds for Regression Problems",
  booktitle =    "Statistical Analysis of Measurement Error Models and
                 Applications, Contemporary Mathematics 112",
  editor =       "Philip J. Brown and Wayne A. Fuller",
  pages =        "195--208",
  publisher =    pub-AMS # ", " # pub-AMS:adr,
  year =         "1990",
}

@Article{Higham:1990:EFM,
  author =       "Nicholas J. Higham",
  title =        "Exploiting Fast Matrix Multiplication within the Level
                 3 {BLAS}",
  journal =      j-TOMS,
  volume =       "16",
  number =       "4",
  month =        dec,
  pages =        "352--368",
  year =         "1990",
}

@Article{Higham:1990:BEG,
  author =       "Nicholas J. Higham",
  title =        "Bounding the Error in {Gaussian} Elimination for
                 Tridiagonal Systems",
  journal =      j-SIMAX,
  volume =       "11",
  number =       "4",
  month =        oct,
  pages =        "521--530",
  year =         "1990",
}

@Article{Higham:1990:SAA,
  author =       "Nicholas J. Higham",
  title =        "Stability Analysis of Algorithms for Solving Confluent
                 {Vandermonde}-like Systems",
  journal =      j-SIMAX,
  volume =       "11",
  number =       "1",
  month =        jan,
  pages =        "23--41",
  year =         "1990",
}

@Article{Higham:1991:TMP,
  author =       "Nicholas J. Higham",
  title =        "Three Measures of Precision in Floating Point
                 Arithmetic",
  journal =      "NA Digest",
  volume =       "Volume 91, Issue 16",
  year =         "1991",
  note =         "Electronic mail magazine:
                 \path|na.help@na-net.ornl.gov|",
}

@Article{Higham:1991:IRE,
  author =       "Nicholas J. Higham",
  title =        "Iterative Refinement Enhances the Stability of {$QR$}
                 Factorization Methods for Solving Linear Equations",
  journal =      j-BIT,
  volume =       "31",
  pages =        "447--468",
  year =         "1991",
}

@Article{Higham:1992:EMN,
  author =       "Nicholas J. Higham",
  title =        "Estimating the Matrix {$p$}-norm",
  journal =      j-NUM-MATH,
  volume =       "62",
  pages =        "539--555",
  year =         "1992",
}

@Article{Higham:1992:SMM,
  author =       "Nicholas J. Higham",
  title =        "Stability of a Method for Multiplying Complex Matrices
                 with Three Real Matrix Multiplications",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "3",
  month =        jul,
  pages =        "681--687",
  year =         "1992",
}

@Article{Higham:1993:ODS,
  author =       "Nicholas J. Higham",
  title =        "Optimization by Direct Search in Matrix Computations",
  journal =      j-SIMAX,
  volume =       "14",
  number =       "2",
  month =        apr,
  pages =        "317--333",
  year =         "1993",
}

@Article{Higham:1993:AFP,
  author =       "Nicholas J. Higham",
  title =        "The Accuracy of Floating Point Summation",
  journal =      j-SISC,
  volume =       "14",
  number =       "4",
  pages =        "783--799",
  month =        jul,
  year =         "1993",
}

@Article{Higham:1993:PTB,
  author =       "Nicholas J. Higham",
  title =        "Perturbation Theory and Backward Error for
                 {$AX-XB=C$}",
  journal =      j-BIT,
  volume =       "33",
  pages =        "124--136",
  year =         "1993",
}

@InProceedings{Higham:1994:SCP,
  author =       "Nicholas J. Higham",
  title =        "A Survey of Componentwise Perturbation Theory in
                 Numerical Linear Algebra",
  booktitle =    "{Mathematics of Computation} \textup{1943--1993}: {A}
                 Half Century of Computational Mathematics",
  series =       "Proceedings of Symposia in Applied Mathematics",
  volume =       "48",
  editor =       "Walter Gautschi",
  pages =        "49--77",
  publisher =    pub-AMS # ", " # pub-AMS:adr,
  year =         "1994",
}

@Article{Higham:1994:MSD,
  author =       "Nicholas J. Higham",
  title =        "The Matrix Sign Decomposition and Its Relation to the
                 Polar Decomposition",
  journal =      j-LAA,
  volume =       "212/213",
  pages =        "3--20",
  year =         "1994",
}

@Article{Higham:1995:CNT,
  author =       "Desmond J. Higham",
  title =        "Condition Numbers and Their Condition Numbers",
  journal =      j-LAA,
  volume =       "214",
  pages =        "193--213",
  year =         "1995",
}

@TechReport{Higham:1995:TMT,
  author =       "Nicholas J. Higham",
  title =        "The {Test Matrix Toolbox} for {MATLAB} (Version 3.0)",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  type =         t-NAREP,
  number =       "No. 276",
  month =        sep,
  year =         "1995",
  pages =        "70",
}

@Article{Higham:1995:SPT,
  author =       "Nicholas J. Higham",
  title =        "Stability of Parallel Triangular System Solvers",
  journal =      j-SISC,
  volume =       "16",
  number =       "2",
  pages =        "400--413",
  month =        mar,
  year =         "1995",
}

@Article{Higham:1997:SDP,
  author =       "Nicholas J. Higham",
  title =        "Stability of the Diagonal Pivoting Method with Partial
                 Pivoting",
  journal =      j-SIMAX,
  volume =       "18",
  number =       "1",
  pages =        "52--65",
  month =        jan,
  year =         "1997",
}

@Article{Higham:1997:IRL,
  author =       "Nicholas J. Higham",
  title =        "Iterative Refinement for Linear Systems and {LAPACK}",
  journal =      j-IMAJNA,
  volume =       "17",
  number =       "4",
  pages =        "495--509",
  year =         "1997",
}

@Article{Higham:1997:SIM,
  author =       "Nicholas J. Higham",
  title =        "Stable Iterations for the Matrix Square Root",
  journal =      j-NUM-ALG,
  volume =       "15",
  number =       "2",
  pages =        "227--242",
  year =         "1997",
}

@Article{Higham:1998:FCS,
  author =       "Nicholas J. Higham",
  title =        "Factorizing Complex Symmetric Matrices with Positive
                 Definite Real and Imaginary Parts",
  journal =      j-MATH-COMP,
  volume =       "67",
  number =       "224",
  month =        oct,
  pages =        "1591--1599",
  year =         "1998",
}

@Article{Higham:1999:SBF,
  author =       "Nicholas J. Higham",
  title =        "Stability of Block $\mathrm{LDL^T}$ Factorization of a
                 Symmetric Tridiagonal Matrix",
  journal =      j-LAA,
  volume =       "287",
  pages =        "181--189",
  year =         "1999",
}

@InProceedings{Higham:1999:NAS,
  author =       "Nicholas J. Higham",
  title =        "Notes on Accuracy and Stability of Algorithms in
                 Numerical Linear Algebra",
  booktitle =    "The Graduate Student's Guide to Numerical Analysis
                 '\textup{98}",
  editor =       "Mark Ainsworth and Jeremy Levesley and Marco
                 Marletta",
  pages =        "48--82",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  year =         "1999",
}

@Book{Higham:1998:HWM,
  author =       "Nicholas J. Higham",
  title =        "Handbook of Writing for the Mathematical Sciences",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  edition =      "Second",
  year =         "1998",
  ISBN =         "0-89871-420-6",
  pages =        "xvi+302",
}

@Book{Higham:2002:ASN,
  author =       "Nicholas J. Higham",
  title =        "Accuracy and Stability of Numerical Algorithms",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  edition =      "Second",
  year =         "2002",
  pages =        "xxx+680",
  ISBN =         "0-89871-521-0",
}

@Article{Higham:1989:LGF,
  author =       "Nicholas J. Higham and Desmond J. Higham",
  title =        "Large Growth Factors in {Gaussian} Elimination with
                 Pivoting",
  journal =      j-SIMAX,
  volume =       "10",
  number =       "2",
  month =        apr,
  pages =        "155--164",
  year =         "1989",
}

@Article{Higham:1992:BEC,
  author =       "Desmond J. Higham and Nicholas J. Higham",
  title =        "Backward Error and Condition of Structured Linear
                 Systems",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "1",
  month =        jan,
  pages =        "162--175",
  year =         "1992",
}

@Article{Higham:1992:CPT,
  author =       "Desmond J. Higham and Nicholas J. Higham",
  title =        "Componentwise Perturbation Theory for Linear Systems
                 with Multiple Right-Hand Sides",
  journal =      j-LAA,
  volume =       "174",
  pages =        "111--129",
  year =         "1992",
}

@Book{Higham:2000:MG,
  author =       "Desmond J. Higham and Nicholas J. Higham",
  title =        "{MATLAB} Guide",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "2000",
  pages =        "xxii+283",
  ISBN =         "0-89871-516-4",
}

@Article{Higham:2000:NAQ,
  author =       "Nicholas J. Higham and Hyun-Min Kim",
  title =        "Numerical Analysis of a Quadratic Matrix Equation",
  journal =      j-IMAJNA,
  volume =       "20",
  number =       "4",
  pages =        "499--519",
  year =         "2000",
}

@InProceedings{Higham:1993:CEA,
  author =       "Nicholas J. Higham and Philip A. Knight",
  title =        "Componentwise Error Analysis for Stationary Iterative
                 Methods",
  booktitle =    "Linear Algebra, Markov Chains, and Queueing Models",
  editor =       "Carl D. Meyer and Robert J. Plemmons",
  series =       "IMA Volumes in Mathematics and Its Applications",
  volume =       "48",
  pages =        "29--46",
  publisher =    pub-Springer # ", " # pub-Springer:adr-NY,
  year =         "1993",
}

@Article{Higham:1993:FPB,
  author =       "Nicholas J. Higham and Philip A. Knight",
  title =        "Finite Precision Behavior of Stationary Iteration for
                 Solving Singular Systems",
  journal =      j-LAA,
  volume =       "192",
  pages =        "165--186",
  year =         "1993",
}

@Article{Higham:1995:MPF,
  author =       "Nicholas J. Higham and Philip A. Knight",
  title =        "Matrix Powers in Finite Precision Arithmetic",
  journal =      j-SIMAX,
  volume =       "16",
  number =       "2",
  pages =        "343--358",
  month =        apr,
  year =         "1995",
}

@Article{Hilbert:1894:BTL,
  author =       "David Hilbert",
  title =        "{Ein Beitrag zur Theorie des Legendre'schen
                 Polynoms}",
  journal =      "Acta Mathematica",
  volume =       "18",
  pages =        "155--159",
  year =         "1894",
}

@Book{Hildebrand:1974:INA,
  author =       "F. B. Hildebrand",
  title =        "Introduction to Numerical Analysis",
  edition =      "Second",
  publisher =    pub-MH,
  address =      pub-MH:adr,
  year =         "1974",
  ISBN =         "0-486-65363-3",
  pages =        "xiii+669",
  note =         "Reprinted by Dover, New York, 1987",
}

@Article{Higham:1994:PAC,
  author =       "Nicholas J. Higham and Pythagoras Papadimitriou",
  title =        "A Parallel Algorithm for Computing the Polar
                 Decomposition",
  journal =      j-PAR-COMP,
  volume =       "20",
  number =       "8",
  month =        aug,
  pages =        "1161--1173",
  year =         "1994",
}

@Article{Higham:1994:SPI,
  author =       "Nicholas J. Higham and Alex Pothen",
  title =        "Stability of the Partitioned Inverse Method for
                 Parallel Solution of Sparse Triangular Systems",
  journal =      j-SISC,
  volume =       "15",
  number =       "1",
  pages =        "139--148",
  month =        jan,
  year =         "1994",
}

@InProceedings{Higham:1987:NLA,
  author =       "Nicholas J. Higham and G. W. Stewart",
  title =        "Numerical Linear Algebra in Statistical Computing",
  booktitle =    "The State of the Art in Numerical Analysis",
  editor =       "A. Iserles and M. J. D. Powell",
  pages =        "41--57",
  publisher =    pub-OUP,
  year =         "1987",
}

@Article{Higham:2000:BAM,
  author =       "Nicholas J. Higham and Fran\c{c}oise Tisseur",
  title =        "A Block Algorithm for Matrix 1-Norm Estimation, with
                 an Application to 1-Norm Pseudospectra",
  journal =      j-SIMAX,
  volume =       "21",
  number =       "4",
  pages =        "1185--1201",
  year =         "2000",
}

@TechReport{Higham:2001:BEM,
  author =       "Nicholas J. Higham and Fran\c{c}oise Tisseur",
  title =        "Bounds for Eigenvalues of Matrix Polynomials",
  institution =  inst-MCCM,
  address =      inst-MCCM:adr,
  type =         t-NAREP,
  number =       "371",
  month =        jan,
  pages =        "16",
  year =         "2001",
  note =         "To appear in " # j-LAA,
}

@Article{Higham:1993:SO,
  author =       "Desmond J. Higham and Lloyd N. Trefethen",
  title =        "Stiffness of {ODE}s",
  journal =      j-BIT,
  volume =       "33",
  pages =        "285--303",
  year =         "1993",
}

@InProceedings{Hida:2001:AQD,
  author =       "Yozo Hida and Xiaoye S. Li and David H. Bailey",
  title =        "Algorithms for Quad-Double Precision Floating Point
                 Arithmetic",
  booktitle =    "Proc. 15th IEEE Symposium on Computer Arithmetic",
  publisher =    "IEEE Computer Society Press, Los Alamitos, CA, USA",
  pages =        "155--162",
  year =         "2001",
}

@Book{Hardy:1952:I,
  author =       "G. H. Hardy and J. E. Littlewood and G. P{\'o}lya",
  title =        "Inequalities",
  edition =      "Second",
  publisher =    pub-CUP,
  pages =        "xii+324",
  year =         "1952",
}

@Article{Holt:1988:TPL,
  author =       "R. C. Holt and J. R. Cordy",
  title =        "The {Turing} Programming Language",
  journal =      j-CACM,
  volume =       "31",
  number =       "12",
  pages =        "1410--1423",
  year =         "1988",
}

@InProceedings{Hodel:1992:RAL,
  author =       "A. Scottedward Hodel",
  title =        "Recent Applications of the {Lyapunov} Equation in
                 Control Theory",
  booktitle =    "Iterative Methods in Linear Algebra",
  editor =       "R. Beauwens and P. de Groen",
  pages =        "217--227",
  publisher =    "Elsevier Science Publishers B.V. (North-Holland), " #
                 pub-NH:adr,
  year =         "1992",
}

@Book{Hodges:1983:ATE,
  author =       "Andrew Hodges",
  title =        "{Alan Turing}: {The} Enigma",
  publisher =    "Burnett Books",
  address =      "London",
  year =         "1983",
  pages =        "xix+586",
  note =         "1992 edition with preface, Vintage, London",
  ISBN =         "0-09-911641-3",
}

@Article{Hoffmann:1987:SLS,
  author =       "W. Hoffmann",
  title =        "Solving Linear Systems on a Vector Computer",
  journal =      j-JCAM,
  volume =       "18",
  pages =        "353--367",
  year =         "1987",
}

@Article{Hoffmann:1989:IAG,
  author =       "W. Hoffmann",
  title =        "Iterative Algorithms for {Gram-Schmidt}
                 Orthogonalization",
  journal =      j-COMPUTING,
  volume =       "41",
  pages =        "335--348",
  year =         "1989",
}

@Article{Hoffmann:1989:PAR,
  author =       "Christoph M. Hoffmann",
  title =        "The Problems of Accuracy and Robustness in Geometric
                 Computation",
  journal =      "Computer",
  volume =       "March",
  pages =        "31--41",
  year =         "1989",
}

@Book{Hockney:1988:PCA,
  author =       "R. W. Hockney and C. R. Jesshope",
  title =        "Parallel Computers \textup{2}: {Architecture},
                 Programming and Algorithms",
  publisher =    "Adam Hilger",
  address =      "Bristol",
  year =         "1988",
  pages =        "xv+625",
  ISBN =         "0-85274-812-4",
}

@Book{Horn:1985:MA,
  author =       "Roger A. Horn and Charles R. Johnson",
  title =        "Matrix Analysis",
  publisher =    pub-CUP,
  year =         "1985",
  ISBN =         "0-521-30586-1",
  pages =        "xiii+561",
}

@Book{Horn:1991:TMA,
  author =       "Roger A. Horn and Charles R. Johnson",
  title =        "Topics in Matrix Analysis",
  publisher =    pub-CUP,
  year =         "1991",
  ISBN =         "0-521-30587-X",
  pages =        "viii+607",
}

@Article{Horning:1979:NPR,
  author =       "Jim Horning",
  title =        "Note on Program Reliability",
  journal =      "ACM SIGSOFT Software Engineering Notes",
  volume =       "4",
  number =       "4",
  pages =        "6",
  year =         "1979",
  note =         "Cited in \cite{Tropp:1984:FA}",
}

@Article{Hochbruck:1995:PKS,
  author =       "Marlis Hochbruck and Gerhard Starke",
  title =        "Preconditioned {Krylov} Subspace Methods for
                 {Lyapunov} Matrix Equations",
  journal =      j-SIMAX,
  volume =       "16",
  number =       "1",
  pages =        "156--171",
  year =         "1995",
}

@Article{Hotelling:1943:SNM,
  author =       "Harold Hotelling",
  title =        "Some New Methods in Matrix Calculation",
  journal =      "Ann. Math. Statist.",
  volume =       "14",
  number =       "1",
  pages =        "1--34",
  year =         "1943",
}

@Article{Hough:1981:API,
  author =       "David Hough",
  title =        "Applications of the Proposed {IEEE 754} Standard for
                 Floating-Point Arithmetic",
  journal =      "Computer",
  volume =       "14",
  pages =        "70--74",
  year =         "1981",
}

@Article{Hough:1989:RS,
  author =       "David Hough",
  title =        "Random Story",
  journal =      "NA Digest",
  volume =       "Volume 89, Issue 1",
  year =         "1989",
}

@Article{hous58,
  author =       "Alston S. Householder",
  title =        "Unitary Triangularization of a Nonsymmetric Matrix",
  journal =      j-ACM,
  volume =       "5",
  pages =        "339--342",
  year =         "1958",
}

@Book{Householder:1964:TMN,
  author =       "Alston S. Householder",
  title =        "The Theory of Matrices in Numerical Analysis",
  publisher =    pub-Blaisdell,
  address =      pub-Blaisdell:adr-NY,
  year =         "1964",
  note =         "Reprinted by Dover, New York, 1975",
  pages =        "xi+257",
  ISBN =         "0-486-61781-5",
}

@Article{Hough:1997:COD,
  author =       "Patricia D. Hough and Stephen A. Vavasis",
  title =        "Complete Orthogonal Decomposition for Weighted Least
                 Squares",
  journal =      j-SIMAX,
  volume =       "18",
  number =       "2",
  pages =        "369--392",
  year =         "1997",
}

@Book{hp82,
  key =          "Hewlett-Packard",
  title =        "{HP-\textup{15}C} Advanced Functions Handbook",
  publisher =    "Hewlett-Packard",
  address =      "Portable Computer Division, Corvallis, OR, USA",
  year =         "1982",
  note =         "Part number 00015-90011 Rev.~C",
  pages =        "221",
}

@Book{hp93,
  key =          "Hewlett-Packard",
  title =        "{HP \textup{48}G} Series User's Guide",
  publisher =    "Hewlett-Packard",
  address =      "Corvallis Division, Corvallis, OR, USA",
  year =         "1993",
  note =         "Part number 00048-90126, Edition 3",
}

@Article{Henderson:1983:HKP,
  author =       "Harold V. Henderson and Friedrich Pukelsheim and
                 Shayle R. Searle",
  title =        "On the History of the {Kronecker} Product",
  journal =      j-LMA,
  volume =       "14",
  pages =        "113--120",
  year =         "1983",
}

@Book{Hedayat:1999:OAT,
  author =       "A. S. Hedayat and N. J. A. Sloane and John Stufken",
  title =        "Orthogonal Arrays: {Theory} and Applications",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-NY,
  year =         "1999",
  ISBN =         "0-387-98766-5",
  pages =        "xxiii+416",
}

@InProceedings{Hull:1979:CNS,
  author =       "T. E. Hull",
  title =        "Correctness of Numerical Software",
  editor =       "Lloyd D. Fosdick",
  booktitle =    "Performance Evaluation of Numerical Software",
  publisher =    pub-NH # ", " # pub-NH:adr,
  year =         "1979",
  pages =        "3--15",
}

@InProceedings{Hull:1982:PCE,
  author =       "T. E. Hull",
  title =        "Precision Control, Exception Handling and {A} Choice
                 of Numerical Algorithms",
  booktitle =    "Numerical Analysis Proceedings, Dundee 1981",
  editor =       "G. A. Watson",
  series =       "Lecture Notes in Mathematics",
  volume =       "912",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  pages =        "169--178",
  year =         "1982",
}

@Article{Hunt:1997:ROA,
  author =       "Julian Hunt",
  title =        "Rounding and Other Approximations for Measurements,
                 Records and Targets",
  journal =      j-MATH-TODAY,
  volume =       "33",
  nuber =        "3",
  pages =        "73--77",
  year =         "1997",
}

@Article{Hu:1992:KSM,
  author =       "D. Y. Hu and L. Reichel",
  title =        "Krylov Subspace Methods for the {Sylvester} Equation",
  journal =      j-LAA,
  volume =       "172",
  pages =        "283--313",
  year =         "1992",
}

@Article{Hull:1966:TPM,
  author =       "T. E. Hull and J. R. Swenson",
  title =        "Tests of Probabilistic Models for Propagation of
                 Roundoff Errors",
  journal =      j-CACM,
  volume =       "9",
  number =       "2",
  pages =        "108--113",
  year =         "1966",
}

@Misc{Hyman:1957:EEG,
  author =       "M. A. Hyman",
  title =        "Eigenvalues and Eigenvectors of General Matrices",
  howpublished = "Presented at the 12th National Meeting of the
                 Association for Computing Machinery, Houston, Texas",
  year =         "1957",
  note =         "Cited in \cite{Wilkinson:1963:REA}",
}

@Book{IBM:1988:ESS,
  author =       "IBM",
  title =        "Engineering and Scientific Subroutine Library, Guide
                 and Reference, Release 3",
  publisher =    "Fourth Edition (Program Number 5668-863)",
  year =         "1988",
}

@Article{Group:1981:PSB,
  author =       "{IEEE Computer Society Microprocessor Standards
                 Committee, Floating-Point Working Group}",
  title =        "A Proposed Standard for Binary Floating-Point
                 Arithmetic, {Draft} 8.0 of {IEEE Task P754} (With
                 Introductory Comments by {David Stevenson})",
  journal =      "Computer",
  volume =       "14",
  pages =        "51--62",
  year =         "1981",
}

@Book{ieee85,
  key =          "IEEE Computer Society",
  title =        "{IEEE} Standard for Binary Floating-Point Arithmetic,
                 {ANSI/IEEE} Standard 754-1985",
  publisher =    "Institute of Electrical and Electronics Engineers",
  address =      "New York",
  year =         "1985",
  note =         "Reprinted in SIGPLAN Notices, 22(2):9--25, 1987",
}

@Book{ieee87,
  key =          "IEEE Computer Society",
  title =        "A Radix-Independent Standard for Floating-Point
                 Arithmetic, {IEEE} Standard 854-1987",
  publisher =    "IEEE Computer Society",
  address =      "New York",
  year =         "1987",
}

@Article{Ikebe:1979:IHM,
  author =       "Yasuhiko Ikebe",
  title =        "On Inverses of {Hessenberg} Matrices",
  journal =      j-LAA,
  volume =       "24",
  pages =        "93--97",
  year =         "1979",
}

@Article{Ikramov:2000:BGF,
  author =       "Khakim D. Ikramov and Andrey B. Kucherov",
  title =        "Bounding the Growth Factor in {Gaussian} Elimination
                 for {Buckley's} Class of Complex Symmetric Matrices",
  journal =      j-NLAA,
  volume =       "7",
  number =       "5",
  pages =        "269--274",
  year =         "2000",
}

@Article{Ikramov:1998:RNC,
  author =       "Khakim D. Ikramov",
  title =        "A Remark on ``{A} Note on Constructing a Symmetric
                 Matrix with Specified Diagonal Entries and
                 Eigenvalues''",
  journal =      j-BIT,
  volume =       "38",
  number =       "4",
  pages =        "807",
  year =         "1998",
}

@Misc{Committee:1993:RGL,
  author =       "{ILAS Education Committee}",
  title =        "Report on Graduate Linear Algebra Courses",
  howpublished = "Manuscript from the International Linear Algebra
                 Society",
  year =         "1993",
  month =        nov,
  pages =        "4",
  note =         "\path|http://gauss.technion.ac.il/iic/GRAD-ED.SYLLABI|",
}

@Article{Incertis:1985:FMC,
  author =       "F. Incertis",
  title =        "A Faster Method of Computing Matrix {Pythagorean}
                 Sums",
  journal =      j-IEEE-AC,
  volume =       "AC-30",
  number =       "3",
  pages =        "273--275",
  year =         "1985",
}

@Book{Ince:1992:CWM,
  editor =       "D. C. Ince",
  title =        "Collected Works of {A. M. Turing}: {Mechanical}
                 Intelligence",
  publisher =    pub-NH,
  address =      pub-NH:adr,
  year =         "1992",
  pages =        "xix+227",
  ISBN =         "0-444-88058-5",
}

@Article{Ipsen:1994:USM,
  author =       "Ilse C. F. Ipsen and Carl D. Meyer",
  title =        "Uniform Stability of {Markov} Chains",
  journal =      j-SIMAX,
  volume =       "15",
  number =       "4",
  pages =        "1061--1074",
  year =         "1994",
}

@InProceedings{Iri:1991:HAD,
  author =       "Masao Iri",
  title =        "History of Automatic Differentiation and Rounding
                 Error Estimation",
  editor =       "Andreas Griewank and George F. Corliss",
  booktitle =    "Automatic Differentiation of Algorithms: {Theory},
                 Implementation, and Application",
  publisher =    pub-SIAM # ", " # pub-SIAM:adr,
  pages =        "3--16",
  year =         "1991",
}

@Book{Isaacson:1966:ANM,
  author =       "Eugene Isaacson and Herbert Bishop Keller",
  title =        "Analysis of Numerical Methods",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  year =         "1966",
  pages =        "xv+541",
  note =         "Reprinted by Dover, New York, 1994",
  ISBN =         "0-486-68029-0",
}

@Article{Jang:1997:CLS,
  author =       "Ho-Jong Jang",
  title =        "A Constrained Least-Squares Approach to the Rapid
                 Reanalysis of Structures",
  journal =      j-LAA,
  volume =       "265",
  pages =        "185--202",
  year =         "1997",
}

@Article{Jalby:1991:SAI,
  author =       "William Jalby and Bernard Philippe",
  title =        "Stability Analysis and Improvement of the Block
                 {Gram--Schmidt} Algorithm",
  journal =      j-SISSC,
  volume =       "12",
  number =       "5",
  pages =        "1058--1073",
  year =         "1991",
}

@Article{Jansen:1986:HAA,
  author =       "Paul Jansen and Peter Weidner",
  title =        "High-Accuracy Arithmetic Software---Some Tests of the
                 {ACRITH} Problem-Solving Routines",
  journal =      j-TOMS,
  volume =       "12",
  number =       "1",
  pages =        "62--70",
  year =         "1986",
}

@Article{Jankowski:1977:IRI,
  author =       "M. Jankowski and H. Wo{\'z}niakowski",
  title =        "Iterative Refinement Implies Numerical Stability",
  journal =      j-BIT,
  volume =       "17",
  pages =        "303--311",
  year =         "1977",
}

@Article{Jankowski:1985:ASC,
  author =       "M. Jankowski and H. Wo{\'z}niakowski",
  title =        "The Accurate Solution of Certain Continuous Problems
                 Using Only Single Precision Arithmetic",
  journal =      j-BIT,
  volume =       "25",
  pages =        "635--651",
  year =         "1985",
}

