%%% -*-BibTeX-*-
%%% /u/sy/beebe/tex/bib/gvl.bib, Mon Oct 15 18:20:08 1990
%%% Edit by Nelson H. F. Beebe <beebe at magna.math.utah.edu>
%%%
%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Nelson H. F. Beebe",
%%%     version         = "1.10",
%%%     date            = "07 May 1999",
%%%     time            = "14:01:42 MDT",
%%%     filename        = "gvl.bib",
%%%     address         = "Center for Scientific Computing
%%%                        University of Utah
%%%                        Department of Mathematics, 322 INSCC
%%%                        155 S 1400 E RM 233
%%%                        Salt Lake City, UT 84112-0090
%%%                        USA",
%%%     telephone       = "+1 801 581 5254",
%%%     FAX             = "+1 801 585 1640, +1 801 581 4148",
%%%     checksum        = "47976 8776 30547 253698",
%%%     email           = "beebe at math.utah.edu, beebe at acm.org,
%%%                        beebe at ieee.org (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "BibTeX, bibliography, matrix computations",
%%%     supported       = "yes",
%%%     docstring       = "This is the Golub/Van Loan Matrix
%%%                        Computations bibliography.
%%%
%%%                        At version 1.10, the year coverage looked
%%%                        like this:
%%%
%%%                             1846 (  1)     1894 (  0)     1942 (  0)
%%%                             1851 (  0)     1899 (  0)     1947 (  1)
%%%                             1853 (  0)     1901 (  1)     1949 (  0)
%%%                             1854 (  0)     1902 (  0)     1950 (  1)
%%%                             1855 (  0)     1903 (  0)     1951 (  1)
%%%                             1856 (  0)     1904 (  0)     1952 (  2)
%%%                             1859 (  0)     1907 (  0)     1955 (  4)
%%%                             1860 (  0)     1908 (  0)     1956 (  1)
%%%                             1861 (  0)     1909 (  1)     1957 (  2)
%%%                             1862 (  0)     1910 (  0)     1958 (  6)
%%%                             1863 (  0)     1911 (  0)     1959 (  5)
%%%                             1864 (  0)     1912 (  0)     1960 (  7)
%%%                             1865 (  0)     1913 (  0)     1961 (  7)
%%%                             1866 (  0)     1914 (  0)     1962 (  5)
%%%                             1867 (  0)     1915 (  0)     1963 (  6)
%%%                             1868 (  0)     1916 (  0)     1964 (  9)
%%%                             1869 (  0)     1917 (  0)     1965 ( 14)
%%%                             1870 (  0)     1918 (  0)     1966 ( 15)
%%%                             1871 (  0)     1919 (  0)     1967 ( 13)
%%%                             1872 (  0)     1920 (  0)     1968 ( 28)
%%%                             1873 (  1)     1921 (  0)     1969 ( 21)
%%%                             1874 (  0)     1922 (  0)     1970 ( 34)
%%%                             1875 (  0)     1923 (  0)     1971 ( 32)
%%%                             1876 (  0)     1924 (  0)     1972 ( 20)
%%%                             1877 (  0)     1925 (  0)     1973 ( 38)
%%%                             1878 (  0)     1926 (  0)     1974 ( 33)
%%%                             1879 (  0)     1927 (  0)     1975 ( 36)
%%%                             1880 (  0)     1928 (  0)     1976 ( 40)
%%%                             1881 (  0)     1929 (  0)     1977 ( 37)
%%%                             1882 (  0)     1930 (  0)     1978 ( 28)
%%%                             1883 (  0)     1931 (  1)     1979 ( 36)
%%%                             1884 (  0)     1932 (  0)     1980 ( 26)
%%%                             1885 (  0)     1933 (  0)     1981 ( 29)
%%%                             1886 (  0)     1934 (  0)     1982 ( 25)
%%%                             1887 (  0)     1935 (  0)     1983 ( 34)
%%%                             1888 (  0)     1936 (  0)     1984 ( 43)
%%%                             1889 (  0)     1937 (  0)     1985 ( 35)
%%%                             1890 (  0)     1938 (  0)     1986 ( 55)
%%%                             1891 (  0)     1939 (  1)     1987 ( 59)
%%%                             1892 (  0)     1940 (  0)     1988 ( 62)
%%%                             1893 (  0)     1941 (  0)     1989 (  5)
%%%
%%%                             Article:        673
%%%                             Book:            68
%%%                             InCollection:    37
%%%                             InProceedings:   16
%%%                             Manual:           3
%%%                             PhdThesis:       13
%%%                             Proceedings:      5
%%%                             TechReport:      46
%%%
%%%                             Total entries:  861
%%%
%%%                        The checksum field above contains a CRC-16
%%%                        checksum as the first value, followed by the
%%%                        equivalent of the standard UNIX wc (word
%%%                        count) utility output of lines, words, and
%%%                        characters.  This is produced by Robert
%%%                        Solovay's checksum utility.",
%%%  }
%%% ====================================================================