@Article{Jennings:1982:BSV,
  author =       "A. Jennings",
  title =        "Bounds for the Singular Values of a Matrix",
  journal =      j-IMAJNA,
  volume =       "2",
  pages =        "459--474",
  year =         "1982",
}

@Article{Jennings:1974:DEA,
  author =       "L. S. Jennings and M. R. Osborne",
  title =        "A Direct Error Analysis for Least Squares",
  journal =      j-NUM-MATH,
  volume =       "22",
  pages =        "325--332",
  year =         "1974",
}

@Article{Jong:1977:TFD,
  author =       "Lieuwe Sytse de Jong",
  title =        "Towards a Formal Definition of Numerical Stability",
  journal =      j-NUM-MATH,
  volume =       "28",
  pages =        "211--219",
  year =         "1977",
}

@Article{Jones:1993:BKF,
  author =       "Mark T. Jones and Merrell L. Patrick",
  title =        "{Bunch--Kaufman} Factorization for Real Symmetric
                 Indefinite Banded Matrices",
  journal =      j-SIMAX,
  volume =       "14",
  number =       "2",
  pages =        "553--559",
  year =         "1993",
}

@Article{Jones:1994:FSI,
  author =       "Mark T. Jones and Merrell L. Patrick",
  title =        "Factoring Symmetric Indefinite Matrices on
                 High-Performance Architectures",
  journal =      j-SIMAX,
  volume =       "15",
  number =       "1",
  pages =        "273--283",
  year =         "1994",
}

@Article{Jordan:1968:EEG,
  author =       "T. L. Jordan",
  title =        "Experiments on Error Growth Associated with Some
                 Linear Least-Squares Procedures",
  journal =      j-MATH-COMP,
  volume =       "22",
  pages =        "579--588",
  year =         "1968",
}

@Book{Joseph:1991:CPN,
  author =       "George Gheverghese Joseph",
  title =        "The Crest of the Peacock: {Non-European} Roots of
                 Mathematics",
  publisher =    pub-Penguin,
  address =      pub-Penguin:adr-L,
  year =         "1991",
  pages =        "xv+371",
  ISBN =         "0-14-012529-9",
}

@Article{Jones:1974:NSE,
  author =       "William B. Jones and W. J. Thron",
  title =        "Numerical Stability in Evaluating Continued
                 Fractions",
  journal =      j-MATH-COMP,
  volume =       "28",
  number =       "127",
  pages =        "795--810",
  year =         "1974",
}

@Article{Jankowski:1983:NFP,
  author =       "M. Jankowski and A. Smoktunowicz and H.
                 Wo{\'z}niakowski",
  title =        "A Note on Floating-Point Summation of Very Many
                 Terms",
  journal =      "J. Information Processing and Cybernetics-EIK",
  volume =       "19",
  number =       "9",
  pages =        "435--440",
  year =         "1983",
}

@Article{Kahan:1963:ANIa,
  author =       "W. Kahan and I. Farkas",
  title =        "Algorithm 168: {Newton} Interpolation with Backward
                 Divided Differences",
  journal =      j-CACM,
  volume =       "6",
  number =       "4",
  pages =        "165",
  year =         "1963",
}

@Article{Kahan:1963:ANIb,
  author =       "W. Kahan and I. Farkas",
  title =        "Algorithm 169: {Newton} Interpolation with Forward
                 Divided Differences",
  journal =      j-CACM,
  volume =       "6",
  number =       "4",
  pages =        "165",
  year =         "1963",
}

@Article{Kaagstrom:1994:PAG,
  author =       "Bo K{\aa}gstr{\"o}m",
  title =        "A Perturbation Analysis of the Generalized {Sylvester}
                 Equation {$(AR-LB, DR-LE) = (C,F)$}",
  journal =      j-SIMAX,
  volume =       "15",
  number =       "4",
  pages =        "1045--1060",
  year =         "1994",
}

@Unpublished{Kahan:2001:WVT,
  author =       "W. Kahan",
  title =        "What has the Volume of a Tetrahedron to do with
                 Computer Programming Languages?",
  note =         "Manuscript",
  year =         "2001",
  month =        apr,
  pages =        "31",
}

@Article{Kahan:1965:FRR,
  author =       "W. Kahan",
  title =        "Further Remarks on Reducing Truncation Errors",
  journal =      j-CACM,
  volume =       "8",
  number =       "1",
  pages =        "40",
  year =         "1965",
}

@Article{Kahan:1966:NLA,
  author =       "W. Kahan",
  title =        "Numerical Linear Algebra",
  journal =      "Canadian Math. Bulletin",
  volume =       "9",
  pages =        "757--801",
  year =         "1966",
}

@InProceedings{Kahan:1972:SEA,
  author =       "W. Kahan",
  title =        "A Survey of Error Analysis",
  booktitle =    "Proc. IFIP Congress, Ljubljana",
  series =       "Information Processing 71",
  publisher =    pub-NH # ", " # pub-NH:adr,
  pages =        "1214--1239",
  year =         "1972",
}

@TechReport{Kahan:1973:IAL,
  author =       "W. Kahan",
  title =        "Implementation of Algorithms (Lecture Notes by {W. S.
                 Haugeland} and {D. Hough})",
  type =         "Technical Report",
  number =       "20",
  institution =  inst-Berkeley-CS,
  address =      inst-Berkeley:adr,
  year =         "1973",
}

@InProceedings{Kahan:1980:IAO,
  author =       "W. Kahan",
  title =        "Interval Arithmetic Options in the Proposed {IEEE}
                 Floating Point Arithmetic Standard",
  editor =       "Karl L. E. Nickel",
  booktitle =    "Interval Mathematics 1980",
  publisher =    pub-AP # ", " # pub-AP:adr-NY,
  pages =        "99--128",
  year =         "1980",
}

@TechReport{Kahan:1981:WDW,
  author =       "W. Kahan",
  title =        "Why Do We Need a Floating-Point Arithmetic Standard?",
  type =         "Technical Report",
  institution =  inst-Berkeley,
  address =      inst-Berkeley:adr,
  month =        feb,
  year =         "1981",
  pages =        "41",
}

@InProceedings{Kahan:1983:MWS,
  author =       "W. Kahan",
  title =        "Mathematics Written in Sand---The {HP-15C}, {Intel}
                 8087, etc.",
  booktitle =    "Statistical Computing Section, Proceedings of the
                 American Statistical Association, Toronto",
  year =         "1983",
  pages =        "12--26",
}

@TechReport{Kahan:1986:SRC,
  author =       "W. Kahan",
  title =        "To Solve a Real Cubic Equation",
  type =         "Technical Report",
  number =       "PAM-352",
  institution =  "Center for Pure and Applied Mathmatics, University of
                 California",
  address =      inst-Berkeley:adr,
  month =        nov,
  pages =        "20",
  year =         "1986",
}

@InProceedings{Kahan:1987:BCC,
  author =       "W. Kahan",
  title =        "Branch Cuts for Complex Elementary Functions or Much
                 Ado About Nothing's Sign Bit",
  editor =       "A. Iserles and M. J. D. Powell",
  booktitle =    "The State of the Art in Numerical Analysis",
  publisher =    pub-OUP,
  pages =        "165--211",
  year =         "1987",
}

@Unpublished{Kahan:1987:DPI,
  author =       "W. Kahan",
  title =        "Doubled-Precision {IEEE} Standard 754 Floating-Point
                 Arithmetic",
  note =         "Manuscript",
  month =        feb,
  year =         "1987",
}

@Unpublished{Kahan:1990:HCA,
  author =       "W. Kahan",
  title =        "How {Cray}'s Arithmetic Hurts Scientific Computation
                 (and What Might be Done About It)",
  note =         "Manuscript prepared for the Cray User Group meeting in
                 Toronto",
  year =         "1990",
  month =        jun,
  pages =        "42",
}

@Article{Kahan:1991:ARL,
  author =       "W. Kahan",
  title =        "Analysis and Refutation of the {LCAS}",
  journal =      j-SIGNUM,
  volume =       "26",
  number =       "3",
  pages =        "2--15",
  year =         "1991",
}

@Unpublished{Kahan:1994:CBV,
  author =       "W. Kahan",
  title =        "Computer Benchmarks Versus Accuracy",
  note =         "Draft manuscript",
  year =         "1994",
  month =        jun,
}

@Unpublished{Kahan:1996:IPE,
  author =       "W. Kahan",
  title =        "The Improbability of Probabilistic Error Analyses for
                 Numerical Computations",
  note =         "Manuscript",
  year =         "1996",
  month =        mar,
  pages =        "34",
}

@Unpublished{Kahan:1996:LNS,
  author =       "W. Kahan",
  title =        "Lecture Notes on the Status of {IEEE Standard} 754 for
                 Binary Floating-Point Arithmetic",
  note =         "Manuscript",
  year =         "1996",
  month =        may,
  pages =        "30",
}

@Unpublished{Kahan:1997:MAA,
  author =       "W. Kahan",
  title =        "Miscalculating Area and Angles of a Needle-Like
                 Triangle",
  note =         "Manuscript",
  year =         "1997",
  month =        jul,
  pages =        "20",
}

@InProceedings{Kahan:1985:AIA,
  author =       "W. Kahan and E. LeBlanc",
  title =        "Anomalies in the {IBM ACRITH} Package",
  booktitle =    "Proceedings of the 7th Symposium on Computer
                 Arithmetic",
  editor =       "Kai Hwang",
  pages =        "322--331",
  publisher =    "IEEE Computer Society Press, Silver Spring, MD, USA",
  year =         "1985",
}

@Article{Karp:1997:HPD,
  author =       "Alan H. Karp and Peter Markstein",
  title =        "High-Precision Division and Square Root",
  journal =      j-TOMS,
  volume =       "23",
  number =       "4",
  pages =        "561--589",
  year =         "1997",
}

@Article{Karatsuba:1963:MMN,
  author =       "A. Karatsuba and Yu. Ofman",
  title =        "Multiplication of Multidigit Numbers on Automata",
  journal =      "Soviet Physics---Doklady",
  volume =       "7",
  number =       "7",
  month =        jan,
  pages =        "595--596",
  year =         "1963",
}

@Article{Kahan:1979:PFP,
  author =       "W. Kahan and J. Palmer",
  title =        "On a Proposed Floating-Point Standard",
  journal =      j-SIGNUM,
  volume =       "14",
  pages =        "13--21",
  month =        oct,
  year =         "1979",
}

@Article{Kaagstrom:1992:DSM,
  author =       "Bo K{\aa}gstr{\"o}m and Peter Poromaa",
  title =        "Distributed and Shared Memory Block Algorithms for the
                 Triangular {Sylvester} Equation with {${\rm sep}^{-1}$}
                 Estimators",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "1",
  pages =        "90--101",
  year =         "1992",
}

@Article{Kaagstrom:1996:LSA,
  author =       "Bo K{\aa}gstr{\"o}m and Peter Poromaa",
  title =        "{LAPACK}-Style Algorithms and Software for Solving the
                 Generalized {Sylvester} Equation and Estimating the
                 Separation Between Regular Matrix Pairs",
  journal =      j-TOMS,
  volume =       "22",
  number =       "1",
  pages =        "78--103",
  year =         "1996",
}

@Article{Kaagstrom:1996:CES,
  author =       "Bo K{\aa}gstr{\"o}m and Peter Poromaa",
  title =        "Computing Eigenspaces with Specified Eigenvalues of a
                 Regular Matrix Pair {$(A,B)$} and Condition Estimation:
                 {Theory}, Algorithms and Software",
  journal =      j-NUM-ALG,
  volume =       "12",
  pages =        "369--407",
  year =         "1996",
}

@Article{Kaporin:1999:PAF,
  author =       "Igor Kaporin",
  title =        "A Practical Algorithm for Faster Matrix
                 Multiplication",
  journal =      j-NLAA,
  volume =       "6",
  pages =        "687--700",
  year =         "1999",
}

@Article{Karasalo:1974:CTD,
  author =       "Ilkka Karasalo",
  title =        "A Criterion for Truncation of the {$QR$}-Decomposition
                 Algorithm for the Singular Linear Least Squares
                 Problem",
  journal =      j-BIT,
  volume =       "14",
  pages =        "156--166",
  year =         "1974",
}

@Book{Karlin:1968:TP,
  author =       "Samuel Karlin",
  title =        "Total Positivity",
  volume =       "1",
  publisher =    "Stanford University Press",
  address =      inst-U-STANFORD:adr,
  year =         "1968",
}

@Article{Karpinski:1985:PFP,
  author =       "Richard Karpinski",
  title =        "Paranoia: {A} Floating-Point Benchmark",
  journal =      "BYTE",
  volume =       "10",
  number =       "2",
  pages =        "223--235",
  year =         "1985",
  month =        feb,
}

@Book{Kato:1976:PTL,
  author =       "Tosio Kato",
  title =        "Perturbation Theory for Linear Operators",
  edition =      "Second",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  year =         "1976",
  pages =        "xxi+619",
  ISBN =         "3-540-97588-5",
}

@Article{Kaufman:1983:MMQ,
  author =       "Linda Kaufman",
  title =        "Matrix Methods for Queuing Problems",
  journal =      j-SISSC,
  volume =       "4",
  number =       "3",
  pages =        "525--552",
  year =         "1983",
}

@Article{Kao:2000:LTA,
  author =       "Ming-Yang Kao and Jie Wang",
  title =        "Linear-Time Approximation Algorithms for Computing
                 Numerical Summation with Provably Small Errors",
  journal =      j-SICOMP,
  volume =       "29",
  number =       "5",
  pages =        "1568--1576",
  year =         "2000",
}

@Article{Karlson:1997:EOB,
  author =       "Rune Karlson and Bertil Wald{\'e}n",
  title =        "Estimation of Optimal Backward Perturbation Bounds for
                 the Linear Least Squares Problem",
  journal =      j-BIT,
  volume =       "37",
  number =       "4",
  pages =        "862--869",
  year =         "1997",
}

@Article{Kaagstrom:1989:GSM,
  author =       "Bo K{\aa}gstr{\"o}m and Lars Westin",
  title =        "Generalized {Schur} Methods with Condition Estimators
                 for Solving the Generalized {Sylvester} Equation",
  journal =      j-IEEE-AC,
  volume =       "AC-34",
  number =       "7",
  pages =        "745--751",
  year =         "1989",
}

@Article{Kearfott:1996:AIF,
  author =       "R. Baker Kearfott",
  title =        "Algorithm 763: {INTERVAL\_ARITHMETIC}: {A Fortran 90}
                 Module for an Interval Data Type",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "385--392",
  year =         "1996",
}

@Article{Kearfott:1996:ICI,
  author =       "R. Baker Kearfott",
  title =        "Interval Computations: {Introduction}, Uses, and
                 Resources",
  journal =      "Euromath Bulletin",
  volume =       "2",
  number =       "1",
  pages =        "95--112",
  year =         "1996",
  note =         "\path|http://interval.louisiana.edu/preprints.html|",
}

@Book{Kennedy:1980:SC,
  author =       "William J. {Kennedy, Jr.} and James E. Gentle",
  title =        "Statistical Computing",
  publisher =    "Marcel Dekker",
  address =      "New York",
  year =         "1980",
  pages =        "xi+591",
  ISBN =         "0-8247-6898-1",
}

@Article{Kenney:1990:SAD,
  author =       "Charles Kenney and Gary Hewer",
  title =        "The Sensitivity of the Algebraic and Differential
                 {Riccati} Equations",
  journal =      j-SICOPT,
  volume =       "28",
  number =       "1",
  pages =        "50--69",
  year =         "1990",
}

@Article{Kenney:1988:CSR,
  author =       "Charles Kenney and Alan J. Laub",
  title =        "Controllability and Stability Radii for Companion Form
                 Systems",
  journal =      "Math. Control Signals Systems",
  volume =       "1",
  pages =        "239--256",
  year =         "1988",
}

@Article{Kenney:1994:SSS,
  author =       "Charles S. Kenney and Alan J. Laub",
  title =        "Small-Sample Statistical Condition Estimates for
                 General Matrix Functions",
  journal =      j-SISC,
  volume =       "15",
  number =       "1",
  pages =        "36--61",
  year =         "1994",
}

@Article{Keller:1965:SSS,
  author =       "Herbert B. Keller",
  title =        "On the Solution of Singular and Semidefinite Linear
                 Systems by Iteration",
  journal =      j-SINUM,
  volume =       "2",
  number =       "2",
  pages =        "281--290",
  year =         "1965",
}

@Book{Kelley:1995:IML,
  author =       "C. T. Kelley",
  title =        "Iterative Methods for Linear and Nonlinear Equations",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "1995",
  pages =        "xiii+165",
  ISBN =         "0-89871-352-8",
}

@Book{Kelley:1999:IMO,
  author =       "C. T. Kelley",
  title =        "Iterative Methods for Optimization",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "1999",
  pages =        "xv+180",
  ISBN =         "0-89871-433-8",
}

@Article{Kerr:1990:FCT,
  author =       "Thomas H. Kerr",
  title =        "Fallacies in Computational Testing of Matrix Positive
                 Definiteness/Semidefiniteness",
  journal =      "IEEE Trans. Aerospace and Electronic Systems",
  volume =       "26",
  number =       "2",
  pages =        "415--421",
  year =         "1990",
}

@InProceedings{Krishnan:2001:PEM,
  author =       "Shankar Krishnan and Mark Foskey and Tim Culver and
                 John Keyser and Dinesh Manocha",
  title =        "{PRECISE}: {Efficient} Multiprecision Evaluation of
                 Algebraic Roots and Predicates for Reliable Geometric
                 Computation",
  editor =       "David Eppstein and Dan Halperin and Dinesh Manocha",
  booktitle =    "Proc. ACM Symposium on Computational Geometry",
  publisher =    "ACM Press",
  pages =        "274--283",
  year =         "2001",
}

@Article{Kielbasinski:1973:SAC,
  author =       "Andrzej Kie{\l}basi{\'n}ski",
  title =        "Summation algorithm with corrections and some of its
                 applications",
  journal =      "Math. Stos.",
  volume =       "1",
  pages =        "22--41",
  note =         "(In Polish, cited in \cite{Jankowski:1983:NFP} and
                 \cite{Jankowski:1985:ASC})",
  year =         "1973",
}

@Article{Kielbasinski:1981:IRL,
  author =       "Andrzej Kie{\l}basi{\'n}ski",
  title =        "Iterative Refinement for Linear Systems in
                 Variable-Precision Arithmetic",
  journal =      j-BIT,
  volume =       "21",
  pages =        "97--103",
  year =         "1981",
}

@Article{Kielbasinski:1987:NRE,
  author =       "Andrzej Kie{\l}basi{\'n}ski",
  title =        "A Note on Rounding-Error Analysis of {Cholesky}
                 Factorization",
  journal =      j-LAA,
  volume =       "88/89",
  pages =        "487--494",
  year =         "1987",
}

@Book{Kielbasinski:1988:NLA,
  author =       "Andrzej Kie{\l}basi{\'n}ski and Hubert Schwetlick",
  title =        "Numerische Lineare Algebra: {Eine} Computerorientierte
                 Einf{\"u}hrung",
  publisher =    "VEB Deutscher",
  address =      "Berlin",
  year =         "1988",
  pages =        "472",
  ISBN =         "3-87144-999-7",
}

@Book{Kielbasinski:1992:NAL,
  author =       "Andrzej Kie{\l}basi{\'n}ski and Hubert Schwetlick",
  title =        "Numeryczna Algebra Liniowa: {Wprowadzenie} do
                 Oblicze{\'n} Zautomatyzowanych",
  publisher =    "Wydawnictwa Naukowo-Techniczne",
  address =      "Warszawa",
  year =         "1992",
  pages =        "502",
  ISBN =         "83-204-1260-9",
}

@Article{Kittaneh:1995:SVC,
  author =       "Fuad Kittaneh",
  title =        "Singular Values of Companion Matrices and Bounds on
                 Zeros of Polynomials",
  journal =      j-SIMAX,
  volume =       "16",
  number =       "1",
  pages =        "333--340",
  year =         "1995",
}

@Book{Klatte:1993:CXC,
  author =       "R. Klatte and U. W. Kulisch and C. Lawo and M. Rauch
                 and A. Wiethoff",
  title =        "{C-XSC}: {A} {C++} Class Library for Extended
                 Scientific Computing",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  year =         "1993",
  ISBN =         "0-387-56328-8",
}

@Book{Klatte:1992:PXL,
  author =       "R. Klatte and U. W. Kulisch and M. Neaga and D. Ratz
                 and Ch. Ullrich",
  title =        "{PASCAL-XSC}---{Language} Reference with Examples",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  year =         "1992",
}

@Article{Kenney:1992:MSA,
  author =       "Charles S. Kenney and Alan J. Laub and Philip M.
                 Papadopoulos",
  title =        "Matrix-Sign Algorithms for {Riccati} Equations",
  journal =      "IMA J. Math. Control Inform.",
  volume =       "9",
  pages =        "331--344",
  year =         "1992",
}

@Article{Kenney:1998:SCEa,
  author =       "Charles Kenney and Alan J. Laub and M. S. Reese",
  title =        "Statistical Condition Estimation for Linear Systems",
  journal =      j-SISC,
  volume =       "19",
  number =       "2",
  pages =        "566--583",
  year =         "1998",
}

@Article{Kenney:1998:SCEb,
  author =       "Charles Kenney and Alan J. Laub and M. S. Reese",
  title =        "Statistical Condition Estimation for Linear Least
                 Squares",
  journal =      j-SIMAX,
  volume =       "19",
  number =       "4",
  pages =        "906--923",
  year =         "1998",
}

@Book{Kahaner:1989:NMS,
  author =       "David K. Kahaner and Cleve B. Moler and Stephen G.
                 Nash",
  title =        "Numerical Methods and Software",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  year =         "1989",
  ISBN =         "0-13-627258-4",
  pages =        "xii+495",
}

@PhdThesis{Knight:1993:EAS,
  author =       "Philip A. Knight",
  title =        "Error Analysis of Stationary Iteration and Associated
                 Problems",
  school =       inst-U-Manchester,
  address =      inst-U-Manchester:adr,
  pages =        "135",
  month =        sep,
  year =         "1993",
}

@Article{Knight:1995:FRM,
  author =       "Philip A. Knight",
  title =        "Fast Rectangular Matrix Multiplication and {$QR$}
                 Decomposition",
  journal =      j-LAA,
  year =         "1995",
  volume =       "221",
  pages =        "69--81",
}

@Article{Knuth:1962:EPC,
  author =       "Donald E. Knuth",
  title =        "Evaluation of Polynomials by Computer",
  journal =      j-CACM,
  volume =       "5",
  number =       "12",
  pages =        "595--599",
  year =         "1962",
}

@Article{Knuth:1992:TNN,
  author =       "Donald E. Knuth",
  title =        "Two Notes on Notation",
  journal =      j-AMM,
  volume =       "99",
  number =       "5",
  pages =        "403--422",
  year =         "1992",
}

@Book{Knuth:1999:DT,
  author =       "Donald E. Knuth",
  title =        "Digital Typography",
  publisher =    "Center for the Study of Language and Information",
  address =      "Stanford University, Stanford, CA, USA",
  series =       "CSLI Lecture Notes Number 78",
  year =         "1999",
  pages =        "xv+685",
  ISBN =         "0-575-86010-4",
}

@Book{Knuth:1997:ACP,
  author =       "Donald E. Knuth",
  title =        "The Art of Computer Programming, Volume 1, Fundamental
                 Algorithms",
  edition =      "Third",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  year =         "1997",
  pages =        "xix+650",
  ISBN =         "0-201-89683-4",
}

@Book{Knuth:1998:ACP,
  author =       "Donald E. Knuth",
  title =        "The Art of Computer Programming, Volume 2,
                 Seminumerical Algorithms",
  edition =      "Third",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  year =         "1998",
  pages =        "xiii+762",
  ISBN =         "0-201-89684-2",
}

@Book{Korner:1988:FA,
  author =       "T. W. K{\"o}rner",
  title =        "Fourier Analysis",
  publisher =    pub-CUP,
  address =      pub-CUP:adr,
  year =         "1988",
  pages =        "xii+591",
  ISBN =         "0-521-38991-7",
}

@Article{Kosowski:2000:CUT,
  author =       "Przemys{\l}aw Kosowski and Alicja Smoktunowicz",
  title =        "On Constructing Unit Triangular Matrices with
                 Prescribed Singular Values",
  journal =      j-COMPUTING,
  volume =       "64",
  pages =        "279--285",
  year =         "2000",
}

@Article{Kostlan:1992:SGM,
  author =       "Eric Kostlan",
  title =        "On the Spectra of {Gaussian} Matrices",
  journal =      j-LAA,
  volume =       "162--164",
  pages =        "385--388",
  year =         "1992",
}

@Article{Kovarik:1976:CAS,
  author =       "Z. V. Kovarik",
  title =        "Compatibility of Approximate Solutions of Inaccurate
                 Linear Equations",
  journal =      j-LAA,
  volume =       "15",
  pages =        "217--225",
  year =         "1976",
}

@InProceedings{Kreczmar:1976:MRS,
  author =       "Antoni Kreczmar",
  title =        "On Memory Requirements of {Strassen's} Algorithms",
  series =       "Lecture Notes in Computer Science",
  volume =       "45",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  pages =        "404--407",
  year =         "1976",
}

@InProceedings{Kubota:1991:PFP,
  author =       "Koichi Kubota",
  title =        "{PADRE2}, a {Fortran} Precompiler Yielding Error
                 Estimates and Second Derivatives",
  editor =       "Andreas Griewank and George F. Corliss",
  booktitle =    "Automatic Differentiation of Algorithms: {Theory},
                 Implementation, and Application",
  publisher =    pub-SIAM # ", " # pub-SIAM:adr,
  pages =        "251--262",
  year =         "1991",
}

@Article{Kuki:1973:SSA,
  author =       "H. Kuki and W. J. Cody",
  title =        "A Statistical Study of the Accuracy of Floating Point
                 Number Systems",
  journal =      j-CACM,
  volume =       "16",
  number =       "4",
  pages =        "223--230",
  year =         "1973",
}

@Book{Kulisch:1981:CAT,
  author =       "Ulrich W. Kulisch and Willard L. Miranker",
  title =        "Computer Arithmetic in Theory and in Practice",
  publisher =    pub-AP,
  address =      pub-AP:adr-NY,
  year =         "1981",
  pages =        "xiii+249",
  ISBN =         "0-12-428650-X",
}

@Article{Kulisch:1986:ADC,
  author =       "Ulrich W. Kulisch and Willard L. Miranker",
  title =        "The Arithmetic of the Digital Computer: {A} New
                 Approach",
  journal =      j-SIREV,
  volume =       "28",
  number =       "1",
  pages =        "1--40",
  year =         "1986",
}

@Book{Kuperman:1971:ALA,
  author =       "I. B. Kuperman",
  title =        "Approximate Linear Algebraic Equations",
  publisher =    "Van Nostrand Reinhold",
  address =      "London",
  year =         "1971",
  pages =        "xi+225",
}

@Article{Kuczynski:1992:ELE,
  author =       "J. Kuczy{\'n}ski and H. Wo{\'z}niakowski",
  title =        "Estimating the Largest Eigenvalue by the Power and
                 {Lanczos} Algorithms with a Random Start",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "4",
  pages =        "1094--1122",
  year =         "1992",
}

@Article{Laderman:1976:NAM,
  author =       "J. D. Laderman",
  title =        "A Noncommutative Algorithm for Multiplying {$3 \times
                 3$} Matrices Using 23 Multiplications",
  journal =      j-BAMS,
  volume =       "82",
  number =       "1",
  pages =        "126--128",
  year =         "1976",
}

@Book{Lawson:1995:SLS,
  author =       "Charles L. Lawson and Richard J. Hanson",
  title =        "Solving Least Squares Problems",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "1995",
  ISBN =         "0-89871-356-0",
  note =         "Revised republication of work first published in 1974
                 by Prentice-Hall",
  pages =        "xii+337",
}

@Article{Laszlo:1994:ALB,
  author =       "Lajos L{\'a}szl{\'o}",
  title =        "An Attainable Lower Bound for the Best Normal
                 Approximation",
  journal =      j-SIMAX,
  volume =       "15",
  number =       "3",
  pages =        "1035--1043",
  year =         "1994",
}

@Article{Lay-Yong:1989:MSL,
  author =       "Lam Lay-Yong and Shen Kangshen",
  title =        "Methods of Solving Linear Equations in Traditional
                 {China}",
  journal =      "Historia Mathematica",
  volume =       "16",
  number =       "2",
  pages =        "107--122",
  year =         "1989",
}

@Book{Lanczos:1956:AA,
  author =       "Cornelius Lanczos",
  title =        "Applied Analysis",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  year =         "1956",
  pages =        "xx+539",
  ISBN =         "0-486-65656-X",
  note =         "Reprinted by Dover, New York, 1988",
}

@Article{Lancaster:1966:EAN,
  author =       "Peter Lancaster",
  title =        "Error Analysis for the {Newton-Raphson} Method",
  journal =      j-NUM-MATH,
  volume =       "9",
  pages =        "55--68",
  year =         "1966",
}

@Article{Lancaster:1970:ESL,
  author =       "Peter Lancaster",
  title =        "Explicit Solutions of Linear Matrix Equations",
  journal =      j-SIREV,
  volume =       "12",
  number =       "4",
  pages =        "544--566",
  year =         "1970",
}

@Article{Langlois:2001:ALC,
  author =       "Philippe Langlois",
  title =        "Automatic Linear Correction of Rounding Errors",
  journal =      j-BIT,
  volume =       "41",
  number =       "3",
  pages =        "515--539",
  year =         "2001",
}

@Article{Larson:1978:ECE,
  author =       "John L. Larson and Ahmed H. Sameh",
  title =        "Efficient Calculation of the Effects of Roundoff
                 Errors",
  journal =      j-TOMS,
  volume =       "4",
  number =       "3",
  pages =        "228--236",
  year =         "1978",
  note =         "Errata 5(3):372, 1979",
}

@Article{Larson:1980:ARE,
  author =       "John L. Larson and Ahmed H. Sameh",
  title =        "Algorithms for Roundoff Error Analysis---{A} Relative
                 Error Approach",
  journal =      j-COMPUTING,
  volume =       "24",
  pages =        "275--297",
  year =         "1980",
}

@Article{Laub:1979:SMS,
  author =       "Alan J. Laub",
  title =        "A {Schur} Method for Solving Algebraic {Riccati}
                 Equations",
  journal =      j-IEEE-AC,
  volume =       "AC-24",
  number =       "6",
  pages =        "913--921",
  year =         "1979",
}

@Article{Lauchli:1961:JEA,
  author =       "Peter L{\"a}uchli",
  title =        "{Jordan-Elimination} und {Ausgleichung} nach kleinsten
                 {Quadraten}",
  journal =      j-NUM-MATH,
  volume =       "3",
  pages =        "226--240",
  year =         "1961",
}

@Article{Porte:1974:ESE,
  author =       "M. La Porte and J. Vignes",
  title =        "Etude Statistique des Erreurs Dans l'Arithm\'etique
                 des Ordinateurs; Application au Contr{\^o}le des
                 {R}\'esultats d'Algorithmes Num\'eriques",
  journal =      j-NUM-MATH,
  volume =       "23",
  pages =        "63--72",
  year =         "1974",
}

@Book{Lavington:1980:EBC,
  author =       "Simon Lavington",
  title =        "Early {British} Computers: {The} Story of Vintage
                 Computers and the People Who Built Them",
  publisher =    "Manchester University Press",
  year =         "1980",
  ISBN =         "0-7190-0803-4",
  pages =        "139",
}

@TechReport{Li:2000:DIT,
  author =       "X. S. Li and J. W. Demmel and D. H. Bailey and G.
                 Henry and Y. Hida and J. Iskandar and W. Kahan and A.
                 Kapur and M. C. Martin and T. Tung and D. J. Yoo",
  title =        "Design, Implementation and Testing of {Extended and
                 Mixed Precision BLAS}",
  institution =  inst-CS-U-Tenn,
  address =      inst-CS-U-Tenn:adr,
  type =         "Technical Report",
  number =       "CS-00-451",
  month =        oct,
  year =         "2000",
  pages =        "61",
  note =         "LAPACK Working Note 149",
}

@Article{Lehmer:1943:TMP,
  author =       "D. H. Lehmer",
  title =        "Tables to Many Places of Decimals",
  journal =      "Mathematical Tables and Other Aids to Computation",
  volume =       "1",
  number =       "1",
  pages =        "30--31",
  year =         "1943",
}

@Article{Lehoucq:1996:CEU,
  author =       "R. B. Lehoucq",
  title =        "The Computation of Elementary Unitary Matrices",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "393--400",
  year =         "1996",
}

@Article{Lemeire:1975:BCN,
  author =       "Frans Lemeire",
  title =        "Bounds for Condition Numbers of Triangular and
                 Trapezoid Matrices",
  journal =      j-BIT,
  volume =       "15",
  pages =        "58--64",
  year =         "1975",
}

@InProceedings{Lefevre:2001:WCC,
  author =       "Vincent Lef{\`e}vre and Jean-Michel Muller",
  title =        "Worst Cases for Correct Rounding of the Elementary
                 Functions in Double Precision",
  booktitle =    "Proc. 15th IEEE Symposium on Computer Arithmetic",
  publisher =    "IEEE Computer Society Press, Los Alamitos, CA, USA",
  year =         "2001",
}

@Article{Leuprecht:1982:PAR,
  author =       "H. Leuprecht and W. Oberaigner",
  title =        "Parallel Algorithms for the Rounding Exact Summation
                 of Floating Point Numbers",
  journal =      j-COMPUTING,
  volume =       "28",
  pages =        "89--104",
  year =         "1982",
}

@Article{Lawson:1979:BLA,
  author =       "C. L. Lawson and R. J. Hanson and D. R. Kincaid and F.
                 T. Krogh",
  title =        "Basic Linear Algebra Subprograms for {Fortran} Usage",
  journal =      j-TOMS,
  volume =       "5",
  number =       "3",
  pages =        "308--323",
  year =         "1979",
}

@Book{LIA94,
  key =          "IEC",
  title =        "{ISO\slash IEC \upshape 10967-1 (1994-12)}:
                 {Information} Technology---Language Independent
                 Arithmetic---Part {$1$}: {Integer} and Floating Point
                 Arithmetic",
  publisher =    pub-IEC,
  address =      pub-IEC:adr,
  pages =        "92",
  year =         "1994",
}

@Article{Lickteig:1987:CCD,
  author =       "Thomas Lickteig",
  title =        "The Computational Complexity of Division in Quadratic
                 Extension Fields",
  journal =      j-SICOMP,
  volume =       "16",
  number =       "2",
  pages =        "278--311",
  year =         "1987",
}

@InProceedings{Li:1998:MSG,
  author =       "Xiaoye S. Li and James W. Demmel",
  title =        "Making Sparse {Gaussian} Elimination Scalable by
                 Static Pivoting",
  booktitle =    "Proceedings of SC98: High Performance Networking and
                 Computing Conference, Orlando, Florida",
  year =         "1998",
  note =         "CD ROM",
}

@Article{Linnainmaa:1974:ASK,
  author =       "Seppo Linnainmaa",
  title =        "Analysis of Some Known Methods of Improving the
                 Accuracy of Floating-Point Sums",
  journal =      j-BIT,
  volume =       "14",
  pages =        "167--202",
  year =         "1974",
}

@Article{Linnainmaa:1975:TAS,
  author =       "Seppo Linnainmaa",
  title =        "Towards Accurate Statistical Estimation of Rounding
                 Errors in Floating-Point Computations",
  journal =      j-BIT,
  volume =       "15",
  pages =        "165--173",
  year =         "1975",
}

@Article{Linnainmaa:1976:TEA,
  author =       "Seppo Linnainmaa",
  title =        "Taylor Expansion of the Accumulated Rounding Error",
  journal =      j-BIT,
  volume =       "16",
  pages =        "146--160",
  year =         "1976",
}

@Article{Linnainmaa:1981:SDP,
  author =       "Seppo Linnainmaa",
  title =        "Software for Doubled-Precision Floating-Point
                 Computations",
  journal =      j-TOMS,
  volume =       "7",
  number =       "3",
  pages =        "272--283",
  year =         "1981",
}

@Article{Linz:1970:AFP,
  author =       "Peter Linz",
  title =        "Accurate Floating-Point Summation",
  journal =      j-CACM,
  volume =       "13",
  number =       "6",
  pages =        "361--362",
  year =         "1970",
}

@Article{Linzer:1992:STB,
  author =       "Elliot Linzer",
  title =        "On the Stability of Transform-Based Circular
                 Deconvolution",
  journal =      j-SINUM,
  volume =       "29",
  number =       "5",
  pages =        "1482--1492",
  year =         "1992",
}

@Article{Liu:1987:PPS,
  author =       "Joseph W. H. Liu",
  title =        "A Partial Pivoting Strategy for Sparse Symmetric
                 Matrix Decomposition",
  journal =      j-TOMS,
  volume =       "13",
  number =       "2",
  pages =        "173--182",
  year =         "1987",
}

@Article{Li:1992:HDA,
  author =       "T. Y. Li and Zhonggang Zeng",
  title =        "Homotopy-Determinant Algorithm for Solving
                 Nonsymmetric Eigenvalue Problems",
  journal =      j-MATH-COMP,
  volume =       "59",
  number =       "200",
  pages =        "483--502",
  year =         "1992",
}

@Article{Lefevre:1998:TCR,
  author =       "Vincent Lef{\`e}vre and Jean-Michel Muller and Arnaud
                 Tisserand",
  title =        "Toward Correctly Rounded Transcendentals",
  journal =      j-IEEE-C,
  volume =       "47",
  number =       "11",
  pages =        "1235--1243",
  year =         "1998",
}

@Article{Loizou:1969:NJC,
  author =       "Georghios Loizou",
  title =        "Nonnormality and {Jordan} Condition Numbers of
                 Matrices",
  journal =      j-ACM,
  volume =       "16",
  number =       "4",
  pages =        "580--584",
  year =         "1969",
}

@Article{Longley:1967:ALS,
  author =       "J. W. Longley",
  title =        "An Appraisal of Least Squares Programs for the
                 Electronic Computer from the Point of View of the
                 User",
  journal =      j-ASA,
  volume =       "62",
  pages =        "819--841",
  year =         "1967",
}

@Article{Laderman:1992:PAA,
  author =       "Julian Laderman and Victor Pan and Xuan-He Sha",
  title =        "On Practical Algorithms for Accelerated Matrix
                 Multiplication",
  journal =      j-LAA,
  volume =       "162--164",
  pages =        "557--588",
  year =         "1992",
}

@Article{Larson:1983:ASR,
  author =       "John L. Larson and Mary E. Pasternak and John A.
                 Wisniewski",
  title =        "Algorithm 594: {Software} for Relative Error
                 Analysis",
  journal =      j-TOMS,
  volume =       "9",
  number =       "1",
  pages =        "125--130",
  year =         "1983",
}

@Article{Lagarias:1998:CPN,
  author =       "Jeffrey C. Lagarias and James A. Reeds and Margaret H.
                 Wright and Paul E. Wright",
  title =        "Convergence Properties of the {Nelder--Mead} Simplex
                 Method in Low Dimensions",
  journal =      j-SIOPT,
  volume =       "9",
  number =       "1",
  pages =        "112--147",
  year =         "1998",
}

@Article{Lewis:2000:DSM,
  author =       "Robert Michael Lewis and Virginia J. Torczon and
                 Michael W. Trossett",
  title =        "Direct Search Methods: {Then} and Now",
  journal =      j-JCAM,
  volume =       "124",
  pages =        "191--207",
  year =         "2000",
}

@Article{Lu:1994:FSC,
  author =       "Hao Lu",
  title =        "Fast Solution of Confluent {Vandermonde} Linear
                 Systems",
  journal =      j-SIMAX,
  volume =       "15",
  number =       "4",
  pages =        "1277--1289",
  year =         "1994",
}

@Article{Lu:1995:FAC,
  author =       "Hao Lu",
  title =        "Fast Algorithms for Confluent {Vandermonde} Linear
                 Systems and Generalized {Trummer's} Problem",
  journal =      j-SIMAX,
  volume =       "16",
  number =       "2",
  pages =        "655--674",
  year =         "1995",
}

@Article{Lu:1996:SVL,
  author =       "Hao Lu",
  title =        "Solution of {Vandermonde}-Like Systems and Confluent
                 {Vandermonde}-Like Systems",
  journal =      j-SIMAX,
  volume =       "17",
  number =       "1",
  pages =        "127--138",
  year =         "1996",
}

@Book{Barker:2001:LUG,
  author =       "V. A. Barker and L. S. Blackford and J. J. Dongarra
                 and J. J. Du Croz and S. J. Hammarling and M. Marinova
                 and J. Wa{\'s}niewski and P. Yalamov",
  title =        "{LAPACK95} Users' Guide",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "2001",
  pages =        "xviii+258",
  ISBN =         "0-89871-504-0",
}

@Book{Anderson:1999:LUG,
  author =       "E. Anderson and Z. Bai and C. H. Bischof and S.
                 Blackford and J. W. Demmel and J. J. Dongarra and J. J.
                 Du Croz and A. Greenbaum and S. J. Hammarling and A.
                 McKenney and D. C. Sorensen",
  title =        "{LAPACK} Users' Guide",
  edition =      "Third",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "1999",
  pages =        "xxvi+407",
  ISBN =         "0-89871-447-8",
}

@Article{Lyness:1976:CNA,
  author =       "J. N. Lyness and J. J. Kaganove",
  title =        "Comments on the Nature of Automatic Quadrature
                 Routines",
  journal =      j-TOMS,
  volume =       "2",
  number =       "1",
  pages =        "65--81",
  year =         "1976",
}

@Article{Lyness:1966:VMS,
  author =       "J. N. Lyness and C. B. Moler",
  title =        "{Van der Monde} Systems and Numerical
                 Differentiation",
  journal =      j-NUM-MATH,
  volume =       "8",
  pages =        "458--464",
  year =         "1966",
}

@Article{Lynn:1964:REM,
  author =       "M. Stuart Lynn",
  title =        "On the Round-Off Error in the Method of Successive
                 Over-Relaxation",
  journal =      j-MATH-COMP,
  volume =       "18",
  number =       "85",
  pages =        "36--49",
  year =         "1964",
}

@Article{Macleod:1989:SSG,
  author =       "Allan J. Macleod",
  title =        "Some Statistics on {Gaussian} Elimination with Partial
                 Pivoting",
  journal =      j-SIGNUM,
  volume =       "24",
  number =       "2/3",
  pages =        "10--14",
  year =         "1989",
}

@Book{Maindonald:1984:SC,
  author =       "J. H. Maindonald",
  title =        "Statistical Computation",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  year =         "1984",
  ISBN =         "0-471-86452-8",
  pages =        "xviii+370",
}

@Article{Matsui:1981:OUF,
  author =       "Shouichi Matsui and Masao Iri",
  title =        "An Overflow/Underflow-Free Floating-Point
                 Representation of Numbers",
  journal =      "J. Information Processing",
  volume =       "4",
  number =       "3",
  pages =        "123--133",
  year =         "1981",
}

@Article{Makhoul:1991:TDP,
  author =       "John Makhoul",
  title =        "{Toeplitz} Determinants and Positive
                 Semidefiniteness",
  journal =      j-IEEE-SP,
  volume =       "39",
  number =       "3",
  pages =        "743--746",
  year =         "1991",
}

@Article{Matula:1985:FPR,
  author =       "David W. Matula and Peter Kornerup",
  title =        "Finite Precision Rational Arithmetic: {Slash} Number
                 Systems",
  journal =      j-IEEE-C,
  volume =       "C-34",
  number =       "1",
  pages =        "3--18",
  year =         "1985",
}

@Article{Malcolm:1971:AFP,
  author =       "Michael A. Malcolm",
  title =        "On Accurate Floating-Point Summation",
  journal =      j-CACM,
  volume =       "14",
  number =       "11",
  pages =        "731--736",
  year =         "1971",
}

@Article{Malcolm:1972:ARP,
  author =       "Michael A. Malcolm",
  title =        "Algorithms to Reveal Properties of Floating-Point
                 Arithmetic",
  journal =      j-CACM,
  volume =       "15",
  number =       "11",
  pages =        "949--951",
  year =         "1972",
}

@Article{Malyshev:2000:NSG,
  author =       "Alexander N. Malyshev",
  title =        "A Note on the Stability of {Gauss-Jordan} Elimination
                 for Diagonally Dominant Matrices",
  journal =      "Computing",
  volume =       "65",
  number =       "3",
  pages =        "281--284",
  year =         "2000",
}

@Article{Malyshev:2001:OBP,
  author =       "Alexander N. Malyshev",
  title =        "Optimal Backward Perturbation Bounds for the {LSS}
                 Problem",
  journal =      j-BIT,
  volume =       "41",
  number =       "2",
  pages =        "430--432",
  year =         "2001",
}

@Article{Magnus:1979:CMS,
  author =       "Jan R. Magnus and Heinz Neudecker",
  title =        "The Commutation Matrix: {Some} Properties and
                 Applications",
  journal =      j-ANN-STAT,
  volume =       "7",
  number =       "2",
  pages =        "381--394",
  year =         "1979",
}

@Book{Magnus:1999:MDC,
  author =       "Jan R. Magnus and Heinz Neudecker",
  title =        "Matrix Differential Calculus with Applications in
                 Statistics and Econometrics",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr-C,
  edition =      "Revised",
  year =         "1999",
  ISBN =         "0-471-98633-X",
  pages =        "xviii+395",
}

@Article{Manteuffel:1981:IAA,
  author =       "Thomas A. Manteuffel",
  title =        "An Interval Analysis Approach to Rank Determination in
                 Linear Least Squares Problems",
  journal =      j-SISSC,
  volume =       "2",
  number =       "3",
  pages =        "335--348",
  year =         "1981",
}

@Article{Malcolm:1974:FMS,
  author =       "Michael A. Malcolm and John Palmer",
  title =        "A Fast Method for Solving a Class of Tridiagonal
                 Linear Systems",
  journal =      j-CACM,
  volume =       "17",
  number =       "1",
  pages =        "14--17",
  year =         "1974",
}

@Book{maple,
  key =          "Maple",
  title =        "Maple",
  publisher =    "Waterloo Maple Inc.",
  address =      "Waterloo, Ontario, Canada",
  note =         "\path|http://www.maplesoft.com|",
}

@Book{Char:1991:MVL,
  author =       "Bruce W. Char and Keith O. Geddes and Gaston H. Gonnet
                 and Benton L. Leong and Michael B. Monagan and Stephen
                 M. Watt",
  title =        "Maple {V} Library Reference Manual",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  year =         "1991",
  pages =        "xxv+698",
  ISBN =         "3-540-97592-6",
}

@Article{Markoff:1994:CFC,
  author =       "John Markoff",
  title =        "Circuit Flaw Causes {Pentium} Chip to Miscalculate,
                 {Intel} Admits",
  journal =      "New York Times",
  year =         "1994",
  note =         "24 November",
}

@Article{Malyshev:2002:COB,
  author =       "Alexander N. Malyshev and Miloud Sadkane",
  title =        "Computation of Optimal Backward Perturbation Bounds
                 for Large Sparse Linear Least Squares Problems",
  journal =      j-BIT,
  volume =       "41",
  number =       "4",
  pages =        "739--747",
  year =         "2002",
}

@Article{Mathias:1992:MPD,
  author =       "Roy Mathias",
  title =        "Matrices with Positive Definite {Hermitian} Part:
                 {Inequalities} and Linear Systems",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "2",
  pages =        "640--654",
  year =         "1992",
}

@Article{Mathias:1995:AEC,
  author =       "Roy Mathias",
  title =        "Accurate Eigensystem Computations by {Jacobi}
                 Methods",
  journal =      j-SIMAX,
  volume =       "16",
  number =       "3",
  pages =        "977--1003",
  year =         "1995",
}

@Article{Mathias:1995:IPP,
  author =       "Roy Mathias",
  title =        "The Instability of Parallel Prefix Matrix
                 Multiplication",
  journal =      j-SISC,
  volume =       "16",
  number =       "4",
  pages =        "956--973",
  year =         "1995",
}

@Article{Mathias:1996:AAO,
  author =       "Roy Mathias",
  title =        "Analysis of Algorithms for Orthogonalizing Products of
                 Unitary Matrices",
  journal =      j-NLAA,
  volume =       "3",
  number =       "2",
  pages =        "125--145",
  year =         "1996",
}

@Book{mathematica,
  key =          "Mathematica",
  title =        "Mathematica",
  publisher =    "Wolfram Research, Inc.",
  address =      "Champaign, IL, USA",
  note =         "\path|http://www.wolfram.com|",
}

@Book{matlab,
  key =          "MathWorks, Inc.",
  title =        "{MATLAB}",
  publisher =    "The MathWorks, Inc.",
  address =      "Natick, MA, USA",
  note =         "\path|http://www.mathworks.com|",
}

@Book{matlab:SMT,
  key =          "MathWorks, Inc.",
  title =        "Symbolic Math Toolbox Version {$2$}: {User's} Guide",
  publisher =    "The MathWorks, Inc.",
  address =      "Natick, MA, USA",
  note =         "Online version",
}

@Article{Mattheij:1984:SLD,
  author =       "R. M. M. Mattheij",
  title =        "The Stability of {LU}-Decompositions of Block
                 Tridiagonal Matrices",
  journal =      "Bull. Austral. Math. Soc.",
  volume =       "29",
  pages =        "177--205",
  year =         "1984",
}

@Article{Mattheij:1984:SBD,
  author =       "R. M. M. Mattheij",
  title =        "Stability of Block {$LU$}-Decompositions of Matrices
                 Arising From {BVP}",
  journal =      j-SIAD,
  volume =       "5",
  number =       "3",
  pages =        "314--331",
  year =         "1984",
}

@Article{Matula:1968:C,
  author =       "David W. Matula",
  title =        "In-and-Out Conversions",
  journal =      j-CACM,
  volume =       "11",
  number =       "1",
  pages =        "47--50",
  year =         "1968",
}

@Article{Matula:1970:FFP,
  author =       "David W. Matula",
  title =        "A Formalization of Floating-Point Numeric Base
                 Conversion",
  journal =      j-IEEE-C,
  volume =       "C-19",
  number =       "8",
  pages =        "681--692",
  year =         "1970",
}

@Book{McCracken:1964:NMF,
  author =       "Daniel D. McCracken and William S. Dorn",
  title =        "Numerical Methods and {Fortran} Programming: {With}
                 Applications in Science and Engineering",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  year =         "1964",
  pages =        "xii+457",
}

@Article{McKeeman:1962:ACE,
  author =       "William Marshall McKeeman",
  title =        "Algorithm 135: {Crout} with Equilibration and
                 Iteration",
  journal =      j-CACM,
  volume =       "5",
  pages =        "553--555",
  year =         "1962",
}

@Article{McKinnon:1998:CNM,
  author =       "K. I. M. McKinnon",
  title =        "Convergence of the {Nelder--Mead} Simplex Method to a
                 Nonstationary Point",
  journal =      j-SIOPT,
  volume =       "9",
  number =       "1",
  pages =        "148--158",
  year =         "1998",
}

@Book{McCullagh:1989:GLM,
  author =       "P. McCullagh and J. A. Nelder",
  title =        "Generalized Linear Models",
  publisher =    "Chapman and Hall",
  address =      "London",
  edition =      "Second",
  year =         "1989",
  pages =        "xix+511",
  ISBN =         "0-412-31760-5",
}

@Article{McCarthy:1974:OCM,
  author =       "Charles McCarthy and Gilbert Strang",
  title =        "Optimal Conditioning of Matrices",
  journal =      j-SINUM,
  volume =       "10",
  number =       "2",
  pages =        "370--388",
  year =         "1974",
}

@Article{McCullough:1999:NRE,
  author =       "B. D. McCullough and H. D. Vinod",
  title =        "The Numerical Reliability of Econometric Software",
  journal =      "Journal of Economic Literature",
  volume =       "37",
  pages =        "633--665",
  year =         "1999",
}

@Article{Meyer:1957:MIL,
  author =       "H. I. Meyer and B. J. Hollingsworth",
  title =        "A Method of Inverting Large Matrices of Special Form",
  journal =      j-MTAC,
  volume =       "11",
  pages =        "94--97",
  year =         "1957",
}

@InProceedings{Meinguet:1969:ES,
  author =       "Jean Meinguet",
  title =        "On the Estimation of Significance",
  editor =       "Elden Hansen",
  booktitle =    "Topics in Interval Analysis",
  publisher =    pub-OUP,
  pages =        "47--64",
  year =         "1969",
}

@Article{Meinguet:1983:REA,
  author =       "Jean Meinguet",
  title =        "Refined Error Analyses of {Cholesky} Factorization",
  journal =      j-SINUM,
  volume =       "20",
  number =       "6",
  pages =        "1243--1250",
  year =         "1983",
}

@Article{Mendelsohn:1956:SEP,
  author =       "N. S. Mendelsohn",
  title =        "Some Elementary Properties of Ill Conditioned Matrices
                 and Linear Equations",
  journal =      j-AMM,
  volume =       "63",
  number =       "5",
  pages =        "285--295",
  year =         "1956",
}

@Article{Meyer:1977:CPM,
  author =       "Carl D. {Meyer, Jr.} and R. J. Plemmons",
  title =        "Convergent Powers of a Matrix With Applications to
                 Iterative Methods for Singular Linear Systems",
  journal =      j-SINUM,
  volume =       "14",
  number =       "4",
  pages =        "699--705",
  year =         "1977",
}

@Book{Metcalf:1999:FE,
  author =       "Michael Metcalf and John K. Reid",
  title =        "Fortran 90/95 Explained",
  edition =      "Second",
  publisher =    pub-OUP,
  year =         "1999",
  pages =        "358",
  ISBN =         "0-19-850558-2",
}

@InProceedings{Metropolis:1977:MSA,
  author =       "N. Metropolis",
  title =        "Methods of Significance Arithmetic",
  editor =       "David A. H. Jacobs",
  booktitle =    "The State of the Art in Numerical Analysis",
  publisher =    pub-AP # ", " # pub-AP:adr-L,
  pages =        "179--192",
  year =         "1977",
}

@Article{Meurant:1992:RIS,
  author =       "G{\'e}rard Meurant",
  title =        "A Review on the Inverse of Symmetric Tridiagonal and
                 Block Tridiagonal Matrices",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "3",
  pages =        "707--728",
  year =         "1992",
}

@Article{Milenkovic:1988:VIG,
  author =       "Victor J. Milenkovic",
  title =        "Verifiable Implementations of Geometric Algorithms
                 Using Finite Precision Arithmetic",
  journal =      "Artificial Intelligence",
  volume =       "37",
  pages =        "377--401",
  year =         "1988",
}

@Article{Miller:1975:CCN,
  author =       "Webb Miller",
  title =        "Computational Complexity and Numerical Stability",
  journal =      j-SICOMP,
  volume =       "4",
  number =       "2",
  pages =        "97--107",
  year =         "1975",
}

@Article{Miller:1975:SRA,
  author =       "Webb Miller",
  title =        "Software for Roundoff Analysis",
  journal =      j-TOMS,
  volume =       "1",
  number =       "2",
  pages =        "108--128",
  year =         "1975",
}

@Article{Miller:1976:GTR,
  author =       "Webb Miller",
  title =        "Graph Transformations for Roundoff Analysis",
  journal =      j-SICOMP,
  volume =       "5",
  number =       "2",
  pages =        "204--216",
  year =         "1976",
}

@Book{Miller:1984:ENS,
  author =       "Webb Miller",
  title =        "The Engineering of Numerical Software",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  year =         "1984",
  pages =        "viii+167",
  ISBN =         "0-13-279043-2",
}

@Article{Miller:1988:ISM,
  author =       "D. F. Miller",
  title =        "The Iterative Solution of the Matrix Equation
                 {$XA+BX+C=0$}",
  journal =      j-LAA,
  volume =       "105",
  pages =        "131--137",
  year =         "1988",
}

@Book{Mirsky:1961:ILA,
  author =       "L. Mirsky",
  title =        "An Introduction to Linear Algebra",
  publisher =    pub-OUP,
  year =         "1961",
  pages =        "viii+440",
  note =         "Reprinted by Dover, New York, 1990",
  ISBN =         "0-486-66434-1",
}

@Article{Miller:19xx:SRA,
  author =       "Webb Miller and David Spooner",
  title =        "Software for Roundoff Analysis, {II}",
  journal =      j-TOMS,
  volume =       "4",
  number =       "4",
  pages =        "369--387",
  year =         "{\noopsort{a}}1978",
}

@Article{Miller:19xx:ASR,
  author =       "Webb Miller and David Spooner",
  title =        "Algorithm 532: {Software} for Roundoff Analysis",
  journal =      j-TOMS,
  volume =       "4",
  number =       "4",
  pages =        "388--390",
  year =         "{\noopsort{b}}1978",
}

@Article{Mitchell:1948:IMO,
  author =       "Herbert F. {Mitchell, Jr.}",
  title =        "Inversion of a Matrix of Order 38",
  journal =      j-MTAC,
  volume =       "3",
  pages =        "161--166",
  year =         "1948",
}

@Book{Miller:1980:SRA,
  author =       "Webb Miller and Celia Wrathall",
  title =        "Software for Roundoff Analysis of Matrix Algorithms",
  publisher =    pub-AP,
  address =      pub-AP:adr-NY,
  year =         "1980",
  pages =        "x+151",
  ISBN =         "0-12-497250-0",
}

@Article{Moore:1998:MCP,
  author =       "J. Strother Moore and Thomas W. Lynch and Matt
                 Kaufmann",
  title =        "A Mechanically Checked Proof of the
                 {$\mathrm{AMD}5_K86$} Floating-Point Division Program",
  journal =      j-IEEE-C,
  volume =       "47",
  number =       "9",
  pages =        "913--926",
  year =         "1998",
}

@Article{Moler:1967:IRF,
  author =       "Cleve B. Moler",
  title =        "Iterative Refinement in Floating Point",
  journal =      j-ACM,
  volume =       "14",
  number =       "2",
  pages =        "316--321",
  year =         "1967",
}

@Article{Moler:1972:MCF,
  author =       "Cleve B. Moler",
  title =        "Matrix Computations with {Fortran} and Paging",
  journal =      j-CACM,
  volume =       "15",
  number =       "4",
  pages =        "268--270",
  year =         "1972{\noopsort{a}}",
}

@Article{Moler:1972:ALE,
  author =       "Cleve B. Moler",
  title =        "Algorithm 423: {Linear} Equation Solver",
  journal =      j-CACM,
  volume =       "15",
  number =       "4",
  pages =        "274",
  year =         "1972{\noopsort{b}}",
}

@Article{Moler:1974:CRS,
  author =       "Cleve B. Moler",
  title =        "Cramer's Rule on 2-by-2 Systems",
  journal =      j-SIGNUM,
  volume =       "9",
  number =       "4",
  pages =        "13--14",
  year =         "1974",
}

@InCollection{Moler:1978:TRP,
  author =       "Cleve B. Moler",
  title =        "Three Research Problems in Numerical Linear Algebra",
  editor =       "G. H. Golub and J. Oliger",
  booktitle =    "Numerical Analysis",
  series =       "Proceedings of Symposia in Applied Mathematics",
  volume =       "22",
  publisher =    pub-AMS # ", " # pub-AMS:adr,
  pages =        "1--18",
  year =         "1978",
}

@Article{Moler:1990:TND,
  author =       "Cleve B. Moler",
  title =        "Technical Note: {Double-rounding} and Implications for
                 Numeric Computations",
  journal =      "The MathWorks Newsletter",
  volume =       "4",
  pages =        "6",
  year =         "1990",
}

@Article{Moler:1990:CCW,
  author =       "Cleve B. Moler",
  title =        "Cleve's Corner: {The} World's Simplest Impossible
                 Problem",
  journal =      "The MathWorks Newsletter",
  volume =       "4",
  number =       "2",
  pages =        "6--7",
  year =         "1990",
}

@Article{Moler:1995:TTN,
  author =       "Cleve B. Moler",
  title =        "A Tale of Two Numbers",
  journal =      "SIAM News",
  volume =       "28",
  pages =        "1,16",
  month =        jan,
  year =         "1995",
  note =         "Also in \emph{MATLAB News and Notes}, Winter 1995,
                 10--12",
}

@Article{Moller:1965:QDP,
  author =       "Ole M{\o}ller",
  title =        "Quasi Double-Precision in Floating Point Addition",
  journal =      j-BIT,
  volume =       "5",
  pages =        "37--50",
  year =         "1965",
  note =         "See also \cite{Moller:1965:NQD} for remarks on this
                 article",
}

@Article{Moller:1965:NQD,
  author =       "Ole M{\o}ller",
  title =        "Note on Quasi Double-Precision",
  journal =      j-BIT,
  volume =       "5",
  pages =        "251--255",
  year =         "1965",
}

@Article{Moler:1983:RSR,
  author =       "Cleve B. Moler and Donald Morrison",
  title =        "Replacing Square Roots by {Pythagorean} Sums",
  journal =      "IBM J. Res. Develop.",
  volume =       "27",
  number =       "6",
  pages =        "577--581",
  year =         "1983",
}

@Article{Moler:1983:SVA,
  author =       "Cleve B. Moler and Donald Morrison",
  title =        "Singular Value Analysis of Cryptograms",
  journal =      j-AMM,
  volume =       "90",
  pages =        "78--87",
  year =         "1983",
}

@Book{Moore:1966:IA,
  author =       "Ramon E. Moore",
  title =        "Interval Analysis",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  year =         "1966",
  pages =        "xi+145",
}

@Book{Moore:1979:MAI,
  author =       "Ramon E. Moore",
  title =        "Methods and Applications of Interval Analysis",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "1979",
  ISBN =         "0-89871-161-4",
  pages =        "xi+190",
}

@Article{Moler:1978:NDW,
  author =       "Cleve B. Moler and Charles F. Van Loan",
  title =        "Nineteen Dubious Ways to Compute the Exponential of a
                 Matrix",
  journal =      j-SIREV,
  volume =       "20",
  number =       "4",
  pages =        "801--836",
  year =         "1978",
}

@Article{Martin:1966:IRS,
  author =       "R. S. Martin and G. Peters and J. H. Wilkinson",
  title =        "Iterative Refinement of the Solution of a Positive
                 Definite System of Equations",
  journal =      j-NUM-MATH,
  volume =       "8",
  pages =        "203--216",
  year =         "1966",
  note =         "Also in \cite[pp.~31--44]{Wilkinson:1971:LA},
                 Contribution I/2",
}

@Article{Mead:2001:SPS,
  author =       "J. L. Mead and R. E. Renaut and B. D. Welfert",
  title =        "Stability of a Pivoting Strategy for Parallel
                 {Gaussian} Elimination",
  journal =      j-BIT,
  volume =       "41",
  number =       "3",
  pages =        "633--639",
  year =         "2001",
}

@Book{Muirhead:1982:AMS,
  author =       "Robb J. Muirhead",
  title =        "Aspects of Multivariate Statistical Theory",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  year =         "1982",
  pages =        "xix+673",
  ISBN =         "0-471-09442-0",
}

@Article{Muller:1983:REA,
  author =       "K. H. M{\"u}ller",
  title =        "Rounding Error Analysis of {Horner's} Scheme",
  journal =      j-COMPUTING,
  volume =       "30",
  pages =        "285--303",
  year =         "1983",
}

@Book{Muller:1989:AO,
  author =       "Jean-Michel Muller",
  title =        "Arithm{\'e}tique des Ordinateurs",
  publisher =    "Masson",
  address =      "Paris",
  year =         "1989",
  pages =        "214",
  ISBN =         "2-225-81689-1",
  note =         "In French. Cited in \cite{Francois:1991:SPM}",
}

@Book{Muller:1997:EFA,
  author =       "Jean-Michel Muller",
  title =        "Elementary Functions: {Algorithms} and
                 Implementation",
  publisher =    pub-BH,
  address =      pub-BH:adr,
  year =         "1997",
  pages =        "xv+204",
  ISBN =         "0-8176-3990-X",
}

@Article{Merikoski:1997:BUB,
  author =       "Jorma Kaarlo Merikoski and Uoti Arpala and Ari
                 Virtanen and Tin-Yau Tam and Frank Uhlig",
  title =        "A Best Upper Bound for the 2-Norm Condition Number of
                 a Matrix",
  journal =      j-LAA,
  volume =       "254",
  pages =        "355--365",
  year =         "1997",
}

@InProceedings{Nashed:1976:ABG,
  author =       "M. Zuhair Nashed and L. B. Rall",
  title =        "Annotated Bibliography on Generalized Inverses and
                 Applications",
  editor =       "M. Zuhair Nashed",
  booktitle =    "Generalized Inverses and Applications",
  publisher =    pub-AP # ", " # pub-AP:adr-NY,
  year =         "1976",
  pages =        "771--1041",
}

@Book{Nelson:1998:PDM,
  editor =       "David Nelson",
  title =        "The Penguin Dictionary of Mathematics",
  edition =      "Second",
  publisher =    pub-Penguin,
  address =      pub-Penguin:adr-L,
  year =         "1998",
  pages =        "461",
  ISBN =         "0-14-051342-6",
}

@Article{Nelder:1965:SMF,
  author =       "J. A. Nelder and R. Mead",
  title =        "A Simplex Method for Function Minimization",
  journal =      j-COMP-J,
  volume =       "7",
  pages =        "308--313",
  year =         "1965",
}

@Article{Neumann:1984:BEA,
  author =       "M. Neumann and R. J. Plemmons",
  title =        "Backward Error Analysis for Linear Systems Associated
                 with Inverses of {$H$}-Matrices",
  journal =      j-BIT,
  volume =       "24",
  pages =        "102--112",
  year =         "1984",
}

@Article{Neal:1992:GAG,
  author =       "Larry Neal and George Poole",
  title =        "A Geometric Analysis of {Gaussian} Elimination. {II}",
  journal =      j-LAA,
  volume =       "173",
  pages =        "239--264",
  year =         "1992",
}

@Article{Newman:1958:EMI,
  author =       "Morris Newman and John Todd",
  title =        "The Evaluation of Matrix Inversion Programs",
  journal =      j-SIAM,
  volume =       "6",
  number =       "4",
  pages =        "466--476",
  year =         "1958",
}

@Article{Neumaier:1974:REV,
  author =       "A. Neumaier",
  title =        "Rundungsfehleranalyse einiger {Verfahren zur Summation
                 endlicher Summen}",
  journal =      j-ZAMM,
  volume =       "54",
  pages =        "39--51",
  year =         "1974",
}

@Article{Neumaier:1985:IPR,
  author =       "A. Neumaier",
  title =        "Inner Product Rounding Error Analysis in the Presence
                 of Underflow",
  journal =      j-COMPUTING,
  volume =       "34",
  pages =        "365--373",
  year =         "1985",
}

@Article{Neumaier:1986:CMM,
  author =       "A. Neumaier",
  title =        "On the Comparison of {$H$}-Matrices with
                 {$M$}-Matrices",
  journal =      j-LAA,
  volume =       "83",
  pages =        "135--141",
  year =         "1986",
}

@Article{Newbery:1973:EAF,
  author =       "A. C. R. Newbery",
  title =        "Error Analysis for {Fourier} Series Evaluation",
  journal =      j-MATH-COMP,
  volume =       "27",
  number =       "123",
  pages =        "639--644",
  year =         "1973",
}

@Article{Newbery:1974:EAP,
  author =       "A. C. R. Newbery",
  title =        "Error Analysis for Polynomial Evaluation",
  journal =      j-MATH-COMP,
  volume =       "28",
  number =       "127",
  pages =        "789--793",
  year =         "1974",
}

@Article{Newcomb:1881:NFU,
  author =       "Simon Newcomb",
  title =        "Note on the Frequency of Use of the Different Digits
                 in Natural Numbers",
  journal =      "Amer. J. Math.",
  volume =       "4",
  pages =        "39--40",
  year =         "1881",
}

@InCollection{Newman:1962:MC,
  author =       "Morris Newman",
  title =        "Matrix Computations",
  editor =       "John Todd",
  booktitle =    "Survey of Numerical Analysis",
  publisher =    pub-MH,
  address =      pub-MH:adr,
  pages =        "222--254",
  year =         "1962",
}

@Article{Nickel:1970:KBS,
  author =       "K. Nickel",
  title =        "Das {Kahan-Babu\u{s}kasche Summierungsverfahren in
                 Triplex-ALGOL} 60",
  journal =      j-ZAMM,
  volume =       "50",
  pages =        "369--373",
  year =         "1970",
}

@InProceedings{Nickel:1977:IA,
  author =       "Karl Nickel",
  title =        "Interval-Analysis",
  editor =       "David A. H. Jacobs",
  booktitle =    "The State of the Art in Numerical Analysis",
  publisher =    pub-AP # ", " # pub-AP:adr-L,
  pages =        "193--225",
  year =         "1977",
}

@Article{Notay:1993:CRC,
  author =       "Yvan Notay",
  title =        "On the Convergence Rate of the Conjugate Gradients in
                 Presence of Rounding Errors",
  journal =      j-NUM-MATH,
  volume =       "65",
  pages =        "301--317",
  year =         "1993",
}

@Book{Nocedal:1999:NO,
  author =       "Jorge Nocedal and Stephen J. Wright",
  title =        "Numerical Optimization",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-NY,
  year =         "1999",
  pages =        "xx+636",
  ISBN =         "0-387-98793-2",
}

@Article{Oettli:1964:CAS,
  author =       "W. Oettli and W. Prager",
  title =        "Compatibility of Approximate Solution of Linear
                 Equations With Given Error Bounds for Coefficients and
                 Right-Hand Sides",
  journal =      j-NUM-MATH,
  volume =       "6",
  pages =        "405--409",
  year =         "1964",
}

@Article{Oettli:1965:SSL,
  author =       "W. Oettli",
  title =        "On the Solution Set of a Linear System with Inaccurate
                 Coefficients",
  journal =      j-SINUM,
  volume =       "2",
  number =       "1",
  pages =        "115--118",
  year =         "1965",
}

@Article{OLeary:1980:EMC,
  author =       "Dianne Prost O'Leary",
  title =        "Estimating Matrix Condition Numbers",
  journal =      j-SISSC,
  volume =       "1",
  number =       "2",
  pages =        "205--209",
  year =         "1980",
}

@Article{Oliver:1977:EAM,
  author =       "J. Oliver",
  title =        "An Error Analysis of the Modified {Clenshaw} Method
                 for Evaluating {Chebyshev} and {Fourier} Series",
  journal =      j-JIMA,
  volume =       "20",
  pages =        "379--391",
  year =         "1977",
}

@Article{Oliver:1979:REP,
  author =       "J. Oliver",
  title =        "Rounding Error Propagation in Polynomial Evaluation
                 Schemes",
  journal =      j-JCAM,
  volume =       "5",
  number =       "2",
  pages =        "85--97",
  year =         "1979",
}

@Article{Olver:1978:NAE,
  author =       "F. W. J. Olver",
  title =        "A New Approach to Error Arithmetic",
  journal =      j-SINUM,
  volume =       "15",
  number =       "2",
  pages =        "368--393",
  year =         "1978",
}

@InProceedings{Olver:1983:EAC,
  author =       "F. W. J. Olver",
  title =        "Error Analysis of Complex Arithmetic",
  booktitle =    "Computational Aspects of Complex Analysis",
  series =       "NATO Advanced Study Institute Series C",
  volume =       "102",
  editors =      "H. Werner and L. Wuytack and E. Ng. and H. J.
                 B{\"u}nger",
  publisher =    pub-reidel # ", " # pub-reidel:adr,
  pages =        "279--292",
  year =         "1983",
}

@Article{Olver:1986:EBP,
  author =       "F. W. J. Olver",
  title =        "Error Bounds for Polynomial Evaluation and Complex
                 Arithmetic",
  journal =      j-IMAJNA,
  volume =       "6",
  pages =        "373--379",
  year =         "1986",
}

@Article{Olver:1982:PEB,
  author =       "F. W. J. Olver and J. H. Wilkinson",
  title =        "{\em A posteriori\/} Error Bounds for {Gaussian}
                 Elimination",
  journal =      j-IMAJNA,
  volume =       "2",
  pages =        "377--406",
  year =         "1982",
}

@Article{Oettli:1965:ASL,
  author =       "W. Oettli and W. Prager and J. H. Wilkinson",
  title =        "Admissible Solutions of Linear Systems With Not
                 Sharply Defined Coefficients",
  journal =      j-SINUM,
  volume =       "2",
  number =       "2",
  pages =        "291--299",
  year =         "1965",
}

@Article{Ortega:1963:EAH,
  author =       "James M. Ortega",
  title =        "An Error Analysis of {Householder's} Method for the
                 Symmetric Eigenvalue Problem",
  journal =      j-NUM-MATH,
  volume =       "5",
  pages =        "211--225",
  year =         "1963",
}

@Book{Ortega:1972:NAS,
  author =       "James M. Ortega",
  title =        "Numerical Analysis: {A} Second Course",
  publisher =    pub-AP,
  address =      pub-AP:adr-NY,
  year =         "1972",
  pages =        "xiii+201",
  ISBN =         "0-89871-250-5 (original), 0-89871-250-5 (SIAM)",
  note =         "Republished by " # pub-SIAM # ", " # pub-SIAM:adr # ",
                 1990",
}

@Book{Ostrowski:1973:SEE,
  author =       "A. M. Ostrowski",
  title =        "Solution of Equations in {Euclidean and Banach}
                 Spaces",
  publisher =    pub-AP,
  address =      pub-AP:adr-NY,
  year =         "1973",
  pages =        "xx+412",
  note =         "Third edition of Solution of Equations and Systems of
                 Equations",
}

@Book{Overton:2001:NCI,
  author =       "Michael L. Overton",
  title =        "Numerical Computing with {IEEE} Floating Point
                 Arithmetic: {Including} One Theorem, One Rule of Thumb,
                 and One Hundred and One Exercises",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "2001",
  pages =        "xiv+104",
  ISBN =         "0-89871-482-6",
}

@Article{Parlett:2000:RRR,
  author =       "Beresford N. Parlett and Inderjit S. Dhillon",
  title =        "Relatively Robust Representations of Symmetric
                 Tridiagonals",
  journal =      j-LAA,
  volume =       "309",
  pages =        "121--151",
  year =         "2000",
}

@Book{Patterson:1998:COD,
  author =       "David A. Patterson and John L. Hennessy",
  title =        "Computer Organization and Design: {The}
                 Hardware/Software Interface",
  publisher =    "Morgan Kaufmann",
  address =      "San Francisco, CA, USA",
  edition =      "Second",
  year =         "1998",
  pages =        "xxix+759+appendices",
  ISBN =         "1-55860-428-6",
}

@Article{Paige:1973:EAM,
  author =       "C. C. Paige",
  title =        "An Error Analysis of a Method for Solving Matrix
                 Equations",
  journal =      j-MATH-COMP,
  volume =       "27",
  number =       "122",
  pages =        "355--359",
  year =         "1973",
}

@InProceedings{Paige:1990:SAG,
  author =       "C. C. Paige",
  title =        "Some Aspects of Generalized {QR} Factorizations",
  booktitle =    "Reliable Numerical Computation",
  editor =       "M. G. Cox and S. J. Hammarling",
  pages =        "73--91",
  publisher =    pub-OUP,
  year =         "1990",
}

@Article{Pan:2000:ECR,
  author =       "C.-T. Pan",
  title =        "On the Existence and Computation of Rank-Revealing
                 {LU} Factorizations",
  journal =      j-LAA,
  volume =       "316",
  pages =        "199--222",
  year =         "2000",
}

@Book{Pan:2001:SMP,
  author =       "Victor Y. Pan",
  title =        "Structured Matrices and Polynomials: {Unified}
                 Superfast Algorithms",
  publisher =    pub-BH,
  address =      pub-BH:adr,
  year =         "2001",
  pages =        "xxiv+278",
  ISBN =         "0-8176-4240-4",
}

@InProceedings{Pan:1978:SAO,
  author =       "Victor Y. Pan",
  title =        "Strassen Algorithm is Not Optimal. {Trilinear}
                 Technique of Aggregating, Uniting and Canceling for
                 Constructing Fast Algorithms for Matrix
                 Multiplication",
  booktitle =    "Proc. 19th Annual Symposium on the Foundations of
                 Computer Science",
  publisher =    "Ann Arbor, MI, USA",
  pages =        "166--176",
  year =         "1978",
}

@Article{Pan:1984:HCW,
  author =       "Victor Y. Pan",
  title =        "How Can We Speed up Matrix Multiplication?",
  journal =      j-SIREV,
  volume =       "26",
  number =       "3",
  pages =        "393--415",
  year =         "1984",
}

@Book{Parhami:2000:CAA,
  author =       "Behrooz Parhami",
  title =        "Computer Arithmetic: {Algorithms} and Hardware
                 Designs",
  publisher =    pub-OUP,
  address =      pub-OUP:adr-NY,
  pages =        "xx+490",
  year =         "2000",
  ISBN =         "0-19-512583-5",
}

@Article{Parlett:1964:LMA,
  author =       "Beresford N. Parlett",
  title =        "{Laguerre's} Method Applied to the Matrix Eigenvalue
                 Problem",
  journal =      j-MATH-COMP,
  volume =       "18",
  pages =        "464--485",
  year =         "1964",
}

@Article{Parlett:1965:MEP,
  author =       "Beresford N. Parlett",
  title =        "Matrix Eigenvalue Problems",
  journal =      j-AMM,
  volume =       "72",
  number =       "2",
  pages =        "59--66",
  month =        feb,
  year =         "1965",
}

@Article{Parlett:1971:AAR,
  author =       "Beresford N. Parlett",
  title =        "Analysis of Algorithms for Reflections in Bisectors",
  journal =      j-SIREV,
  volume =       "13",
  number =       "2",
  pages =        "197--208",
  year =         "1971",
}

@InProceedings{Parlett:1990:CJH,
  author =       "Beresford N. Parlett",
  title =        "The Contribution of {J. H. Wilkinson} to Numerical
                 Analysis",
  editor =       "Stephen G. Nash",
  booktitle =    "A History of Scientific Computing",
  publisher =    pub-AW # ", " # pub-AW:adr,
  pages =        "17--30",
  year =         "1990",
}

@Book{Parlett:1998:SEP,
  author =       "Beresford N. Parlett",
  title =        "The Symmetric Eigenvalue Problem",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "1998",
  pages =        "xxiv+398",
  ISBN =         "0-89871-402-8",
  note =         "Unabridged, amended version of book first published by
                 " # pub-PH # " in 1980",
}

@Article{Pan:1991:INI,
  author =       "Victor Y. Pan and Robert Schreiber",
  title =        "An Improved {Newton} Iteration for the Generalized
                 Inverse of a Matrix, with Applications",
  journal =      j-SISSC,
  volume =       "12",
  number =       "5",
  pages =        "1109--1130",
  year =         "1991",
}

@Article{Paterson:1973:NNM,
  author =       "Michael S. Paterson and Larry J. Stockmeyer",
  title =        "On the Number of Nonscalar Multiplications Necessary
                 to Evaluate Polynomials",
  journal =      j-SICOMP,
  volume =       "2",
  number =       "1",
  pages =        "60--66",
  year =         "1973",
}

@TechReport{patriot92,
  key =          "United States General Accounting Office",
  title =        "Patriot Missile Defense: {Software} Problem Led to
                 System Failure at {Dhahran}, {Saudi Arabia}",
  institution =  "Information Management and Technology Division, United
                 States General Accounting Office",
  address =      "Washington, D.C.",
  type =         "Report",
  number =       "GAO/IMTEC-92-26",
  month =        feb,
  pages =        "16",
  year =         "1992",
}

@Article{Paige:1994:HGC,
  author =       "C. C. Paige and M. Wei",
  title =        "History and Generality of the {CS} Decomposition",
  journal =      j-LAA,
  volume =       "208/209",
  pages =        "303--326",
  year =         "1994",
}

@Unpublished{Paxson:1991:PTI,
  author =       "Vern Paxson",
  title =        "A Program for Testing {IEEE} Decimal--Binary
                 Conversion",
  year =         "1991",
  month =        may,
  pages =        "40",
  note =         "Manuscript.
                 \path|ftp://ftp.ee.lbl.gov/testbase-report.ps.Z|",
}

@Article{Pan:2001:CNC,
  author =       "Victor Y. Pan and Y. Yu",
  title =        "Certification of Numerical Computation of the Sign of
                 the Determinant of a Matrix",
  journal =      "Algorithmica",
  volume =       "30",
  number =       "4",
  pages =        "708--724",
  year =         "2001",
}

@InCollection{Pan:1999:NIS,
  author =       "Victor Y. Pan and Sheryl Branham and Rhys E. Rosholt
                 and Ai-Long Zheng",
  title =        "Newton's Iteration for Structured Matrices",
  editor =       "Thomas Kailath and Ali H. Sayed",
  booktitle =    "Fast Reliable Algorithms for Matrices with Structure",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "1999",
  pages =        "189--210",
}

@Article{Pena:1996:PSL,
  author =       "J. M. Pe{\~n}a",
  title =        "Pivoting Strategies Leading to Small Bounds of the
                 Errors for Certain Linear Systems",
  journal =      j-IMAJNA,
  volume =       "16",
  number =       "2",
  pages =        "141--153",
  year =         "1996",
}

@Article{Pena:1998:PSL,
  author =       "J. M. Pe{\~n}a",
  title =        "Pivoting Strategies Leading to Diagonal Dominance by
                 Rows",
  journal =      j-NUM-MATH,
  volume =       "81",
  pages =        "293--304",
  year =         "1998",
}

@Article{Penzl:1998:NSG,
  author =       "Thilo Penzl",
  title =        "Numerical Solution of Generalized {Lyapunov}
                 Equations",
  journal =      j-Adv-Comp-Math,
  volume =       "8",
  pages =        "33--48",
  year =         "1998",
}

@Article{Percival:2002:RMM,
  author =       "Colin Percival",
  title =        "Rapid Multiplication Modulo the Sum and Difference of
                 Highly Composite Numbers",
  journal =      j-MATH-COMP,
  year =         "2002",
  note =         "To appear",
}

@Book{Petersen:1981:ET,
  author =       "Karl Petersen",
  title =        "Ergodic Theory",
  publisher =    pub-CUP,
  address =      pub-CUP:adr,
  year =         "1981",
  pages =        "xi+329",
  ISBN =         "0-521-23632-0",
}

@Article{Peters:1970:LSP,
  author =       "G. Peters and J. H. Wilkinson",
  title =        "The Least Squares Problem and Pseudo-Inverses",
  journal =      j-COMP-J,
  volume =       "13",
  number =       "3",
  pages =        "309--316",
  year =         "1970",
}

@Article{Peters:1971:PPA,
  author =       "G. Peters and J. H. Wilkinson",
  title =        "Practical Problems Arising in the Solution of
                 Polynomial Equations",
  journal =      j-JIMA,
  volume =       "8",
  pages =        "16--35",
  year =         "1971",
}

@Article{Peters:1975:SGJ,
  author =       "G. Peters and J. H. Wilkinson",
  title =        "On the Stability of {Gauss-Jordan} Elimination With
                 Pivoting",
  journal =      j-CACM,
  volume =       "18",
  number =       "1",
  pages =        "20--24",
  year =         "1975",
}

@Article{Tao:1984:CSM,
  author =       "Pham Dinh Tao",
  title =        "Convergence of a Subgradient Method for Computing the
                 Bound Norm of Matrices",
  journal =      j-LAA,
  volume =       "62",
  pages =        "163--182",
  year =         "1984",
  note =         "In French",
}

@Article{Tao:1984:SMC,
  author =       "Pham Dinh Tao",
  title =        "Some Methods for Computing the Maximum of Quadratic
                 Form on the Unit Ball of the Maximum Norm",
  journal =      j-NUM-MATH,
  volume =       "45",
  pages =        "377--401",
  year =         "1984",
  note =         "In French",
}

@Article{Pichat:1972:CSA,
  author =       "M. Pichat",
  title =        "Correction d'une Somme en Arithm\'etique \`a Virgule
                 Flottante",
  journal =      j-NUM-MATH,
  volume =       "19",
  pages =        "400--406",
  year =         "1972",
}

@Article{Pierce:1992:FAC,
  author =       "Daniel J. Pierce and Robert J. Plemmons",
  title =        "Fast Adaptive Condition Estimation",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "1",
  pages =        "274--291",
  year =         "1992",
}

@Book{Peitgen:1992:FCP,
  author =       "Heinz-Otto Peitgen and Hartmut J{\"u}rgens and Dietmar
                 Saupe",
  title =        "Fractals for the Classroom. Part One: Introduction to
                 Fractals and Chaos",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-NY,
  year =         "1992",
  pages =        "xiv+450",
  ISBN =         "0-387-97041-X",
}

@Article{Plauger:1988:PFP,
  author =       "P. J. Plauger",
  title =        "Properties of Floating-Point Arithmetic",
  journal =      "Computer Language",
  volume =       "5",
  number =       "3",
  pages =        "17--22",
  year =         "1988",
}

@Article{Plemmons:1974:LLS,
  author =       "Robert J. Plemmons",
  title =        "Linear Least Squares by Elimination and {MGS}",
  journal =      j-ACM,
  volume =       "21",
  number =       "4",
  pages =        "581--585",
  year =         "1974",
}

@Article{Plemmons:1976:RSD,
  author =       "R. J. Plemmons",
  title =        "Regular Splittings and the Discrete {Neumann}
                 Problem",
  journal =      j-NUM-MATH,
  volume =       "25",
  pages =        "153--161",
  year =         "1976",
}

@Article{Polman:1987:IBF,
  author =       "Ben Polman",
  title =        "Incomplete Blockwise Factorizations of (Block)
                 {$H$}-Matrices",
  journal =      j-LAA,
  volume =       "90",
  pages =        "119--132",
  year =         "1987",
}

@Article{Poole:2000:RPS,
  author =       "George Poole and Larry Neal",
  title =        "The Rook's Pivoting Strategy",
  journal =      j-JCAM,
  volume =       "123",
  pages =        "353--369",
  year =         "2000",
}

@InProceedings{Powell:1969:AHT,
  author =       "M. J. D. Powell and J. K. Reid",
  title =        "On Applying {Householder} Transformations to Linear
                 Least Squares Problems",
  booktitle =    "Proc. IFIP Congress 1968",
  publisher =    pub-NH # ", " # pub-NH:adr,
  pages =        "122--126",
  year =         "1969",
}

@Article{Poljak:1993:CRN,
  author =       "Svatopluk Poljak and Ji{\v{r}\'{\i}} Rohn",
  title =        "Checking Robust Nonsingularity is {NP}-Hard",
  journal =      "Math. Control Signals Systems",
  volume =       "6",
  pages =        "1--9",
  year =         "1993",
}

@Article{Powell:1970:SNM,
  author =       "M. J. D. Powell",
  title =        "A Survey of Numerical Methods for Unconstrained
                 Optimization",
  journal =      j-SIREV,
  volume =       "12",
  number =       "1",
  pages =        "79--97",
  year =         "1970",
}

@Article{Powell:1975:VUM,
  author =       "M. J. D. Powell",
  title =        "A View of Unconstrained Minimization Algorithms That
                 Do Not Require Derivatives",
  journal =      j-TOMS,
  volume =       "1",
  number =       "2",
  pages =        "97--107",
  year =         "1975",
}

@Article{Power:1986:CDH,
  author =       "Stephen Power",
  title =        "The {Cholesky} Decomposition in {Hilbert} Space",
  journal =      j-IMA-BULL,
  volume =       "22",
  number =       "11/12",
  pages =        "186--187",
  year =         "1986",
}

@Article{Powell:1998:DSA,
  author =       "M. J. D. Powell",
  title =        "Direct Search Algorithms for Optimization
                 Calculations",
  journal =      "Acta Numerica",
  volume =       "7",
  pages =        "287--336",
  year =         "1998",
}

@InProceedings{Priest:1991:AAP,
  author =       "Douglas M. Priest",
  title =        "Algorithms for Arbitrary Precision Floating Point
                 Arithmetic",
  editor =       "Peter Kornerup and David W. Matula",
  booktitle =    "Proc. 10th IEEE Symposium on Computer Arithmetic",
  publisher =    "IEEE Computer Society Press, Los Alamitos, CA, USA",
  pages =        "132--143",
  year =         "1991",
}

@PhdThesis{Priest:1992:PFP,
  author =       "Douglas M. Priest",
  title =        "On Properties of Floating Point Arithmetics:
                 {Numerical} Stability and the Cost of Accurate
                 Computations",
  school =       "Mathematics Department, University of California",
  address =      inst-Berkeley:adr,
  month =        nov,
  year =         "1992",
  pages =        "126",
  note =         "\path|ftp://ftp.icsi.berkeley.edu/pub/theory/priest-thesis.ps.Z|",
}

@Article{Pryce:1981:REA,
  author =       "J. D. Pryce",
  title =        "Round-Off Error Analysis with Fewer Tears",
  journal =      j-IMA-BULL,
  volume =       "17",
  pages =        "40--47",
  year =         "1981",
}

@Article{Pryce:1984:NMR,
  author =       "J. D. Pryce",
  title =        "A New Measure of Relative Error for Vectors",
  journal =      j-SINUM,
  volume =       "21",
  number =       "1",
  pages =        "202--215",
  year =         "1984",
}

@Article{Pryce:1985:MEA,
  author =       "J. D. Pryce",
  title =        "Multiplicative Error Analysis of Matrix Transformation
                 Algorithms",
  journal =      j-IMAJNA,
  volume =       "5",
  pages =        "437--445",
  year =         "1985",
}

@Misc{Embree:19xx:PG,
  author =       "Mark Embree and Lloyd N. Trefethen",
  title =        "Pseudospectra Gateway",
  note =         "\path|http://www.comlab.ox.ac.uk/pseudospectra/|",
}

@Book{Press:1992:NRF,
  author =       "William H. Press and Saul A. Teukolsky and William T.
                 Vetterling and Brian P. Flannery",
  title =        "Numerical Recipes in {FORTRAN}: {The} Art of
                 Scientific Computing",
  edition =      "Second",
  publisher =    pub-CUP,
  year =         "1992",
  ISBN =         "0-521-43064-X",
  pages =        "xxvi+963",
}

@Article{Puschmann:1983:CPR,
  author =       "Heinrich Puschmann and Joaqu{\'\i}n Cort\'es",
  title =        "The Coordinex Problem and its Relation to the
                 Conjecture of {Wilkinson}",
  journal =      j-NUM-MATH,
  volume =       "42",
  pages =        "291--297",
  year =         "1983",
}

@Article{Puglisi:1992:MHM,
  author =       "Chiara Puglisi",
  title =        "Modification of the {Householder} Method Based on the
                 Compact {WY} Representation",
  journal =      j-SISSC,
  volume =       "13",
  number =       "3",
  pages =        "723--726",
  year =         "1992",
}

@Article{Puschmann:1985:ZUV,
  author =       "Heinrich Puschmann and Marcelo Nordio",
  title =        "Zwei {Unzal{\"a}ssige} {Verst{\"a}rkungen} der
                 {Vermutung} von {Wilkinson}",
  journal =      j-LAA,
  volume =       "72",
  pages =        "167--176",
  year =         "1985",
  note =         "In German",
}

@Article{Quintana:2001:NPM,
  author =       "Enrique S. Quintana and Gregorio Quintana and Xiaobai
                 Sun and Robert van de Geijn",
  title =        "A Note on Parallel Matrix Inversion",
  journal =      j-SISC,
  volume =       "22",
  number =       "5",
  pages =        "1762--1771",
  year =         "2001",
}

@Article{Quinn:1991:TMY,
  author =       "Thomas R. Quinn and Scott Tremaine and Martin Duncan",
  title =        "A Three Million Year Integration of the Earth's
                 Orbit",
  journal =      "Astron. J.",
  volume =       "101",
  number =       "6",
  pages =        "2287--2305",
  year =         "1991",
}

@Article{Quinn:1983:EPR,
  author =       "Kevin Quinn",
  title =        "Ever Had Problems Rounding Off Figures? {This} Stock
                 Exchange Has",
  journal =      "Wall Street Journal",
  year =         "1983",
  page =         "37",
  note =         "8 November",
}

@Article{Quinlan:1994:REL,
  author =       "Gerald D. Quinlan",
  title =        "Round-Off Error in Long-Term Orbital Integrations
                 Using Multistep Methods",
  journal =      "Celestial Mechanics and Dynamical Astronomy",
  volume =       "58",
  pages =        "339--351",
  year =         "1994",
}

@Article{Quinn:1990:REL,
  author =       "Thomas Quinn and Scott Tremaine",
  title =        "Roundoff Error in Long-Term Planetary Orbit
                 Integrations",
  journal =      "Astron. J.",
  volume =       "99",
  number =       "3",
  pages =        "1016--1023",
  year =         "1990",
}

@Article{Raimi:1969:PDF,
  author =       "Ralph A. Raimi",
  title =        "The Peculiar Distribution of First Digits",
  journal =      "Scientific American",
  volume =       "221",
  number =       "6",
  pages =        "109--120",
  year =         "1969",
}

@Article{Raimi:1976:FDP,
  author =       "Ralph A. Raimi",
  title =        "The First Digit Problem",
  journal =      j-AMM,
  volume =       "83",
  pages =        "521--538",
  year =         "1976",
}

@Book{Rall:1981:ADT,
  author =       "Louis B. Rall",
  title =        "Automatic Differentiation: {Techniques} and
                 Applications",
  series =       "Lecture Notes in Computer Science",
  volume =       "120",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  year =         "1981",
  pages =        "viii+165",
}

@InProceedings{Rall:1991:TMC,
  author =       "Louis B. Rall",
  title =        "Tools for Mathematical Computation",
  booktitle =    "Computer Aided Proofs in Analysis",
  editor =       "Kenneth R. Meyer and Dieter S. Schmidt",
  series =       "IMA Volumes in Mathematics and Its Applications",
  volume =       "28",
  pages =        "217--228",
  publisher =    pub-Springer # ", " # pub-Springer:adr-NY,
  year =         "1991",
}

@Article{Ramos:1971:REA,
  author =       "George U. Ramos",
  title =        "Roundoff Error Analysis of the Fast {Fourier}
                 Transform",
  journal =      j-MATH-COMP,
  volume =       "25",
  number =       "116",
  pages =        "757--768",
  year =         "1971",
}

@Book{Randell:1975:ODC,
  editor =       "Brian Randell",
  title =        "The Origins of Digital Computers: {Selected} Papers",
  edition =      "Third",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  year =         "1975",
  pages =        "xvi+580",
  ISBN =         "3-540-11319-3",
}

@Article{Rath:1982:FGR,
  author =       "Wolfgang Rath",
  title =        "Fast {Givens} Rotations for Orthogonal Similarity
                 Transformations",
  journal =      j-NUM-MATH,
  volume =       "40",
  pages =        "47--56",
  year =         "1982",
}

@Article{Reichel:1990:NIL,
  author =       "Lothar Reichel",
  title =        "Newton Interpolation at {Leja} Points",
  journal =      j-BIT,
  volume =       "30",
  pages =        "332--346",
  year =         "1990",
}

@Article{Reichel:1991:FQD,
  author =       "Lothar Reichel",
  title =        "Fast {QR} Decomposition of {Vandermonde}-Like Matrices
                 and Polynomial Least Squares Approximation",
  journal =      j-SIMAX,
  volume =       "12",
  number =       "3",
  pages =        "552--564",
  year =         "1991",
}

@Article{Reid:2000:ISL,
  author =       "J. K. Reid",
  title =        "Implicit Scaling of Linear Least Squares Problems",
  journal =      j-BIT,
  volume =       "40",
  number =       "1",
  pages =        "146--157",
  year =         "2000",
}

@Article{Reid:1971:NSG,
  author =       "J. K. Reid",
  title =        "A Note on the Stability of {Gaussian} Elimination",
  journal =      j-JIMA,
  volume =       "8",
  pages =        "374--375",
  year =         "1971",
}

@InProceedings{Reid:1987:SM,
  author =       "J. K. Reid",
  title =        "Sparse Matrices",
  editor =       "A. Iserles and M. J. D. Powell",
  booktitle =    "The State of the Art in Numerical Analysis",
  publisher =    pub-OUP,
  pages =        "59--85",
  year =         "1987",
}

@Article{Reiser:1975:EDF,
  author =       "John F. Reiser and Donald E. Knuth",
  title =        "Evading the Drift in Floating-Point Addition",
  journal =      j-INFPL,
  volume =       "3",
  number =       "3",
  pages =        "84--87",
  year =         "1975",
}

@Article{Reichel:1991:CVS,
  author =       "Lothar Reichel and Gerhard Opfer",
  title =        "{Chebyshev}-{Vandermonde} Systems",
  journal =      j-MATH-COMP,
  volume =       "57",
  number =       "196",
  pages =        "703--721",
  year =         "1991",
}

@Article{Reichel:1992:EPE,
  author =       "Lothar Reichel and Lloyd N. Trefethen",
  title =        "Eigenvalues and Pseudo-Eigenvalues of {Toeplitz}
                 Matrices",
  journal =      j-LAA,
  volume =       "162--164",
  pages =        "153--185",
  year =         "1992",
}

@Article{Reddy:1992:SML,
  author =       "Satish C. Reddy and Lloyd N. Trefethen",
  title =        "Stability of the Method of Lines",
  journal =      j-NUM-MATH,
  volume =       "62",
  pages =        "235--267",
  year =         "1992",
}

@Article{Rheinboldt:1976:MIC,
  author =       "Werner C. Rheinboldt",
  title =        "On Measures of Ill-Conditioning for Nonlinear
                 Equations",
  journal =      j-MATH-COMP,
  volume =       "30",
  number =       "133",
  pages =        "104--111",
  year =         "1976",
}

@Article{Rice:1966:TC,
  author =       "John R. Rice",
  title =        "A Theory of Condition",
  journal =      j-SINUM,
  volume =       "3",
  number =       "2",
  pages =        "287--310",
  year =         "1966",
}

@Article{Rice:1966:EGS,
  author =       "John R. Rice",
  title =        "Experiments on {Gram-Schmidt} Orthogonalization",
  journal =      j-MATH-COMP,
  volume =       "20",
  pages =        "325--328",
  year =         "1966",
}

@Article{Rigal:1967:CGS,
  author =       "J. L. Rigal and J. Gaches",
  title =        "On the Compatibility of a Given Solution with the Data
                 of a Linear System",
  journal =      j-ACM,
  volume =       "14",
  number =       "3",
  pages =        "543--548",
  year =         "1967",
}

@Article{Roberts:1980:LMR,
  author =       "J. D. Roberts",
  title =        "Linear Model Reduction and Solution of the Algebraic
                 {Riccati} Equation by Use of the Sign Function",
  journal =      j-IJC,
  volume =       "32",
  number =       "4",
  pages =        "677--687",
  year =         "1980",
  note =         "First issued as report CUED/B-Control/TR13, Department
                 of Engineering, University of Cambridge, 1971",
}

@Article{Rohn:1989:NCN,
  author =       "Ji{\v{r}\'{\i}} Rohn",
  title =        "New Condition Numbers for Matrices and Linear
                 Systems",
  journal =      j-COMPUTING,
  volume =       "41",
  pages =        "167--169",
  year =         "1989",
}

@Article{Rohn:1989:SLI,
  author =       "Ji{\v{r}\'{\i}} Rohn",
  title =        "Systems of Linear Interval Equations",
  journal =      j-LAA,
  volume =       "126",
  pages =        "39--78",
  year =         "1989",
}

@Article{Rohn:1990:NUD,
  author =       "Ji{\v{r}\'{\i}} Rohn",
  title =        "Nonsingularity Under Data Rounding",
  journal =      j-LAA,
  volume =       "139",
  pages =        "171--174",
  year =         "1990",
}

@TechReport{Rohn:1995:NHR,
  author =       "Ji{\v{r}\'{\i}} Rohn",
  title =        "{NP}-Hardness Results for Some Linear and Quadratic
                 Problems",
  institution =  "Institute of Computer Science, Academy of Sciences of
                 the Czech Reupublic",
  address =      "Prague",
  type =         "Technical Report",
  number =       "No. 619",
  month =        jan,
  pages =        "11",
  year =         "1995",
}

@Article{Robertazzi:1988:BOF,
  author =       "T. G. Robertazzi and S. C. Schwartz",
  title =        "Best ``Ordering'' for Floating-Point Addition",
  journal =      j-TOMS,
  volume =       "14",
  number =       "1",
  pages =        "101--110",
  year =         "1988",
}

@Article{Ross:1965:RTE,
  author =       "D. R. Ross",
  title =        "Reducing Truncation Errors Using Cascading
                 Accumulators",
  journal =      j-CACM,
  volume =       "8",
  number =       "1",
  pages =        "32--33",
  year =         "1965",
}

@PhdThesis{Rowan:1990:FSA,
  author =       "Thomas Harvey Rowan",
  title =        "Functional Stability Analysis of Numerical
                 Algorithms",
  school =       "University of Texas at Austin",
  address =      "Austin, TX, USA",
  month =        may,
  year =         "1990",
  pages =        "xii+205",
}

@Article{Routh:1977:PSM,
  author =       "M. W. Routh and P. A. Swartz and M. B. Denton",
  title =        "Performance of the Super Modified Simplex",
  journal =      "Analytical Chemistry",
  volume =       "49",
  number =       "9",
  pages =        "1422--1428",
  year =         "1977",
}

@Article{Ruhe:1983:NAG,
  author =       "Axel Ruhe",
  title =        "Numerical Aspects of {Gram-Schmidt} Orthogonalization
                 of Vectors",
  journal =      j-LAA,
  volume =       "52/53",
  pages =        "591--601",
  year =         "1983",
}

@Article{Rump:2001:SVM,
  author =       "Siegfried M. Rump",
  title =        "Self-Validating Methods",
  journal =      j-LAA,
  volume =       "324",
  pages =        "3--13",
  year =         "2001",
}

@Article{Rump:2002:OSN,
  author =       "Siegfried M. Rump",
  title =        "Optimal Scaling for {$P$}-norms and Componentwise
                 Distance to Singularity",
  journal =      j-IMAJNA,
  year =         "2002",
  note =         "To appear",
}

@Article{Rump:1998:SPS,
  author =       "Siegfried M. Rump",
  title =        "Structured Perturbations and Symmetric Matrices",
  journal =      j-LAA,
  volume =       "278",
  pages =        "121--132",
  year =         "1998",
}

@Article{Rump:1999:ICM,
  author =       "Siegfried M. Rump",
  title =        "Ill-Conditioned Matrices Are Componentwise Near to
                 Singularity",
  journal =      j-SIREV,
  volume =       "41",
  number =       "1",
  pages =        "102--112",
  year =         "1999",
}

@InCollection{Rump:1999:IIL,
  author =       "Siegfried M. Rump",
  title =        "{INTLAB---INTerval LABoratory}",
  editor =       "Tibor Csendes",
  booktitle =    "Developments~in~Reliable Computing",
  publisher =    pub-Kluwer,
  address =      pub-Kluwer:adr,
  pages =        "77--104",
  year =         "1999",
}

@Article{Rump:1999:FPI,
  author =       "Siegfried M. Rump",
  title =        "Fast and Parallel Interval Arithmetic",
  journal =      j-BIT,
  volume =       "39",
  number =       "3",
  pages =        "534--554",
  year =         "1999",
}

@Article{Russinoff:1998:MCP,
  author =       "David M. Russinoff",
  title =        "A Mechanically Checked Proof of {IEEE} Compliance of
                 the Floating Point Multiplication, Division and Square
                 Root Algorithms of the {AMD-K7} Processor",
  journal =      "LMS J. Computer Math.",
  volume =       "1",
  pages =        "148--200",
  year =         "1998",
}

@Article{Rutherford:1947:SCD,
  author =       "D. E. Rutherford",
  title =        "Some Continuant Determinants Arising in Physics and
                 Chemistry",
  journal =      "Proc. Royal Soc. Edin.",
  volume =       "62,A",
  pages =        "229--236",
  year =         "1947",
}

@Article{Rutherford:1952:SCD,
  author =       "D. E. Rutherford",
  title =        "Some Continuant Determinants Arising in Physics and
                 Chemistry---{II}",
  journal =      "Proc. Royal Soc. Edin.",
  volume =       "63,A",
  pages =        "232--241",
  year =         "1952",
}

@InCollection{Rutishauser:1958:SEP,
  author =       "Heinz Rutishauser",
  title =        "Solution of Eigenvalue Problems With the
                 {LR}-Transformation",
  booktitle =    "Further Contributions to the Solution of Simultaneous
                 Linear Equations and the Determination of Eigenvalues",
  series =       "Applied Mathematics Series",
  number =       "49",
  publisher =    "National Bureau of Standards, United States Department
                 of Commerce",
  address =      "Washington, D. C.",
  pages =        "47--81",
  year =         "1958",
}

@InProceedings{Rutishauser:1968:TM,
  author =       "H. Rutishauser",
  title =        "On Test Matrices",
  booktitle =    "Programmation en Math{\'e}matiques Num{\'e}riques,
                 Besan{\c{c}}on, 1966",
  series =       "{\'E}ditions Centre Nat. Recherche Sci., Paris",
  volume =       "7 (no. 165)",
  pages =        "349--365",
  year =         "1968",
}

@Article{Samelson:1953:ORR,
  author =       "Klaus Samelson and Friedrich L. Bauer",
  title =        "{Optimale Rechengenauigkeit} bei {Rechenanlagen} mit
                 gleitendem {Komma}",
  journal =      j-ZAMP,
  volume =       "4",
  pages =        "312--316",
  year =         "1953",
}

@Article{Sameh:1977:STS,
  author =       "Ahmed H. Sameh and Richard P. Brent",
  title =        "Solving Triangular Systems on a Parallel Computer",
  journal =      j-SINUM,
  volume =       "14",
  number =       "6",
  pages =        "1101--1113",
  year =         "1977",
}

@Article{Sanz-Serna:1993:SCS,
  author =       "J. M. Sanz-Serna and S. Larsson",
  title =        "Shadows, Chaos, and Saddles",
  journal =      j-APP-NUM-MATH,
  volume =       "13",
  pages =        "181--190",
  year =         "1993",
}

@InCollection{Savage:1954:TIF,
  author =       "I. Richard Savage and Eugene Lukacs",
  title =        "Tables of Inverse of Finite Segments of the {Hilbert}
                 Matrix",
  editor =       "Olga Taussky",
  booktitle =    "Contributions to the Solution of Systems of Linear
                 Equations and the Determination of Eigenvalues",
  series =       "Applied Mathematics Series",
  number =       "39",
  publisher =    "National Bureau of Standards, United States Department
                 of Commerce",
  address =      "Washington, D. C.",
  pages =        "105--108",
  year =         "1954",
}

@TechReport{Saunders:1972:LSL,
  author =       "M. A. Saunders",
  title =        "Large-Scale Linear Programming Using the {Cholesky}
                 Factorization",
  type =         "Report",
  number =       "CS 252",
  institution =  inst-CS-U-STANFORD,
  year =         "1972",
  month =        jan,
}

@Article{Sautter:1978:EAG,
  author =       "Werner Sautter",
  german_title = "Fehleranalyse f{\"ur} die {Gau\ss}-Elimination zur
                 Berechnung der L{\"o}sung minimaler L{\"a}nge",
  title =        "Error Analysis of {Gauss} Elimination for the Best
                 Least Squares Problem",
  journal =      j-NUM-MATH,
  volume =       "30",
  pages =        "165--184",
  year =         "1978",
}

@Book{Smith:1976:MER,
  author =       "B. T. Smith and J. M. Boyle and J. J. Dongarra and B.
                 S. Garbow and Y. Ikebe and V. C. Klema and C. B.
                 Moler",
  title =        "Matrix Eigensystem Routines---{EISPACK} Guide",
  series =       "Lecture Notes in Computer Science",
  edition =      "Second",
  volume =       "6",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  pages =        "vii+551",
  ISBN =         "3-540-06710-8",
  year =         "1976",
}

@Book{Scarborough:1950:NMA,
  author =       "James B. Scarborough",
  title =        "Numerical Mathematical Analysis",
  edition =      "Second",
  publisher =    pub-JH,
  address =      pub-JH:adr,
  year =         "1950",
  pages =        "xviii+511",
}

@Article{Schatzman:1996:ADF,
  author =       "James C. Schatzman",
  title =        "Accuracy of the Discrete {Fourier} Transform and the
                 Fast {Fourier} Transform",
  journal =      j-SISC,
  volume =       "17",
  number =       "5",
  pages =        "1150--1166",
  year =         "1996",
}

@Article{Schelin:1983:CFA,
  author =       "Charles W. Schelin",
  title =        "Calculator Function Approximation",
  journal =      j-AMM,
  volume =       "90",
  number =       "5",
  pages =        "317--325",
  year =         "1983",
}

@TechReport{Schryer:1981:TCF,
  author =       "N. L. Schryer",
  title =        "A Test of a Computer's Floating-Point Arithmetic
                 Unit",
  institution =  inst-ATT,
  address =      inst-ATT:adr,
  type =         "Computing Science Technical Report",
  number =       "No. 89",
  year =         "1981",
}

@InProceedings{Schryer:1984:DCF,
  author =       "N. L. Schryer",
  title =        "Determination of Correct Floating-Point Model
                 Parameters",
  editor =       "Wayne R. Cowell",
  booktitle =    "Sources and Development of Mathematical Software",
  publisher =    pub-PH # ", " # pub-PH:adr,
  pages =        "360--366",
  year =         "1984",
}

@InProceedings{Schreiber:1988:BAP,
  author =       "Robert S. Schreiber",
  title =        "Block Algorithms for Parallel Machines",
  editor =       "M. H. Schultz",
  booktitle =    "Numerical Algorithms for Modern Parallel Computer
                 Architectures",
  series =       "IMA Volumes In Mathematics and Its Applications",
  number =       "13",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  pages =        "197--207",
  year =         "1988",
}

@Article{Schreiber:1989:HRS,
  author =       "Robert S. Schreiber",
  title =        "{Hough's} Random Story Explained",
  journal =      "NA Digest",
  volume =       "Volume 89, Issue 3",
  year =         "1989",
}

@Article{schu33,
  author =       "G{\"u}nther Schulz",
  title =        "{Iterative Berechnung} der Reziproken {Matrix}",
  journal =      j-ZAMM,
  volume =       "13",
  pages =        "57--59",
  year =         "1933",
}

@Article{Schreiber:1988:BRT,
  author =       "Robert S. Schreiber and Beresford N. Parlett",
  title =        "Block Reflectors: {Theory} and Computation",
  journal =      j-SINUM,
  volume =       "25",
  number =       "1",
  pages =        "189--205",
  year =         "1988",
}

@Article{Schonfelder:1980:ECP,
  author =       "J. L. Schonfelder and M. Razaz",
  title =        "Error Control with Polynomial Approximations",
  journal =      j-IMAJNA,
  volume =       "1",
  pages =        "105--114",
  year =         "1980",
}

@Article{Schneider:1962:CTS,
  author =       "Hans Schneider and W. Gilbert Strang",
  title =        "Comparison Theorems for Supremum Norms",
  journal =      j-NUM-MATH,
  volume =       "4",
  pages =        "15--20",
  year =         "1962",
}

@Article{Schreiber:1989:SEW,
  author =       "Robert S. Schreiber and Charles F. Van Loan",
  title =        "A Storage Efficient {WY} Representation for Products
                 of {Householder} Transformations",
  journal =      j-SISSC,
  volume =       "10",
  pages =        "53--57",
  year =         "1989",
}

@Article{Schneider:1998:MWN,
  author =       "Hans Schneider and Hans F. Weinberger",
  title =        "On Matrices for Which Norm Bounds Are Attained",
  journal =      j-LAA,
  volume =       "275--276",
  pages =        "563--577",
  year =         "1998",
}

@Article{Scherer:1980:SNR,
  author =       "R. Scherer and K. Zeller",
  title =        "Shorthand Notation for Rounding Errors",
  journal =      j-COMPUTING,
  volume =       "Suppl. 2",
  pages =        "165--168",
  year =         "1980",
}

@Book{Sedgewick:1988:A,
  author =       "Robert Sedgewick",
  title =        "Algorithms",
  edition =      "Second",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  year =         "1988",
  pages =        "xii+657",
  ISBN =         "0-201-06673-4",
}

@Misc{Severance:1998:IOM,
  author =       "Charles Severance",
  title =        "An Interview with the Old Man of Floating-Point.
                 {Reminiscences} Elicited from {William Kahan by Charles
                 Severance}",
  year =         "1998",
  month =        feb,
  note =         "\path|http://www.cs.berkeley.edu/~wkahan/ieee754status/754story.html|.
                 A shortened version appears in \emph{Computer},
                 31(3):114--115, March 1998.",
}

@Book{shal73,
  author =       "Lawrence F. Shampine and Richard C. {Allen, Jr.}",
  title =        "Numerical Computing: {An} Introduction",
  publisher =    "W. B. Saunders",
  address =      "Philadelphia, PA, USA",
  year =         "1973",
  pages =        "vii+258",
  ISBN =         "0-7216-8150-6",
}

@Book{Shampine:1994:NSO,
  author =       "Lawrence F. Shampine",
  title =        "Numerical Solution of Ordinary Differential
                 Equations",
  publisher =    pub-CH,
  address =      pub-CH:adr-NY,
  year =         "1994",
  pages =        "x+484",
  ISBN =         "0-412-05151-6",
}

@Article{Shapiro:1982:OSM,
  author =       "Alexander Shapiro",
  title =        "Optimally Scaled Matrices, Necessary and Sufficient
                 Conditions",
  journal =      j-NUM-MATH,
  volume =       "39",
  pages =        "239--245",
  year =         "1982",
}

@Article{Shapiro:1985:OBD,
  author =       "Alexander Shapiro",
  title =        "Optimal Block Diagonal {$l_2$}-Scaling of Matrices",
  journal =      j-SINUM,
  volume =       "22",
  number =       "1",
  pages =        "81--94",
  year =         "1985",
}

@Article{Shapiro:1991:UBN,
  author =       "Alexander Shapiro",
  title =        "Upper Bounds for Nearly Optimal Diagonal Scaling of
                 Matrices",
  journal =      j-LMA,
  volume =       "29",
  pages =        "147--147",
  year =         "1991",
}

@TechReport{Sharangpani:1994:SAF,
  author =       "H. P. Sharangpani and M. L. Barton",
  title =        "Statistical Analysis of Floating Point Flaw in the
                 {Pentium} Processor (1994)",
  institution =  "Intel Corporation",
  year =         "1994",
  month =        nov,
  pages =        "31",
}

@Article{Shroff:1992:ACE,
  author =       "Gautam M. Shroff and Christian H. Bischof",
  title =        "Adaptive Condition Estimation for Rank-One Updates of
                 {QR} Factorizations",
  journal =      j-SIMAX,
  volume =       "13",
  number =       "4",
  pages =        "1264--1278",
  year =         "1992",
}

@Article{Shewchuk:1997:APF,
  author =       "Jonathan Richard Shewchuk",
  title =        "Adaptive Precision Floating-Point Arithmetic and Fast
                 Robust Geometric Predicates",
  journal =      "Discrete and Computational Geometry",
  volume =       "18",
  number =       "3",
  pages =        "305--363",
  year =         "1997",
}

@Article{Shampine:1997:MOS,
  author =       "Lawrence F. Shampine and Mark W. Reichelt",
  title =        "The {MATLAB} {ODE} Suite",
  journal =      j-SISC,
  volume =       "18",
  number =       "1",
  pages =        "1--22",
  year =         "1997",
}

@Article{Shepherd:1989:MCW,
  author =       "David Shepherd and Greg Wilson",
  title =        "Making Chips that Work",
  journal =      "New Scientist",
  pages =        "61--64",
  year =         "1989",
  note =         "13 May",
}

@Article{Skeel:1979:SNS,
  author =       "Robert D. Skeel",
  title =        "Scaling for Numerical Stability in {Gaussian}
                 Elimination",
  journal =      j-ACM,
  volume =       "26",
  number =       "3",
  pages =        "494--526",
  year =         "1979",
}

@Article{Skeel:1980:IRI,
  author =       "Robert D. Skeel",
  title =        "Iterative Refinement Implies Numerical Stability for
                 {Gaussian} Elimination",
  journal =      j-MATH-COMP,
  volume =       "35",
  number =       "151",
  pages =        "817--832",
  year =         "1980",
}

@Article{Skeel:1981:EER,
  author =       "Robert D. Skeel",
  title =        "Effect of Equilibration on Residual Size for Partial
                 Pivoting",
  journal =      j-SINUM,
  volume =       "18",
  number =       "3",
  pages =        "449--454",
  year =         "1981",
}

@TechReport{Skeel:1989:SNB,
  author =       "Robert D. Skeel",
  title =        "Safety in Numbers: {The} Boundless Errors of Numerical
                 Computation",
  institution =  "Department of Computer Science, University of
                 Illinois",
  address =      "Urbana, IL, USA",
  type =         "Working Document",
  number =       "89-3",
  pages =        "9",
  year =         "1989",
}

@Book{Skeel:1993:ENC,
  author =       "Robert D. Skeel and Jerry B. Keiper",
  title =        "Elementary Numerical Computing with {Mathematica}",
  publisher =    pub-MH,
  address =      pub-MH:adr,
  year =         "1993",
  pages =        "xiv+434",
  ISBN =         "0-07-057820-6",
}

@Book{Blackford:1997:SUG,
  author =       "L. S. Blackford and J. Choi and A. Cleary and E.
                 D'Azevedo and J. Demmel and I. Dhillon and J. Dongarra
                 and S. Hammarling and G. Henry and A. Petitet and K.
                 Stanley and D. Walker and R. C. Whaley",
  title =        "{ScaLAPACK} Users' Guide",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "1997",
  pages =        "xxvi+325",
  ISBN =         "0-89871-397-8",
}

@Article{Smale:1990:SRF,
  author =       "Steve Smale",
  title =        "Some Remarks on the Foundations of Numerical
                 Analysis",
  journal =      j-SIREV,
  volume =       "32",
  number =       "2",
  pages =        "211--220",
  year =         "1990",
}

@Article{Smith:1962:ACD,
  author =       "Robert L. Smith",
  title =        "Algorithm 116: {Complex} Division",
  journal =      j-CACM,
  volume =       "5",
  number =       "8",
  pages =        "435",
  year =         "1962",
}

@Article{Smith:1965:ASO,
  author =       "Francis J. Smith",
  title =        "An Algorithm for Summing Orthogonal Polynomial Series
                 and their Derivatives with Applications to
                 Curve-Fitting and Interpolation",
  journal =      j-MATH-COMP,
  volume =       "19",
  pages =        "33--36",
  year =         "1965",
}

@Book{Smith:1975:SAP,
  author =       "Jon M. Smith",
  title =        "Scientific Analysis on the Pocket Calculator",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  year =         "1975",
  pages =        "xii+380",
  ISBN =         "0-471-79997-1",
}

@Article{Smith:1991:AFP,
  author =       "David M. Smith",
  title =        "Algorithm 693: {A} {FORTRAN} Package for
                 Floating-Point Multiple-Precision Arithmetic",
  journal =      j-TOMS,
  volume =       "17",
  number =       "2",
  pages =        "273--283",
  year =         "1991",
}

@Article{Smith:1998:AMP,
  author =       "David M. Smith",
  title =        "Algorithm 786: {Multiple}-Precision Complex Arithmetic
                 and Functions",
  journal =      j-TOMS,
  volume =       "24",
  number =       "4",
  pages =        "359--367",
  year =         "1998",
}

@Article{Smoktunowicz:1995:NSC,
  author =       "Alicja Smoktunowicz",
  title =        "A Note on the Strong Componentwise Stability of
                 Algorithms for Solving Symmetric Linear Systems",
  journal =      "Demonstratio Mathematica",
  volume =       "28",
  number =       "2",
  pages =        "443--448",
  year =         "1995",
}

@Article{Smoktunowicz:1984:BCI,
  author =       "Alicja Smoktunowicz and Jolanta Sokolnicka",
  title =        "Binary Cascades Iterative Refinement in
                 Doubled-Mantissa Arithmetics",
  journal =      j-BIT,
  volume =       "24",
  pages =        "123--127",
  year =         "1984",
}

@Article{Snyder:1955:ISS,
  author =       "James N. Snyder",
  title =        "On the Improvement of the Solutions to a Set of
                 Simultaneous Linear Equations using the {ILLIAC}",
  journal =      "Mathematical Tables and Other Aids to Computation",
  volume =       "9",
  pages =        "177--184",
  year =         "1955",
}

@Article{Sorensen:1985:APP,
  author =       "D. C. Sorensen",
  title =        "Analysis of Pairwise Pivoting in {Gaussian}
                 Elimination",
  journal =      j-IEEE-C,
  volume =       "C-34",
  pages =        "274--278",
  year =         "1985",
}

@Article{Soderstrom:1974:NPI,
  author =       "Torsten S{\"o}derstr{\"o}m and G. W. Stewart",
  title =        "On the Numerical Properties of an Iterative Method for
                 Computing the {Moore--Penrose} Generalized Inverse",
  journal =      j-SINUM,
  volume =       "11",
  number =       "1",
  pages =        "61--74",
  year =         "1974",
}

@Article{Spiess:1976:UZD,
  author =       "J. Spie{\ss}",
  title =        "Untersuchungen des {Zeitgewinns} durch neue
                 {Algorithmen} zur {Matrix-Multiplikation}",
  journal =      j-COMPUTING,
  volume =       "17",
  pages =        "23--36",
  year =         "1976",
}

@Article{Stegun:1956:PC,
  author =       "Irene A. Stegun and Milton Abramowitz",
  title =        "Pitfalls in Computation",
  journal =      j-SIAM,
  volume =       "4",
  number =       "4",
  pages =        "207--219",
  year =         "1956",
}

@Book{Stoer:1980:INA,
  author =       "Josef Stoer and R. Bulirsch",
  title =        "Introduction to Numerical Analysis",
  publisher =    "Springer-Verlag",
  address =      "New York",
  year =         "1980",
  pages =        "ix+609",
  ISBN =         "0-387-90420-4",
}

@Book{Sterbenz:1974:FPC,
  author =       "Pat H. Sterbenz",
  title =        "Floating-Point Computation",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  year =         "1974",
  pages =        "xiv+316",
  ISBN =         "0-13-322495-3",
}

@Article{Stewart:1971:EAA,
  author =       "G. W. Stewart",
  title =        "Error Analysis of the Algorithm for Shifting the Zeros
                 of a Polynomial by Synthetic Division",
  journal =      j-MATH-COMP,
  volume =       "25",
  number =       "113",
  pages =        "135--139",
  year =         "1971",
}

@Book{Stewart:1973:IMC,
  author =       "G. W. Stewart",
  title =        "Introduction to Matrix Computations",
  publisher =    pub-AP,
  address =      pub-AP:adr-NY,
  year =         "1973",
  pages =        "xiii+441",
  ISBN =         "0-12-670350-7",
}

@Article{Stewart:1973:EPB,
  author =       "G. W. Stewart",
  title =        "Error and Perturbation Bounds for Subspaces Associated
                 with Certain Eigenvalue Problems",
  journal =      j-SIREV,
  volume =       "15",
  number =       "4",
  pages =        "727--764",
  year =         "1973",
}

@Article{Stewart:1974:MPE,
  author =       "G. W. Stewart",
  title =        "Modifying Pivot Elements in {Gaussian} Elimination",
  journal =      j-MATH-COMP,
  volume =       "28",
  number =       "126",
  pages =        "537--542",
  year =         "1974",
}

@Article{Stewart:1977:PPI,
  author =       "G. W. Stewart",
  title =        "On the Perturbation of Pseudo-Inverses, Projections
                 and Linear Least Squares Problems",
  journal =      j-SIREV,
  volume =       "19",
  number =       "4",
  pages =        "634--662",
  year =         "1977",
}

@Article{Stewart:1977:PBF,
  author =       "G. W. Stewart",
  title =        "Perturbation Bounds for the {$QR$} Factorization of a
                 Matrix",
  journal =      j-SINUM,
  volume =       "14",
  number =       "3",
  pages =        "509--518",
  year =         "1977",
}

@InProceedings{Stewart:1977:RDL,
  author =       "G. W. Stewart",
  title =        "Research, Development, and {LINPACK}",
  editor =       "John R. Rice",
  booktitle =    "Mathematical Software {III}",
  publisher =    pub-AP # ", " # pub-AP:adr-NY,
  pages =        "1--14",
  year =         "1977",
}

@Article{Stewart:1980:EGR,
  author =       "G. W. Stewart",
  title =        "The Efficient Generation of Random Orthogonal Matrices
                 With an Application to Condition Estimators",
  journal =      j-SINUM,
  volume =       "17",
  number =       "3",
  pages =        "403--409",
  year =         "1980",
}

@Article{Stewart:1985:NCD,
  author =       "G. W. Stewart",
  title =        "A Note on Complex Division",
  journal =      j-TOMS,
  volume =       "11",
  number =       "3",
  pages =        "238--241",
  year =         "1985",
}

@Article{Stewart:1990:SPT,
  author =       "G. W. Stewart",
  title =        "Stochastic Perturbation Theory",
  journal =      j-SIREV,
  volume =       "32",
  number =       "4",
  pages =        "579--610",
  year =         "1990",
}

@TechReport{Stewart:1992:NGS,
  author =       "G. W. Stewart",
  title =        "Note on a Generalized {Sylvester} Equation",
  institution =  inst-IMA,
  address =      inst-IMA:adr,
  type =         "IMA Preprint Series",
  number =       "\#985",
  pages =        "3",
  month =        may,
  year =         "1992",
}

@Article{Stewart:1993:PLC,
  author =       "G. W. Stewart",
  title =        "On the Perturbation of {LU}, {Cholesky}, and {QR}
                 Factorizations",
  journal =      j-SIMAX,
  volume =       "14",
  number =       "4",
  pages =        "1141--1145",
  year =         "1993",
}

@Article{Stewart:1993:EHS,
  author =       "G. W. Stewart",
  title =        "On the Early History of the Singular Value
                 Decomposition",
  journal =      j-SIREV,
  volume =       "35",
  number =       "4",
  pages =        "551--566",
  year =         "1993",
}

@Book{Gauss:1995:TCO,
  author =       "Carl Friedrich Gauss",
  title =        "Theory of the Combination of Observations Least
                 Subject to Errors. {Part} One, Part Two, Supplement",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "1995",
  pages =        "xi+241",
  ISBN =         "0-89871-347-1",
  note =         "Translated from the Latin by G. W. Stewart",
}

@Article{Stewart:1995:GSG,
  author =       "G. W. Stewart",
  title =        "{Gauss}, Statistics, and {Gaussian} Elimination",
  journal =      j-COMPUT-GRAPH-STAT,
  volume =       "4",
  number =       "1",
  pages =        "1--11",
}

@Article{Stewart:1997:PCF,
  author =       "G. W. Stewart",
  title =        "On the Perturbation of {$LU$} and {Cholesky} Factors",
  journal =      j-IMAJNA,
  volume =       "17",
  number =       "1",
  pages =        "1--6",
  year =         "1997",
}

@Article{Stewart:1997:TMG,
  author =       "G. W. Stewart",
  title =        "The Triangular Matrices of {Gaussian} Elimination and
                 Related Decompositions",
  journal =      j-IMAJNA,
  volume =       "17",
  number =       "1",
  pages =        "7--16",
  year =         "1997",
}

@Article{Stewart:1997:MCS,
  author =       "G. W. Stewart",
  title =        "On {Markov} Chains with Sluggish Transients",
  journal =      "Communication in Statistics, Stochastic Models",
  volume =       "13",
  pages =        "85--95",
  year =         "1997",
}

@Article{Stewart:1998:AM,
  author =       "G. W. Stewart",
  title =        "On the Adjugate Matrix",
  journal =      j-LAA,
  volume =       "283",
  pages =        "151--164",
  year =         "1998",
}

@Article{Stewart:1997:CFS,
  author =       "Michael Stewart",
  title =        "{Cholesky} Factorization of Semidefinite {Toeplitz}
                 Matrices",
  journal =      j-LAA,
  volume =       "254",
  pages =        "497--525",
  year =         "1997",
}

@Book{Stewart:2001:MAV,
  author =       "G. W. Stewart",
  title =        "Matrix Algorithms. {Volume II}: Eigensystems",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "2001",
  pages =        "xix+469",
  ISBN =         "0-89871-503-2",
}

@Article{Starke:1991:S,
  author =       "Gerhard Starke and Wilhelm Niethammer",
  title =        "{SOR} for {$AX-XB=C$}",
  journal =      j-LAA,
  volume =       "154--156",
  pages =        "355--375",
  year =         "1991",
}

@Book{Stoer:1972:ENM,
  author =       "Josef Stoer",
  title =        "Einf{\"u}hrung in die Numerische Mathematik {I}",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  year =         "1972",
  pages =        "ix+250",
  ISBN =         "0-387-05750-1",
}

@Article{Stone:1962:BPR,
  author =       "Betty Jane Stone",
  title =        "Best Possible Ratios of Certain Matrix Norms",
  journal =      j-NUM-MATH,
  volume =       "4",
  pages =        "114--116",
  year =         "1962",
}

@Article{Stoutemyer:1977:AEA,
  author =       "David R. Stoutemyer",
  title =        "Automatic Error Analysis Using Computer Algebraic
                 Manipulation",
  journal =      j-TOMS,
  volume =       "3",
  number =       "1",
  pages =        "26--43",
  year =         "1977",
}

@Article{Stoutemyer:1991:CMC,
  author =       "David R. Stoutemyer",
  title =        "Crimes and Misdemeanours in the Computer Algebra
                 Trade",
  journal =      j-NAMS,
  volume =       "38",
  number =       "7",
  pages =        "778--785",
  year =         "1991",
}

@Article{Strassen:1969:GEO,
  author =       "V. Strassen",
  title =        "Gaussian Elimination is Not Optimal",
  journal =      j-NUM-MATH,
  volume =       "13",
  pages =        "354--356",
  year =         "1969",
}

@Article{Strang:1986:PTM,
  author =       "Gilbert Strang",
  title =        "A Proposal for {Toeplitz} Matrix Calculations",
  journal =      "Studies in Applied Mathematics",
  volume =       "74",
  pages =        "171--176",
  year =         "1986",
}

@Book{Strang:1993:ILA,
  author =       "Gilbert Strang",
  title =        "Introduction to Linear Algebra",
  publisher =    pub-Wellesley,
  address =      pub-Wellesley:adr,
  year =         "1993",
  ISBN =         "0-9614088-5-5",
  pages =        "viii+472",
}

@Book{Stewart:1990:MPT,
  author =       "G. W. Stewart and {Ji-guang} Sun",
  title =        "Matrix Perturbation Theory",
  publisher =    pub-AP,
  address =      pub-AP:adr-L,
  year =         "1990",
  pages =        "xv+365",
  ISBN =         "0-12-670230-6",
}

@Article{Stummel:1980:REA,
  author =       "F. Stummel",
  title =        "Rounding Error Analysis of Elementary Numerical
                 Algorithms",
  journal =      j-COMPUTING,
  volume =       "Suppl. 2",
  pages =        "169--195",
  year =         "1980",
}

@Article{Stummel:1981:PTE,
  author =       "F. Stummel",
  title =        "Perturbation Theory For Evaluation Algorithms of
                 Arithmetic Expressions",
  journal =      j-MATH-COMP,
  volume =       "37",
  number =       "156",
  pages =        "435--473",
  year =         "1981",
}

@Article{Stummel:1982:OEE,
  author =       "F. Stummel",
  title =        "Optimal Error Estimates For {Gaussian} Elimination in
                 Floating-Point Arithmetic",
  journal =      j-ZAMM,
  volume =       "62",
  pages =        "T355--T357",
  year =         "1982",
}

@Article{Stummel:1985:FEAa,
  author =       "Friedrich Stummel",
  title =        "Forward Error Analysis of {Gaussian} Elimination,
                 {Part I}: {Error} and Residual Estimates",
  journal =      j-NUM-MATH,
  volume =       "46",
  pages =        "365--395",
  year =         "1985",
}

@Article{Stummel:1985:FEAb,
  author =       "Friedrich Stummel",
  title =        "Forward Error Analysis of {Gaussian} Elimination,
                 {Part II}: {Stability} Theorems",
  journal =      j-NUM-MATH,
  volume =       "46",
  pages =        "397--415",
  year =         "1985",
}

@Article{Stummel:1985:SOE,
  author =       "F. Stummel",
  title =        "Strict Optimal Error Estimates for {Gaussian}
                 Elimination",
  journal =      j-ZAMM,
  volume =       "65",
  pages =        "T405--T407",
  year =         "1985",
}

@Article{Steele:1990:HPF,
  author =       "Guy L. {Steele, Jr.} and Jon L. White",
  title =        "How to Print Floating-Point Numbers Accurately",
  journal =      "SIGPLAN Notices",
  volume =       "25",
  number =       "6",
  pages =        "112--126",
  year =         "1990",
}

@Article{Stoer:1962:TDM,
  author =       "Josef Stoer and C. Witzgall",
  title =        "Transformations by Diagonal Matrices in a Normed
                 Space",
  journal =      j-NUM-MATH,
  volume =       "4",
  pages =        "158--171",
  year =         "1962",
}

@Article{Sun:1995:BKR,
  author =       "Xiaobai Sun and Christian H. Bischof",
  title =        "A Basis-Kernel Representation of Orthogonal Matrices",
  journal =      j-SIMAX,
  volume =       "16",
  number =       "4",
  pages =        "1184--1196",
  year =         "1995",
}

@Article{Sun:1991:PBC,
  author =       "{Ji-guang} Sun",
  title =        "Perturbation Bounds for the {Cholesky} and {$QR$}
                 Factorizations",
  journal =      j-BIT,
  volume =       "31",
  pages =        "341--352",
  year =         "1991",
}

@Article{Sun:1992:REP,
  author =       "{Ji-guang} Sun",
  title =        "Rounding-Error and Perturbation Bounds for the
                 {Cholesky} and {$LDL^T$} Factorizations",
  journal =      j-LAA,
  volume =       "173",
  pages =        "77--97",
  year =         "1992",
}

@Article{Sun:1992:CPB,
  author =       "{Ji-guang} Sun",
  title =        "Componentwise Perturbation Bounds for Some Matrix
                 Decompositions",
  journal =      j-BIT,
  volume =       "32",
  number =       "4",
  pages =        "702--714",
  year =         "1992",
}

@Article{Sun:1995:NBP,
  author =       "{Ji-guang} Sun",
  title =        "A Note on Backward Perturbations for the {Hermitian}
                 Eigenvalue Problem",
  journal =      j-BIT,
  volume =       "35",
  pages =        "385--393",
  year =         "1995",
}

@Article{Sun:1995:PBQ,
  author =       "{Ji-guang} Sun",
  title =        "On Perturbation Bounds for the {QR} Factorization",
  journal =      j-LAA,
  volume =       "215",
  pages =        "95--111",
  year =         "1995",
}

@Article{Sun:1996:OBP,
  author =       "{Ji-guang} Sun",
  title =        "Optimal Backward Perturbation Bounds for the Linear
                 Least-Squares Problem with Multiple Right-Hand Sides",
  journal =      j-IMAJNA,
  volume =       "16",
  number =       "1",
  pages =        "1--11",
  year =         "1996",
}

@Article{Sun:1997:OBPa,
  author =       "{Ji-guang} Sun",
  title =        "On Optimal Backward Perturbation Bounds for the Linear
                 Least Squares Problem",
  journal =      j-BIT,
  volume =       "37",
  number =       "1",
  pages =        "179--188",
  year =         "1997",
}

@Article{Sun:1998:BSB,
  author =       "{Ji-guang} Sun",
  title =        "Bounds for the Structured Backward Errors of
                 {Vandermonde} Systems",
  journal =      j-SIMAX,
  volume =       "20",
  number =       "1",
  pages =        "45--59",
  year =         "1998",
}

@Book{sunM92,
  key =          "Sun",
  title =        "{SPARCompiler FORTRAN}: {Numerical} Computation
                 Guide",
  publisher =    "Sun Microsystems, Inc.",
  address =      "Mountain View, CA, USA",
  month =        oct,
  year =         "1992",
  note =         "Part No. 800-7097-11, Revision A",
}

@Book{sunM92a,
  key =          "Sun",
  title =        "{SPARCompiler FORTRAN} \textup{2.0.1}: {User's}
                 Guide",
  publisher =    "Sun Microsystems, Inc.",
  address =      "Mountain View, CA, USA",
  month =        oct,
  year =         "1992",
  note =         "Part No. 800-6552-11, Revision A",
}

@Article{Sun:1997:OBPb,
  author =       "{Ji-guang} Sun and Zheng Sun",
  title =        "Optimal Backward Perturbation Bounds for
                 Underdetermined Systems",
  journal =      j-SIMAX,
  volume =       "18",
  number =       "2",
  pages =        "393--402",
  year =         "1997",
}

@Article{Sleijpen:2000:DER,
  author =       "Gerard L. G. Sleijpen and Henk A. {Van der Vorst} and
                 Jan Modersitzki",
  title =        "Differences in the Effects of Rounding Errors in
                 {Krylov} Solvers for Symmetric Indefinite Linear
                 Systems",
  journal =      j-SIMAX,
  volume =       "22",
  number =       "3",
  pages =        "726--751",
  year =         "2000",
}

@Article{Swartzlander:1975:SLN,
  author =       "Earl E. {Swartzlander, Jr.} and Aristides G.
                 Alexopolous",
  title =        "The Sign/Logarithm Number System",
  journal =      j-IEEE-C,
  volume =       "C-24",
  number =       "12",
  pages =        "1238--1242",
  year =         "1975",
}

@InProceedings{Swann:1972:DSM,
  author =       "W. H. Swann",
  title =        "Direct Search Methods",
  booktitle =    "Numerical Methods for Unconstrained Optimization",
  editor =       "W. Murray",
  pages =        "13--28",
  publisher =    pub-AP # ", " # pub-AP:adr-L,
  year =         "1972",
}

@InProceedings{Swann:1974:COD,
  author =       "W. H. Swann",
  title =        "Constrained Optimization by Direct Search",
  booktitle =    "Numerical Methods for Constrained Optimization",
  editor =       "P. E. Gill and W. Murray",
  pages =        "191--217",
  publisher =    pub-AP # ", " # pub-AP:adr-L,
  year =         "1974",
}

@Book{Swartzlander:1980:CA,
  editor =       "Earl E. {Swartzlander, Jr.}",
  title =        "Computer Arithmetic",
  series =       "Benchmark Papers in Electrical Engineering and
                 Computer Science",
  volume =       "21",
  publisher =    "Dowden, Hutchinson and Ross",
  address =      "Stroudsburg, PA, USA",
  year =         "1980",
}

@Article{Sweeney:1965:AFP,
  author =       "D. W. Sweeney",
  title =        "An Analysis of Floating-Point Addition",
  journal =      "IBM Systems Journal",
  volume =       "4",
  pages =        "31--42",
  year =         "1965",
  note =         "Reprinted in
                 \cite[pp.~317--328]{Swartzlander:1980:CA}",
}

@Book{sylv04,
  key =          "Sylvester, James Joseph",
  title =        "The Collected Mathematical Papers of James Joseph
                 Sylvester",
  volume =       "1 (1837--1853)",
  publisher =    pub-CUP,
  year =         "1904",
  pages =        "xii+650",
}

@Article{Sylvester:1850:AAN,
  author =       "J. J. Sylvester",
  title =        "Additions to the Articles, ``{On a New Class of
                 Theorems},'' and ``{On Pascal's Theorem}''",
  journal =      "Philosophical Magazine",
  volume =       "37",
  pages =        "363--370",
  year =         "1850",
  note =         "Reprinted in \cite[pp.~1451--151]{sylv04}",
}

@Article{Sylvester:1851:RBM,
  author =       "J. J. Sylvester",
  title =        "On the Relation Between the Minor Determinants of
                 Linearly Equivalent Quadratic Functions",
  journal =      "Philosophical Magazine",
  volume =       "(Fourth Series) 1",
  pages =        "295--305",
  year =         "1851",
  note =         "Reprinted in \cite[pp.~241--250]{sylv04}",
}

@Article{Sylvester:1884:EM,
  author =       "J. J. Sylvester",
  title =        "Sur l'Equation en Matrices {$px=xq$}",
  journal =      "Comptes Rendus de l'Acad{\'e}mie des Sciences",
  pages =        "67--71 and 115--116",
  year =         "1884",
}

@Article{Tang:1981:BDV,
  author =       "W. P. Tang and G. H. Golub",
  title =        "The Block Decomposition of a {Vandermonde} Matrix and
                 its Applications",
  journal =      j-BIT,
  volume =       "21",
  pages =        "505--517",
  year =         "1981",
}

@InCollection{Taussky:1962:EFM,
  author =       "Olga Taussky and Marvin Marcus",
  title =        "Eigenvalues of Finite Matrices",
  editor =       "John Todd",
  booktitle =    "Survey of Numerical Analysis",
  publisher =    pub-MH,
  address =      pub-MH:adr,
  pages =        "279--313",
  year =         "1962",
}

@Article{Tang:1989:TDI,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Driven Implementation of the Exponential
                 Function in {IEEE} Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "15",
  number =       "2",
  pages =        "144--157",
  year =         "1989",
}

@Article{Tang:1990:AET,
  author =       "Ping Tak Peter Tang",
  title =        "Accurate and Efficient Testing of the Exponential and
                 Logarithm Functions",
  journal =      j-TOMS,
  volume =       "16",
  number =       "3",
  pages =        "185--200",
  year =         "1990",
}

@Article{Tang:1990:TDI,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Driven Implementation of the Logarithm Function
                 in {IEEE} Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "16",
  number =       "3",
  pages =        "378--400",
  year =         "1990",
}

@InProceedings{Tang:1991:TLA,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Lookup Algorithms for Elementary Functions and
                 Their Error Analysis",
  editor =       "Peter Kornerup and David W. Matula",
  booktitle =    "Proc. 10th IEEE Symposium on Computer Arithmetic",
  publisher =    "IEEE Computer Society Press, Los Alamitos, CA, USA",
  pages =        "232--236",
  year =         "1991",
}

@Article{Tang:1992:TDI,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Driven Implementation of the Expm1 Function in
                 {IEEE} Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "211--222",
  year =         "1992",
}

@Book{Taub:1963:JNC,
  editor =       "A. H. Taub",
  title =        "{John von Neumann} Collected Works",
  volume =       "V, {Design of Computers, Theory of Automata and
                 Numerical Analysis}",
  publisher =    "Pergamon",
  address =      "Oxford",
  pages =        "ix+784",
  year =         "1963",
}

@Article{Taussky:1949:RCC,
  author =       "Olga Taussky",
  title =        "A Remark Concerning the Characteristic Roots of the
                 Finite Segments of the {Hilbert} Matrix",
  journal =      "Quarterly Journal of Mathematics",
  volume =       "20",
  pages =        "80--83",
  year =         "1949",
}

@Article{Taussky:1988:HBT,
  author =       "Olga Taussky",
  title =        "How {I} Became a Torchbearer for Matrix Theory",
  journal =      j-AMM,
  volume =       "95",
  number =       "9",
  pages =        "801--812",
  month =        nov,
  year =         "1988",
}

@Article{Tasche:2001:WAC,
  author =       "Manfred Tasche and Hansmartin Zeuner",
  title =        "Worst and Average Case Roundoff Error Analysis for
                 {FFT}",
  journal =      j-BIT,
  volume =       "41",
  number =       "3",
  pages =        "563--581",
  year =         "2001",
}

@Book{Barrett:1994:TSL,
  author =       "Richard Barrett and Michael Berry and Tony F. Chan and
                 James Demmel and June Donato and Jack Dongarra and
                 Victor Eijkhout and Roldan Pozo and Charles Romine and
                 Henk {van der Vorst}",
  title =        "Templates for the Solution of Linear Systems:
                 {Building} Blocks for Iterative Methods",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "1994",
  pages =        "xiii+112",
  ISBN =         "0-89871-328-5",
}

@Article{Thacher:1961:ACP,
  author =       "Henry C. {Thacher, Jr.}",
  title =        "Algorithm 43: {Crout} With Pivoting {II}",
  journal =      j-CACM,
  volume =       "4",
  number =       "4",
  pages =        "176--177",
  year =         "1961",
}

@Book{Thisted:1988:ESC,
  author =       "Ronald A. Thisted",
  title =        "Elements of Statistical Computing: {Numerical}
                 Computation",
  publisher =    "Chapman and Hall",
  address =      "New York",
  year =         "1988",
}

@Book{Thompson:1942:GFC,
  author =       "D'Arcy Wentworth Thompson",
  title =        "On Growth and Form. {The} Complete Revised Edition",
  publisher =    pub-CUP,
  pages =        "viii+1116",
  year =         "1942",
  note =         "Reprinted by Dover, New York, 1992",
  ISBN =         "0-486-67135-6",
}

@Article{Tienari:1970:SMR,
  author =       "Martti Tienari",
  title =        "A Statistical Model of Roundoff Error for Varying
                 Length Floating-Point Arithmetic",
  journal =      j-BIT,
  volume =       "10",
  pages =        "355--365",
  year =         "1970",
}

@Article{Tisseur:2001:QEP,
  author =       "Fran\c{c}oise Tisseur and Karl Meerbergen",
  title =        "The Quadratic Eigenvalue Problem",
  journal =      j-SIREV,
  volume =       "43",
  number =       "2",
  pages =        "235--286",
  year =         "2001",
}

@Article{Tisseur:2001:NMF,
  author =       "Fran\c{c}oise Tisseur",
  title =        "Newton's Method in Floating Point Arithmetic and
                 Iterative Refinement of Generalized Eigenvalue
                 Problems",
  journal =      j-SIMAX,
  volume =       "22",
  number =       "4",
  pages =        "1038--1057",
  year =         "2001",
}

@InCollection{Todd:1954:CFS,
  author =       "John Todd",
  title =        "The Condition of the Finite Segments of the {Hilbert}
                 Matrix",
  editor =       "Olga Taussky",
  booktitle =    "Contributions to the Solution of Systems of Linear
                 Equations and the Determination of Eigenvalues",
  series =       "Applied Mathematics Series",
  number =       "39",
  publisher =    "National Bureau of Standards, United States Department
                 of Commerce",
  address =      "Washington, D. C.",
  pages =        "109--116",
  year =         "1954",
}

@Article{Todd:1961:CPC,
  author =       "John Todd",
  title =        "Computational Problems Concerning the {Hilbert}
                 Matrix",
  journal =      "J. Res. Nat. Bur. Standards--B",
  volume =       "65",
  number =       "1",
  pages =        "19--22",
  year =         "1961",
}

@InProceedings{Todd:1968:CN,
  author =       "J. Todd",
  title =        "On Condition Numbers",
  booktitle =    "Programmation en Math{\'e}matiques Num{\'e}riques,
                 Besan{\c{c}}on, 1966",
  series =       "{\'E}ditions Centre Nat. Recherche Sci., Paris",
  volume =       "7 (no. 165)",
  pages =        "141--159",
  year =         "1968",
}

@Book{Todd:1977:BNM,
  author =       "John Todd",
  title =        "Basic Numerical Mathematics, Vol.~2: Numerical
                 Algebra",
  publisher =    "Birkh{\"a}user, Basel, and Academic Press, New York",
  year =         "1977",
}

@Article{Toledo:1997:LRL,
  author =       "Sivan Toledo",
  title =        "Locality of Reference in {LU} Decomposition with
                 Partial Pivoting",
  journal =      j-SIMAX,
  volume =       "18",
  number =       "4",
  pages =        "1065--1081",
  year =         "1997",
}

@PhdThesis{Torczon:1989:MDS,
  author =       "Virginia J. Torczon",
  title =        "Multi-Directional Search: {A} Direct Search Algorithm
                 for Parallel Machines",
  school =       "Rice University",
  address =      "Houston, TX, USA",
  month =        may,
  year =         "1989",
  pages =        "vii+85",
}

@Article{Torczon:1991:CMS,
  author =       "Virginia J. Torczon",
  title =        "On the Convergence of the Multidirectional Search
                 Algorithm",
  journal =      j-SIOPT,
  volume =       "1",
  number =       "1",
  pages =        "123--145",
  year =         "1991",
}

@Article{Torczon:1997:CPS,
  author =       "Virginia J. Torczon",
  title =        "On the Convergence of Pattern Search Algorithms",
  journal =      j-SIOPT,
  volume =       "7",
  number =       "1",
  pages =        "1--25",
  year =         "1997",
}

@TechReport{Tornheim:1965:MTP,
  author =       "L. Tornheim",
  title =        "Maximum Third Pivot for {Gaussian} Reduction",
  institution =  "Calif. Research Corp.",
  address =      "Richmond, CA",
  type =         "Technical Report",
  year =         "1965",
  note =         "Cited in \cite{Cryer:1968:PSG}",
}

@Article{Toh:1994:PPP,
  author =       "Kim-Chuan Toh and Lloyd N. Trefethen",
  title =        "Pseudozeros of Polynomials and Pseudospectra of
                 Companion Matrices",
  journal =      j-NUM-MATH,
  volume =       "68",
  number =       "3",
  pages =        "403--425",
  year =         "1994",
}

@Article{Traub:1966:APU,
  author =       "J. F. Traub",
  title =        "Associated Polynomials and Uniform Methods for the
                 Solution of Linear Problems",
  journal =      j-SIREV,
  volume =       "8",
  number =       "3",
  pages =        "277--301",
  year =         "1966",
}

@Book{Trefethen:1997:NLA,
  author =       "Lloyd N. Trefethen and David {Bau III}",
  title =        "Numerical Linear Algebra",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "1997",
  pages =        "xii+361",
  ISBN =         "0-89871-361-7",
}

@Article{Trefethen:1985:TMG,
  author =       "Lloyd N. Trefethen",
  title =        "Three Mysteries of {Gaussian} Elimination",
  journal =      j-SIGNUM,
  volume =       "20",
  pages =        "2--5",
  year =         "1985",
}

@InProceedings{Trefethen:1990:ATN,
  author =       "Lloyd N. Trefethen",
  title =        "Approximation Theory and Numerical Linear Algebra",
  booktitle =    "Algorithms for Approximation II",
  editor =       "J. C Mason and M. G. Cox",
  publisher =    pub-CH # ", " # pub-CH:adr-L,
  pages =        "336--360",
  year =         "1990",
}

@InProceedings{Trefethen:1992:PM,
  author =       "Lloyd N. Trefethen",
  title =        "Pseudospectra of Matrices",
  booktitle =    "Numerical Analysis \textup{1991}, Proceedings of the
                 \textup{14}th Dundee Conference",
  series =       "Pitman Research Notes in Mathematics",
  volume =       "260",
  editor =       "D. F. Griffiths and G. A. Watson",
  pages =        "234--266",
  publisher =    pub-Longman-ST # ", " # pub-Longman-ST:adr,
  year =         "1992",
}

@Article{Trefethen:1992:DNA,
  author =       "Lloyd N. Trefethen",
  title =        "The Definition of Numerical Analysis",
  journal =      j-SIAM-NEWS,
  volume =       "25",
  pages =        "6 and 22",
  year =         "1992",
  month =        nov,
}

@InProceedings{Trefethen:1999:SP,
  author =       "Lloyd N. Trefethen",
  title =        "Spectra and Pseudospectra",
  booktitle =    "The Graduate Student's Guide to Numerical Analysis
                 '98",
  editor =       "Mark Ainsworth and Jeremy Levesley and Marco
                 Marletta",
  pages =        "217--250",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  year =         "1999",
}

@Article{Tropp:1984:FA,
  author =       "Henry S. Tropp",
  title =        "{FORTRAN} Anecdotes",
  journal =      j-AHC,
  volume =       "6",
  number =       "1",
  pages =        "59--64",
  year =         "1984",
}

@Article{Tropp:1984:OTE,
  author =       "Henry S. Tropp",
  title =        "Origin of the Term {\emph{Bit}}",
  journal =      j-AHC,
  volume =       "6",
  number =       "2",
  pages =        "152--155",
  year =         "1984",
}

@Article{Trefethen:1990:ACS,
  author =       "Lloyd N. Trefethen and Robert S. Schreiber",
  title =        "Average-Case Stability of {Gaussian} Elimination",
  journal =      j-SIMAX,
  volume =       "11",
  number =       "3",
  pages =        "335--360",
  year =         "1990",
}

@Article{Trefethen:1987:IPS,
  author =       "Lloyd N. Trefethen and Manfred R. Trummer",
  title =        "An Instability Phenomenon in Spectral Methods",
  journal =      j-SINUM,
  volume =       "24",
  number =       "5",
  pages =        "1008--1023",
  year =         "1987",
}

@Article{Tsao:1975:NIH,
  author =       "{Nai-kuan} Tsao",
  title =        "A Note on Implementing the {Householder}
                 Transformation",
  journal =      j-SINUM,
  volume =       "12",
  number =       "1",
  pages =        "53--58",
  year =         "1975",
}

@Article{Tsao:1983:SAE,
  author =       "{Nai-kuan} Tsao",
  title =        "A Simple Approach to the Error Analysis of
                 Division-Free Numerical Algorithms",
  journal =      j-IEEE-C,
  volume =       "C-32",
  number =       "4",
  pages =        "343--351",
  year =         "1983",
}

@Book{Turnbull:1932:ITC,
  author =       "H. W. Turnbull and A. C. Aitken",
  title =        "An Introduction to the Theory of Canonical Matrices",
  publisher =    "Blackie, London and Glasgow",
  year =         "1932",
  pages =        "xiii+200",
  note =         "Reprinted with appendix, 1952",
}

@Article{Tucker:2002:ROS,
  author =       "Warwick Tucker",
  title =        "A Rigorous {ODE} Solver and {Smale's} 14th Problem",
  journal =      j-FOCM,
  volume =       "2",
  number =       "1",
  pages =        "53--117",
  year =         "2002",
}

@Article{Turing:1936:CNA,
  author =       "A. M. Turing",
  title =        "On Computable Numbers, with an Application to the
                 {Entscheidungsproblem}",
  journal =      "Proc. London Math. Soc.",
  volume =       "42",
  pages =        "230--265",
  year =         "1936",
}

@TechReport{Turing:1945:PDM,
  author =       "A. M. Turing",
  title =        "Proposal for Development in the {Mathematics Division}
                 of an {Automatic Computing Engine} {(ACE)}",
  institution =  inst-NPL,
  address =      inst-NPL:adr,
  type =         "{Report E.882, Executive Committee}",
  year =         "1945",
  note =         "Reprinted in \cite[pp.~20-105]{Carpenter:1986:MTA} and
                 \cite[pp.~1--86]{Ince:1992:CWM}",
}

@Article{Turing:1948:REM,
  author =       "A. M. Turing",
  title =        "Rounding-Off Errors in Matrix Processes",
  journal =      j-QJMAM,
  volume =       "1",
  pages =        "287--308",
  year =         "1948",
  note =         "Reprinted in \cite{Britton:1992:CWM} with summary and
                 notes (including corrections)",
}

@Book{Turnbull:1929:TDM,
  author =       "H. W. Turnbull",
  title =        "The Theory of Determinants, Matrices, and Invariants",
  publisher =    "Blackie",
  address =      "London and Glasgow",
  year =         "1929",
  pages =        "xvi+338",
}

@Article{Turner:1982:DLS,
  author =       "Peter R. Turner",
  title =        "The Distribution of Leading Significant Digits",
  journal =      j-IMAJNA,
  volume =       "2",
  pages =        "407--412",
  year =         "1982",
}

@Article{Turner:1984:FRD,
  author =       "Peter R. Turner",
  title =        "Further Revelations on {L.S.D.}",
  journal =      j-IMAJNA,
  volume =       "4",
  pages =        "225--231",
  year =         "1984",
}

@Article{Turner:1991:WRR,
  author =       "Peter R. Turner",
  title =        "Will the ``Real'' Real Arithmetic Please Stand Up?",
  journal =      j-NAMS,
  volume =       "38",
  number =       "4",
  pages =        "298--304",
  year =         "1991",
}

@Article{Tyrtyshnikov:1991:CTM,
  author =       "Evgenij E. Tyrtyshnikov",
  title =        "Cauchy-{Toeplitz} Matrices and Some Applications",
  journal =      j-LAA,
  volume =       "149",
  pages =        "1--18",
  year =         "1991",
}

@Article{Urabe:1968:RED,
  author =       "Minoru Urabe",
  title =        "Roundoff Error Distribution in Fixed-Point
                 Multiplication and a Remark About the Rounding Rule",
  journal =      j-SINUM,
  volume =       "5",
  number =       "2",
  pages =        "202--210",
  year =         "1968",
}

@Book{Uspensky:1948:TE,
  author =       "J. V. Uspensky",
  title =        "Theory of Equations",
  publisher =    pub-MH,
  address =      pub-MH:adr,
  year =         "1948",
  pages =        "vii+353",
}

@Article{Vanderbei:1995:SQD,
  author =       "Robert J. Vanderbei",
  title =        "Symmetric Quasi-Definite Matrices",
  journal =      j-SIOPT,
  volume =       "5",
  number =       "1",
  pages =        "100--113",
  year =         "1995",
}

@Article{Loan:1979:NEM,
  author =       "Charles F. Van Loan",
  title =        "A Note on the Evaluation of Matrix Polynomials",
  journal =      j-IEEE-AC,
  volume =       "AC-24",
  number =       "2",
  pages =        "320--321",
  year =         "1979",
}

@Article{Loan:1985:MWE,
  author =       "Charles F. Van Loan",
  title =        "On the Method of Weighting for Equality-Constrained
                 Least-Squares Problems",
  journal =      j-SINUM,
  volume =       "22",
  number =       "5",
  pages =        "851--864",
  year =         "1985",
}

@Article{Loan:1987:ECE,
  author =       "Charles F. Van Loan",
  title =        "On Estimating the Condition of Eigenvalues and
                 Eigenvectors",
  journal =      j-LAA,
  volume =       "88/89",
  pages =        "715--732",
  year =         "1987",
}

@Book{Loan:1992:CFF,
  author =       "Charles F. Van Loan",
  title =        "Computational Frameworks for the Fast {Fourier}
                 Transform",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "1992",
  pages =        "xiii+273",
  ISBN =         "0-89871-285-8",
}

@Book{Rienen:2001:NMC,
  author =       "Ursula van Rienen",
  title =        "Numerical Methods in Computational Electrodynamics:
                 {Linear} Systems in Practical Applications",
  series =       "Lecture Notes in Computational Science and
                 Engineering",
  number =       "12",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  pages =        "xiii+375",
  ISBN =         "3-540-67629-5",
  year =         "2001",
}

@Article{Varah:1972:SBT,
  author =       "J. M. Varah",
  title =        "On the Solution of Block-Tridiagonal Systems Arising
                 From Certain Finite-Difference Equations",
  journal =      j-MATH-COMP,
  volume =       "26",
  number =       "120",
  pages =        "859--868",
  year =         "1972",
}

@Article{Varah:1975:LBS,
  author =       "J. M. Varah",
  title =        "A Lower Bound for the Smallest Singular Value of a
                 Matrix",
  journal =      j-LAA,
  volume =       "11",
  pages =        "3--5",
  year =         "1975",
}

@Article{Varah:1979:STM,
  author =       "J. M. Varah",
  title =        "On the Separation of Two Matrices",
  journal =      j-SINUM,
  volume =       "16",
  number =       "2",
  pages =        "216--222",
  year =         "1979",
}

@Article{Varga:1976:DDA,
  author =       "Richard S. Varga",
  title =        "On Diagonal Dominance Arguments for Bounding
                 {$\|A^{-1}\|_\infty$}",
  journal =      j-LAA,
  volume =       "14",
  pages =        "211--217",
  year =         "1976",
}

@Book{Varga:1990:SCM,
  author =       "Richard S. Varga",
  title =        "Scientific Computation on Mathematical Problems and
                 Conjectures",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "1990",
  ISBN =         "0-89871-257-2",
  pages =        "vi+122",
}

@Article{Vavasis:1989:GEP,
  author =       "S. A. Vavasis",
  title =        "Gaussian Elimination with Partial Pivoting is
                 {P}-Complete",
  journal =      "SIAM J. Disc. Math.",
  volume =       "2",
  pages =        "413--423",
  year =         "1989",
}

@Article{Verdonk:2001:PRIa,
  author =       "Brigitte Verdonk and Annie Cuyt and Dennis
                 Verschaeren",
  title =        "A Precision and Range Independent Tool for Testing
                 Floating-Point Arithmetic {I}: {Basic} Operations,
                 Square Root and Remainder",
  journal =      j-TOMS,
  volume =       "27",
  number =       "1",
  pages =        "92--118",
  year =         "2001",
}

@Article{Verdonk:2001:PRIb,
  author =       "Brigitte Verdonk and Annie Cuyt and Dennis
                 Verschaeren",
  title =        "A Precision and Range Independent Tool for Testing
                 Floating-Point Arithmetic {II}: {Conversions}",
  journal =      j-TOMS,
  volume =       "27",
  number =       "1",
  pages =        "119--140",
  year =         "2001",
}

@Article{Sluis:1969:CNE,
  author =       "A. van der Sluis",
  title =        "Condition Numbers and Equilibration of Matrices",
  journal =      j-NUM-MATH,
  volume =       "14",
  pages =        "14--23",
  year =         "1969",
}

@Article{Sluis:1970:CEP,
  author =       "A. van der Sluis",
  title =        "Condition, Equilibration and Pivoting in Linear
                 Algebraic Systems",
  journal =      j-NUM-MATH,
  volume =       "15",
  pages =        "74--86",
  year =         "1970",
}

@Article{Sluis:1975:SSL,
  author =       "A. van der Sluis",
  title =        "Stability of the Solutions of Linear Least Squares
                 Problems",
  journal =      j-NUM-MATH,
  volume =       "23",
  pages =        "241--254",
  year =         "1975",
}

@Article{vanVeldhuizen:1977:NPP,
  author =       "M. {van Veldhuizen}",
  title =        "A Note on Partial Pivoting and {Gaussian}
                 Elimination",
  journal =      j-NUM-MATH,
  volume =       "29",
  pages =        "1--10",
  year =         "1977",
}

@Article{Verzuh:1949:SSL,
  author =       "Frank M. Verzuh",
  title =        "The Solution of Simultaneous Linear Equations with the
                 Aid of the 602 Calculating Punch",
  journal =      j-MTAC,
  volume =       "3",
  pages =        "453--462",
  year =         "1949",
}

@InProceedings{Vignes:1986:ESM,
  author =       "J. Vignes and R. Alt",
  title =        "An Efficient Stochastic Method for Round-Off Error
                 Analysis",
  editor =       "Willard L. Miranker and Richard A. Toupin",
  booktitle =    "Accurate Scientific Computations, Proceedings, 1985",
  series =       "Lecture Notes in Computer Science",
  volume =       "235",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  pages =        "183--205",
  year =         "1986",
}

@InProceedings{Vitasek:1969:NSS,
  author =       "Emil Vitasek",
  title =        "The Numerical Stability in Solution of Differential
                 Equations",
  editor =       "J. Ll. Morris",
  booktitle =    "Conference on the Numerical Solution of Differential
                 Equations",
  series =       "Lecture Notes in Mathematics",
  volume =       "109",
  pages =        "87--111",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
}

@Article{Vitenko:1968:OAA,
  author =       "I. V. Viten'ko",
  title =        "Optimum Algorithms for Adding and Multiplying on
                 Computers with a Floating Point",
  journal =      "U.S.S.R. Computational Math. and Math. Phys.",
  volume =       "8",
  number =       "5",
  pages =        "183--195",
  year =         "1968",
}

@Article{Viswanath:1998:CNR,
  author =       "D. Viswanath and L. N. Trefethen",
  title =        "Condition Numbers of Random Triangular Matrices",
  journal =      j-SIMAX,
  volume =       "19",
  number =       "2",
  pages =        "564--581",
  year =         "1998",
}

@Article{Neumann:1947:NIM,
  author =       "John von Neumann and Herman H. Goldstine",
  title =        "Numerical Inverting of Matrices of High Order",
  journal =      j-BAMS,
  volume =       "53",
  pages =        "1021--1099",
  year =         "1947",
  note =         "Reprinted in \cite[pp.~479--557]{Taub:1963:JNC}",
}

@InProceedings{Vorst:1990:CBP,
  author =       "H. A. Van Der Vorst",
  title =        "The Convergence Behaviour of Preconditioned {CG} and
                 {CG-S} in the Presence of Rounding Errors",
  editor =       "Owe Axelsson and {Lily Yu.} Kolotilina",
  booktitle =    "Preconditioned Conjugate Gradient Methods",
  series =       "Lecture Notes in Mathematics",
  volume =       "1457",
  publisher =    pub-Springer # ", " # pub-Springer:adr-B,
  pages =        "126--136",
  year =         "1990",
}

@Article{Wachpress:1988:ISL,
  author =       "Eugene L. Wachpress",
  title =        "Iterative Solution of the {Lyapunov} Matrix Equation",
  journal =      "Appl. Math. Lett.",
  volume =       "1",
  number =       "1",
  pages =        "87--90",
  year =         "1988",
}

@Book{Wallis:1990:IFP,
  editor =       "Peter J. L. Wallis",
  title =        "Improving Floating-Point Programming",
  publisher =    "Wiley",
  address =      "London",
  year =         "1990",
}

@InProceedings{Wallis:1993:HM,
  author =       "W. D. Wallis",
  title =        "Hadamard Matrices",
  booktitle =    "Combinatorial and Graph-Theoretical Problems in Linear
                 Algebra",
  editor =       "Richard A. Brualdi and Shmuel Friedland and Victor
                 Klee",
  series =       "IMA Volumes in Mathematics and Its Applications",
  volume =       "50",
  pages =        "235--243",
  publisher =    pub-Springer # ", " # pub-Springer:adr-NY,
  year =         "1993",
  ISBN =         "0-387-94086-3",
}

@Article{Ward:1976:QAH,
  author =       "Robert C. Ward",
  title =        "The {QR} Algorithm and {Hyman's} Method on Vector
                 Computers",
  journal =      j-MATH-COMP,
  volume =       "30",
  number =       "133",
  pages =        "132--142",
  year =         "1976",
}

@Article{Wareeditor:1960:SCT,
  author =       "Willis H. {Ware, editor}",
  title =        "Soviet Computer Technology---1959",
  journal =      j-CACM,
  volume =       "3",
  number =       "3",
  pages =        "131--166",
  year =         "1960",
}

@Article{Watson:1991:AOS,
  author =       "G. A. Watson",
  title =        "An Algorithm for Optimal {$\ell_2$} Scaling of
                 Matrices",
  journal =      j-IMAJNA,
  volume =       "11",
  pages =        "481--492",
  year =         "1991",
}

@Book{Wedderburn:1934:LM,
  author =       "J. H. M. Wedderburn",
  title =        "Lectures on Matrices",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  series =       "American Mathematical Society Colloquium
                 Publications",
  volume =       "17",
  pages =        "vii+205",
  year =         "1934",
}

@Article{Wedin:1973:PTP,
  author =       "Per-{\AA}ke Wedin",
  title =        "Perturbation Theory for Pseudo-Inverses",
  journal =      j-BIT,
  volume =       "13",
  pages =        "217--232",
  year =         "1973",
}

@Article{Wei:1990:PLS,
  author =       "Musheng Wei",
  title =        "Perturbation of the Least Squares Problem",
  journal =      j-LAA,
  volume =       "141",
  pages =        "177--182",
  year =         "1990",
}

@Book{Wendroff:1966:TNA,
  author =       "Burton Wendroff",
  title =        "Theoretical Numerical Analysis",
  publisher =    "Academic Press",
  address =      "New York",
  pages =        "xi+239",
  year =         "1966",
}

@Article{Werner:1984:PIL,
  author =       "Wilhelm Werner",
  title =        "Polynomial Interpolation: {Lagrange} Versus {Newton}",
  journal =      j-MATH-COMP,
  volume =       "43",
  number =       "167",
  pages =        "205--217",
  year =         "1984",
}

@Book{Westlake:1968:HNM,
  author =       "Joan R. Westlake",
  title =        "A Handbook of Numerical Matrix Inversion and Solution
                 of Linear Equations",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  year =         "1968",
}

@Article{Wegert:1994:BNP,
  author =       "Elias Wegert and Lloyd N. Trefethen",
  title =        "From the {Buffon} Needle Problem to the {Kreiss}
                 Matrix Theorem",
  journal =      j-AMM,
  volume =       "101",
  number =       "2",
  pages =        "132--139",
  year =         "1994",
}

@Book{White:1997:INL,
  author =       "Michael White",
  title =        "{Isaac Newton}: {The} Last Sorcerer",
  publisher =    "Fourth Estate",
  address =      "London",
  year =         "1997",
  pages =        "402",
  ISBN =         "1-85702-706-X",
}

@Book{Williams:1989:EBC,
  editor =       "M. R. Williams and Martin Campbell-Kelly",
  title =        "The Early British Computer Conferences",
  series =       "Charles Babbage Institute Reprint Series for the
                 History of Computing",
  volume =       "14",
  publisher =    pub-MIT,
  address =      pub-MIT:adr,
  year =         "1989",
}

@Article{Wichmann:1989:TFS,
  author =       "B. A. Wichmann",
  title =        "Towards a Formal Specification of Floating Point",
  journal =      j-COMP-J,
  volume =       "32",
  pages =        "432--436",
  year =         "1989",
}

@Article{Wichmann:1992:NUF,
  author =       "B. A. Wichmann",
  title =        "A Note on the Use of Floating Point in Critical
                 Systems",
  journal =      j-COMP-J,
  volume =       "35",
  number =       "1",
  pages =        "41--44",
  year =         "1992",
}

@Article{Wijngaarden:1966:NAI,
  author =       "A. van Wijngaarden",
  title =        "Numerical Analysis as an Independent Science",
  journal =      j-BIT,
  volume =       "6",
  pages =        "66--81",
  year =         "1966",
}

@Article{Wilkinson:1948:ACE,
  author =       "J. H. Wilkinson",
  title =        "The {Automatic Computing Engine} at the {National
                 Physical Laboratory}",
  journal =      "Proc. Roy. Soc. London Ser. A",
  volume =       "195",
  pages =        "285--286",
  year =         "1948",
}

@TechReport{Wilkinson:1948:PRA,
  author =       "J. H. Wilkinson",
  title =        "Progress Report on the {Automatic Computing Engine}",
  institution =  "Mathematics Division, Department of Scientific and
                 Industrial Research, National Physical Laboratory",
  address =      inst-NPL:adr,
  type =         "Report",
  number =       "MA/17/1024",
  month =        apr,
  year =         "1948",
  pages =        "127",
}

@InProceedings{Wilkinson:1954:PA,
  author =       "J. H. Wilkinson",
  title =        "The {Pilot ACE}",
  booktitle =    "Automatic Digital Computation",
  publisher =    "Her Majesty's Stationery Office, London",
  pages =        "5--14",
  year =         "1954",
}

@InProceedings{Wilkinson:1954:LAP,
  author =       "J. H. Wilkinson",
  title =        "Linear Algebra on the {Pilot ACE}",
  booktitle =    "Automatic Digital Computation",
  publisher =    "Her Majesty's Stationery Office, London",
  year =         "1954",
}

@Article{Wilkinson:1955:UIM,
  author =       "J. H. Wilkinson",
  title =        "The Use of Iterative Methods for Finding the Latent
                 Roots and Vectors of Matrices",
  journal =      "Mathematical Tables and Other Aids to Computation",
  volume =       "9",
  pages =        "184--191",
  year =         "1955",
}

@Article{Wilkinson:1960:EAF,
  author =       "J. H. Wilkinson",
  title =        "Error Analysis of Floating-Point Computation",
  journal =      j-NUM-MATH,
  volume =       "2",
  pages =        "319--340",
  year =         "1960",
}

@Article{Wilkinson:1961:EAD,
  author =       "J. H. Wilkinson",
  title =        "Error Analysis of Direct Methods of Matrix Inversion",
  journal =      j-ACM,
  volume =       "8",
  pages =        "281--330",
  year =         "1961",
}

@Article{Wilkinson:1962:EAE,
  author =       "J. H. Wilkinson",
  title =        "Error Analysis of Eigenvalue Techniques Based on
                 Orthogonal Transformations",
  journal =      j-SIAM,
  volume =       "10",
  number =       "1",
  pages =        "162--195",
  year =         "1962",
}

@Book{Wilkinson:1963:REA,
  author =       "J. H. Wilkinson",
  title =        "Rounding Errors in Algebraic Processes",
  publisher =    "Notes on Applied Science No. 32, Her Majesty's
                 Stationery Office",
  address =      "London",
  year =         "1963",
  pages =        "vi+161",
  note =         "Also published by Prentice-Hall, Englewood Cliffs, NJ,
                 USA. Reprinted by Dover, New York, 1994",
  ISBN =         "0-486-67999-3",
}

@InCollection{Wilkinson:1963:PRF,
  author =       "J. H. Wilkinson",
  title =        "Plane-Rotations in Floating-Point Arithmetic",
  booktitle =    "Experimental Arithmetic, High Speed Computing and
                 Mathematics",
  series =       "Proceedings of Symposia in Applied Mathematics",
  volume =       "15",
  publisher =    pub-AMS # ", " # pub-AMS:adr,
  pages =        "185--198",
  year =         "1963",
}

@Book{Wilkinson:1965:AEP,
  author =       "J. H. Wilkinson",
  title =        "The Algebraic Eigenvalue Problem",
  publisher =    pub-OUP,
  year =         "1965",
  pages =        "xviii+662",
  ISBN =         "0-19-853403-5 (\hbk), 0-19-853418-3 (\pbk)",
}

@InProceedings{Wilkinson:1965:EAT,
  author =       "J. H. Wilkinson",
  title =        "Error Analysis of Transformations Based on the Use of
                 Matrices of the Form {$I-2ww^H$}",
  editor =       "Louis B. Rall",
  booktitle =    "Error in Digital Computation",
  volume =       "2",
  publisher =    pub-Wiley # ", " # pub-Wiley:adr,
  pages =        "77--101",
  year =         "1965",
}

@Book{Wilkinson:1967:BZW,
  author =       "J. H. Wilkinson",
  title =        "Bledy Zaokragle{\'n} w Procesach Algebraicznych",
  publisher =    "PWW",
  address =      "Warszawa",
  year =         "1967",
  note =         "Polish translation of \cite{Wilkinson:1963:REA}",
}

@InProceedings{Wilkinson:1968:PEA,
  author =       "J. H. Wilkinson",
  title =        "A Priori Error Analysis of Algebraic Processes",
  editor =       "I. G. Petrovsky",
  booktitle =    "Proc. International Congress of Mathematicians, Moscow
                 1966",
  publisher =    "Mir Publishers, Moscow",
  pages =        "629--640",
  year =         "1968",
}

@Book{Wilkinson:1969:R,
  author =       "J. H. Wilkinson",
  title =        "Rundungsfehler",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  year =         "1969",
  note =         "German translation of \cite{Wilkinson:1963:REA}",
}

@Book{Wilkinson:1970:AEP,
  author =       "J. H. Wilkinson",
  title =        "The Algebraic Eigenvalue Problem",
  publisher =    "Nauka",
  address =      "U.S.S.R. Academy of Sciences",
  year =         "1970",
  pages =        "564",
}

@Article{Wilkinson:1971:MEA,
  author =       "J. H. Wilkinson",
  title =        "Modern Error Analysis",
  journal =      j-SIREV,
  volume =       "13",
  number =       "4",
  pages =        "548--568",
  year =         "1971",
}

@Article{Wilkinson:1971:SCN,
  author =       "J. H. Wilkinson",
  title =        "Some Comments from a Numerical Analyst",
  journal =      j-ACM,
  volume =       "18",
  number =       "2",
  pages =        "137--147",
  year =         "1971",
}

@Article{Wilkinson:1974:NLA,
  author =       "J. H. Wilkinson",
  title =        "Numerical Linear Algebra on Digital Computers",
  journal =      j-IMA-BULL,
  volume =       "10",
  number =       "9/10",
  pages =        "354--356",
  year =         "1974",
}

@Article{Wilkinson:1974:CEA,
  author =       "J. H. Wilkinson",
  title =        "The Classical Error Analyses for the Solution of
                 Linear Systems",
  journal =      j-IMA-BULL,
  volume =       "10",
  number =       "5/6",
  pages =        "175--180",
  year =         "1974",
}

@InBook{Evans:1976:IJH,
  author =       "Christopher Evans",
  title =        "Interview with {J}. {H}. Wilkinson",
  series =       "Pioneers of Computing, 60-Minute Recordings of
                 Interviews",
  number =       "10",
  publisher =    "Science Museum, London",
  year =         "1976",
}

@InCollection{Wilkinson:1980:TWN,
  author =       "J. H. Wilkinson",
  title =        "Turing's Work at the {National Physical Laboratory}
                 and the Construction of {Pilot ACE}, {DEUCE}, and
                 {ACE}",
  editor =       "N. Metropolis and J. Howlett and Gian-Carlo Rota",
  booktitle =    "A History of Computing in the Twentieth Century: {A}
                 Collection of Essays",
  publisher =    "Academic Press",
  address =      "New York",
  year =         "1980",
  pages =        "101--114",
}

@InCollection{Wilkinson:1984:PP,
  author =       "James H. Wilkinson",
  title =        "The Perfidious Polynomial",
  editor =       "G. H. Golub",
  booktitle =    "Studies in Numerical Analysis",
  series =       "Studies in Mathematics",
  volume =       "24",
  publisher =    pub-MAA,
  address =      pub-MAA:adr,
  pages =        "1--28",
  year =         "1984",
}

@InCollection{Wilkinson:1985:SAE,
  author =       "J. H. Wilkinson",
  title =        "The State of the Art in Error Analysis",
  booktitle =    "NAG Newsletter 2/85",
  publisher =    "Numerical Algorithms Group",
  address =      "Oxford, UK",
  pages =        "5--28",
  month =        nov,
  year =         "1985",
}

@Article{Wilkinson:1986:EAR,
  author =       "J. H. Wilkinson",
  title =        "Error Analysis Revisited",
  journal =      j-IMA-BULL,
  volume =       "22",
  number =       "11/12",
  pages =        "192--200",
  year =         "1986",
}

@Article{Anonymous:1987:JW,
  author =       "Anonymous",
  title =        "{James Wilkinson} (1919--1986)",
  journal =      j-AHC,
  volume =       "9",
  number =       "2",
  pages =        "205--210",
  year =         "1987",
  note =         "From the introduction: ``A series of lightly edited
                 extracts from messages that were sent over various
                 computer networks during the period October 5,
                 1986--February 13, 1987''",
}

@Article{Wilkes:1997:AE,
  author =       "M. V. Wilkes",
  title =        "Arithmetic on the {EDSAC}",
  journal =      j-IEEE-AHC,
  volume =       "19",
  number =       "1",
  pages =        "13--15",
  year =         "1997",
}

@Article{Winograd:1968:NAI,
  author =       "S. Winograd",
  title =        "A New Algorithm for Inner Product",
  journal =      j-IEEE-C,
  volume =       "C-18",
  pages =        "693--694",
  year =         "1968",
}

@Article{Winograd:1971:MM,
  author =       "S. Winograd",
  title =        "On Multiplication of {$2 \times 2$} Matrices",
  journal =      j-LAA,
  volume =       "4",
  pages =        "381--388",
  year =         "1971",
}

@Article{Walden:1995:OBP,
  author =       "Bertil Wald{\'e}n and Rune Karlson and {Ji-guang}
                 Sun",
  title =        "Optimal Backward Perturbation Bounds for the Linear
                 Least Squares Problem",
  journal =      j-NLAA,
  volume =       "2",
  number =       "3",
  pages =        "271--286",
  year =         "1995",
}

@Article{Woehr:1997:CWK,
  author =       "Jack Woehr",
  title =        "A Conversation with {William Kahan}",
  journal =      "Dr. Dobb's Journal",
  volume =       "271",
  pages =        "18--32",
  year =         "1997",
  month =        nov,
}

@Article{Wolfe:1964:RTE,
  author =       "Jack M. Wolfe",
  title =        "Reducing Truncation Errors by Programming",
  journal =      j-CACM,
  volume =       "7",
  number =       "6",
  pages =        "355--356",
  year =         "1964",
}

@Book{Wolfram:1999:MB,
  author =       "Stephen Wolfram",
  title =        "The {Mathematica} Book",
  edition =      "Fourth",
  publisher =    "Wolfram Media, Champaign, IL, USA and " # pub-CUP # ",
                 " # pub-CUP:adr,
  year =         "1999",
  pages =        "xxvi+1470",
  ISBN =         "1-57955-004-5 (Wolfram), 0-521-64314-7 (Cambridge)",
}

@Article{wood58,
  author =       "Michael Woodger",
  title =        "The History and Present Use of Digital Computers at
                 the {National Physical Laboratory}",
  journal =      "Process Control and Automation",
  month =        nov,
  pages =        "437--442",
  note =         "Reprinted in \cite[pp.~125-140]{Carpenter:1986:MTA}.",
  year =         "1958",
}

@Article{Wozniakowski:1977:NSS,
  author =       "H. Wo{\'z}niakowski",
  title =        "Numerical Stability for Solving Nonlinear Equations",
  journal =      j-NUM-MATH,
  volume =       "27",
  pages =        "373--390",
  year =         "1977",
}

@Article{Wozniakowski:1977:NSC,
  author =       "H. Wo{\'z}niakowski",
  title =        "Numerical Stability of the {Chebyshev} Method for the
                 Solution of Large Linear Systems",
  journal =      j-NUM-MATH,
  volume =       "28",
  pages =        "191--209",
  year =         "1977",
}

@Article{Wozniakowski:1978:REA,
  author =       "H. Wo{\'z}niakowski",
  title =        "Roundoff-error analysis of iterations for large linear
                 systems",
  journal =      j-NUM-MATH,
  volume =       "30",
  pages =        "301--314",
  year =         "1978",
}

@Article{Wozniakowski:1980:REA,
  author =       "H. Wo{\'z}niakowski",
  title =        "Roundoff-Error Analysis of a New Class of
                 Conjugate-Gradient Algorithms",
  journal =      j-LAA,
  volume =       "29",
  pages =        "507--529",
  year =         "1980",
}

@Article{Whaley:2001:AEO,
  author =       "R. Clint Whaley and Antoine Petitet and Jack J.
                 Dongarra",
  title =        "Automated Empirical Optimization of Software and the
                 {ATLAS} Project",
  journal =      j-PAR-COMP,
  volume =       "27",
  number =       "1--2",
  pages =        "3--25",
  year =         "2001",
}

@Article{Wright:1992:IMC,
  author =       "Margaret H. Wright",
  title =        "Interior Methods for Constrained Optimization",
  journal =      "Acta Numerica",
  pages =        "341--407",
  year =         "1992",
}

@Article{Wright:1993:CPW,
  author =       "Stephen J. Wright",
  title =        "A Collection of Problems for Which {Gaussian}
                 Elimination with Partial Pivoting is Unstable",
  journal =      j-SISSC,
  volume =       "14",
  number =       "1",
  pages =        "231--238",
  year =         "1993",
}

@InProceedings{Wright:1996:DSM,
  author =       "Margaret H. Wright",
  title =        "Direct Search Methods: {Once} Scorned, Now
                 Respectable",
  booktitle =    "Numerical Analysis \textup{1995}, Proceedings of the
                 \textup{16}th Dundee Conference",
  series =       "Pitman Research Notes in Mathematics",
  volume =       "344",
  editor =       "D. F. Griffiths and G. A. Watson",
  pages =        "191--208",
  publisher =    pub-AWLongman # ", " # pub-AWLongman:adr,
  year =         "1996",
}

@Book{Wright:1997:PDI,
  author =       "Stephen J. Wright",
  title =        "Primal-Dual Interior-Point Methods",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  year =         "1997",
  pages =        "xx+289",
  ISBN =         "0-89871-382-X",
}

@Book{Wallis:1972:CRS,
  author =       "W. D. Wallis and Anne Penfold Street and Jennifer
                 Seberry Wallis",
  title =        "Combinatorics: {Room} Squares, Sum-Free Sets,
                 {Hadamard} Matrices",
  series =       "Lecture Notes in Mathematics",
  volume =       "292",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  pages =        "508",
  year =         "1972",
  ISBN =         "3-540-06035-9",
}

@Article{Weiss:1986:ACN,
  author =       "N. Weiss and G. W. Wasilkowski and H. Wo{\'z}niakowski
                 and M. Shub",
  title =        "Average Condition Number for Solving Linear
                 Equations",
  journal =      j-LAA,
  volume =       "83",
  pages =        "79--102",
  year =         "1986",
}

@Article{Yalamov:2000:ASS,
  author =       "Plamen Y. Yalamov",
  title =        "On the Almost Strong Stability of the Circular
                 Deconvolution Algorithm",
  journal =      j-SIMAX,
  volume =       "22",
  number =       "2",
  pages =        "358--363",
  year =         "2000",
}

@TechReport{Yalamov:1995:GSA,
  author =       "P. Y. Yalamov",
  title =        "Graphs and Stability of Algorithms",
  institution =  "University of Rousse",
  address =      "Bulgaria",
  type =         "Preprint",
  number =       "N27",
  year =         "1995",
  pages =        "17",
  month =        feb,
}

@Article{Yeung:1997:PAG,
  author =       "Man-Chung Yeung and Tony. F. Chan",
  title =        "Probabilistic Analysis of {Gaussian} Elimination
                 Without Pivoting",
  journal =      j-SIMAX,
  volume =       "18",
  number =       "2",
  pages =        "499--517",
  year =         "1997",
}

@Article{Yip:1986:NSS,
  author =       "E. L. Yip",
  title =        "A Note on the Stability of Solving a Rank-{$p$}
                 Modification of a Linear System by the
                 {Sherman--Morrison--Woodbury} Formula",
  journal =      j-SISSC,
  volume =       "7",
  number =       "3",
  pages =        "507--513",
  year =         "1986",
}

@Book{Young:1972:SNM,
  author =       "David M. Young and Robert T. Gregory",
  title =        "A Survey of Numerical Mathematics",
  volume =       "1",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  note =         "Reprinted by Dover, New York, 1988",
  year =         "1972",
  pages =        "x+492+appendices",
  ISBN =         "0-486-65691-8",
}

@Article{Yohe:1979:SIA,
  author =       "J. M. Yohe",
  title =        "Software for Interval Arithmetic: {A} Reasonably
                 Portable Package",
  journal =      j-TOMS,
  volume =       "5",
  number =       "1",
  pages =        "50--63",
  year =         "1979",
}

@Article{Yohe:1979:INA,
  author =       "J. M. Yohe",
  title =        "Implementing Nonstandard Arithmetics",
  journal =      j-SIREV,
  volume =       "21",
  number =       "1",
  pages =        "34--56",
  year =         "1979",
}

@Article{Yohe:1980:PSI,
  author =       "J. M. Yohe",
  title =        "Portable Software for Interval Arithmetic",
  journal =      j-COMPUTING,
  volume =       "Suppl. 2",
  pages =        "211--229",
  year =         "1980",
}

@Book{Young:1971:ISL,
  author =       "David M. Young",
  title =        "Iterative Solution of Large Linear Systems",
  publisher =    "Academic Press",
  address =      "New York",
  year =         "1971",
  pages =        "xxiv+570",
  ISBN =         "0-12-773050-8",
}

@Article{Young:1989:HOI,
  author =       "David M. Young",
  title =        "A Historical Overview of Iterative Methods",
  journal =      "Computer Physics Communications",
  volume =       "53",
  pages =        "1--17",
  year =         "1989",
}

@Article{Ypma:1983:ERE,
  author =       "Tjalling J. Ypma",
  title =        "The Effect of Rounding Errors on {Newton}-like
                 Methods",
  journal =      j-IMAJNA,
  volume =       "3",
  pages =        "109--118",
  year =         "1983",
}

@Article{Ypma:1983:FMZ,
  author =       "Tjalling J. Ypma",
  title =        "Finding a Multiple Zero by Transformations and
                 {Newton}-like Methods",
  journal =      j-SIREV,
  volume =       "25",
  number =       "3",
  pages =        "365--378",
  year =         "1983",
}

@Article{Ypma:1995:HDN,
  author =       "Tjalling J. Ypma",
  title =        "Historical Development of the {Newton--Raphson}
                 Method",
  journal =      j-SIREV,
  volume =       "37",
  number =       "4",
  pages =        "531--551",
  year =         "1995",
}

@Article{Yuval:1978:SPS,
  author =       "Gideon Yuval",
  title =        "A Simple Proof of {Strassen's} Result",
  journal =      j-INFPL,
  volume =       "7",
  number =       "6",
  pages =        "285--286",
  year =         "1978",
}

@Article{Zawilski:1991:NSC,
  author =       "Adam T. Zawilski",
  title =        "Numerical Stability of the Cyclic {Richardson}
                 Iteration",
  journal =      j-NUM-MATH,
  volume =       "60",
  pages =        "251--290",
  year =         "1991",
}

@Article{Zha:1993:CPA,
  author =       "Hongyuan Zha",
  title =        "A Componentwise Perturbation Analysis of the {$QR$}
                 Decomposition",
  journal =      j-SIMAX,
  volume =       "14",
  number =       "4",
  pages =        "1124--1131",
  year =         "1993",
}

@Article{Zha:1993:P,
  author =       "Hongyuan Zha",
  title =        "Problem 10312",
  journal =      j-AMM,
  volume =       "100",
  number =       "5",
  pages =        "499",
  year =         "1993",
}

@Article{Zha:1995:NCS,
  author =       "Hongyuan Zha and Zhenyue Zhang",
  title =        "A Note on Constructing a Symmetric Matrix with
                 Specified Diagonal Entries and Eigenvalues",
  journal =      j-BIT,
  volume =       "35",
  pages =        "448--452",
  year =         "1995",
}

@Article{Zielke:1986:RTM,
  author =       "G. Zielke",
  title =        "Report on Test Matrices for Generalized Inverses",
  journal =      j-COMPUTING,
  volume =       "36",
  pages =        "105--162",
  year =         "1986",
}

@Article{Zielke:1988:SRM,
  author =       "Gerhard Zielke",
  title =        "Some Remarks on Matrix Norms, Condition Numbers, and
                 Error Estimates for Linear Equations",
  journal =      j-LAA,
  volume =       "110",
  pages =        "29--41",
  year =         "1988",
}

@Article{Zietak:1985:PCI,
  author =       "K. Zi{\c{e}}tak",
  title =        "On a Particular Case of the Inconsistent Linear Matrix
                 Equation {$AX+YB=C$}",
  journal =      j-LAA,
  volume =       "66",
  pages =        "249--258",
  year =         "1985",
}

@Article{Ziv:1982:RDE,
  author =       "Abraham Ziv",
  title =        "Relative Distance---{An} Error Measure in Round-Off
                 Error Analysis",
  journal =      j-MATH-COMP,
  volume =       "39",
  number =       "160",
  pages =        "563--569",
  year =         "1982",
}

@Article{Ziv:1991:FEE,
  author =       "Abraham Ziv",
  title =        "Fast Evaluation of Elementary Mathematical Functions
                 with Correctly Rounded Last Bit",
  journal =      j-TOMS,
  volume =       "17",
  number =       "3",
  pages =        "410--423",
  year =         "1991",
}

@Article{Ziv:1995:CAE,
  author =       "Abraham Ziv",
  title =        "Converting Approximate Error Bounds into Exact Ones",
  journal =      j-MATH-COMP,
  volume =       "64",
  number =       "209",
  pages =        "265--277",
  year =         "1995",
}

@Article{Zlatev:1986:CNE,
  author =       "Zahari Zlatev and Jerzy Wasniewski and Kjeld
                 Schaumburg",
  title =        "Condition Number Estimators in a Sparse Matrix
                 Software",
  journal =      j-SISSC,
  volume =       "7",
  number =       "4",
  pages =        "1175--1189",
  year =         "1986",
}

@Book{Cox:1990:RNC,
  editor =       "M. G. Cox and S. J. Hammarling",
  title =        "Reliable Numerical Computation",
  publisher =    pub-OUP,
  year =         "1990",
  pages =        "xvi+339",
  ISBN =         "0-19-853564-3",
}

@Proceedings{harv46,
  key =          "Harvard",
  title =        "A Manual of Operation for the Automatic Sequence
                 Controlled Calculator",
  publisher =    pub-Harvard # ", " # pub-Harvard:adr,
  year =         "1946",
  note =         "Reprinted, with new foreword and introduction, Volume
                 8 in the Charles Babbage Institute Reprint Series for
                 the History of Computing, MIT Press, Cambridge, MA,
                 USA, 1985",
}

@Proceedings{harv48,
  key =          "Harvard",
  title =        "Proceedings of a Symposium on Large-Scale Digital
                 Calculating Machinery",
  series =       "The Annals of the Computation Laboratory of Harvard
                 University",
  volume =       "16",
  publisher =    pub-Harvard # ", " # pub-Harvard:adr,
  year =         "1948",
  note =         "Reprinted, with a new introduction by William Aspray,
                 Volume 7 in the Charles Babbage Institute Reprint
                 Series for the History of Computing, MIT Press,
                 Cambridge, MA, USA, 1985",
}

@Proceedings{Kulisch:1983:NAS,
  editor =       "Ulrich W. Kulisch and Willard L. Miranker",
  title =        "A New Approach to Scientific Computation",
  publisher =    pub-AP # ", " # pub-AP:adr-NY,
  year =         "1983",
  pages =        "xv+384",
  ISBN =         "0-12-428660-7",
}

@Book{Wilkinson:1971:LA,
  editor =       "J. H. Wilkinson and C. Reinsch",
  title =        "Linear Algebra",
  series =       "Handbook for Automatic Computation",
  volume =       "II",
  publisher =    pub-Springer,
  address =      pub-Springer:adr-B,
  year =         "1971",
  pages =        "ix+439",
  ISBN =         "3-540-05414-6",
}