% From cs.cornell.edu!cv Fri Oct  5 10:00:53 PDT 1990
%
% Bibliography of the book "Matrix Computations", 2nd Edn.,
%   by Gene H. Golub & Charles F. Van Loan,
%   The Joh ns Hopkins University Press, Baltimore, Maryland 21218, 1989.
% The original bibliography prepared by Charles Van Loan
% (Computer Science, Cornell University, Ithaca, NY 14583)
% was corrected, edited and put in Bibtex format (September 1990)
% by Chris Paige and Clement Pellerin
% (Computer Science, McGill University, Montreal, PQ, Canada H3A 2A7).
% email any corrections to Charlie Van Loan at cv'AT SIGN'cs.cornell.edu
%
% This is the BibTeX file, store it as, for example,   gvl.bib
%
% USE: suppose you want the first reference only to appear, without
%      citing it.  Store in a file called say egcite.tex (without the %s):
%
%     \documentstyle[art12,fullpage]{article}
%     \begin{document}
%           \nocite{Aas71}
%        \bibliographystyle{unsrt}
%        \bibliography{gvl}
%     \end{document}
%
% Then run
%   latex egcite
%   bibtex egcite
%   latex egcite
%   latex egcite
% and use the resulting  egcite.dvi  to give the required output.
% Using \nocite{*} should give you all entries, but you may have to
% \nocite half of them, then the rest, to do this.
%
% Some entries have a \cite in the Note field because they appear
% both in a journal and in a book, Calling
%    latex; bibtex; latex; latex
% fails if you cite one of these entries.
% If this happens you should either call:
%    latex; bibtex; latex; bibtex; latex; latex
% or else you should \nocite{WilR71} at the beginning of your document
%        but don't use \bibliographystyle{unsrt} because WilR71 will come first

% Journals

% First the Full Name is given, then the abbreviation used in the AMS Math
% Reviews, with an indication if it could not be found there.
% Note the 2nd overwrites the 1st, so swap them if you want the full name.

 %{AMS}
 @String{AMSTrans = "American Mathematical Society Translations" }
 @String{AMSTrans = "Amer. Math. Soc. Transl." }
 @String{BullAMS = "Bulletin of the American Mathematical Society" }
 @String{BullAMS = "Bull. Amer. Math. Soc." }
 @String{ProcAMS = "Proceedings of the American Mathematical Society" }
 @String{ProcAMS = "Proc. Amer. Math. Soc." }
 @String{TransAMS = "Transactions of the American Mathematical Society" }
 @String{TransAMS = "Trans. Amer. Math. Soc." }

 %ACM
 @String{CACM = "Communications of the {ACM}" }
 @String{CACM = "Comm. {ACM}" }
 @String{CompServ = "{ACM} Computing Surveys" }
 @String{CompServ = "Comput. Surveys" }
 @String{JACM = "Journal of the {ACM}" }
 @String{JACM = "J. Assoc. Comput. Mach." }
 @String{ACMMathSoft = "{ACM} Transactions on Mathematical Software" }
 @String{ACMMathSoft = "{ACM} Trans. Math. Software" }
 @String{SIGNUM = "{ACM} {SIGNUM} Newsletter" }
 @String{SIGNUM = "{ACM} {SIGNUM} Newslett." }

 @String{AmerSocio = "American Journal of Sociology" }
 @String{AmerSocio = "Amer. J. Sociology" } % didn't find in AMS MR
 @String{AmerStatAssoc = "Journal of the American Statistical Association" }
 @String{AmerStatAssoc = "J. Amer. Statist. Assoc." }
 @String{ApplMathComp = "Applied Mathematics and Computation" }
 @String{ApplMathComp = "Appl. Math. Comput." }
 @String{AmerMathMonthly = "American Mathematical Monthly" }
 @String{AmerMathMonthly = "Amer. Math. Monthly" }
 @String{BIT = "{BIT}" }
 @String{BIT = "{BIT}" }
 @String{BritStatPsych = "British Journal of Mathematical and Statistical
          Psychology" }
 @String{BritStatPsych = "Brit. J. Math. Statist. Psych." }
 @String{CanMathBull = "Canadian Mathematical Bulletin" }
 @String{CanMathBull = "Canad. Math. Bull." }
 @String{CompApplMath = "Journal of Computational and Applied Mathematics" }
 @String{CompApplMath = "J. Comput. Appl. Math." }
 @String{CompPhys = "Journal of Computational Physics" }
 @String{CompPhys = "J. Comput. Phys." }
 @String{CompStruct = "Computers and Structures" }
 @String{CompStruct = "Comput. \& Structures" }
 @String{CompJour = "The Computer Journal" }
 @String{CompJour = "Comput. J." }
 @String{CompSysSci = "Journal of Computer and System Sciences" }
 @String{CompSysSci = "J. Comput. System Sci." }
 @String{Computing = "Computing" }
 @String{Computing = "Computing" }
 @String{ContempMath = "Contemporary Mathematics" }
 @String{ContempMath = "Contemp. Math." }
 @String{Crelle = "Crelle's Journal" }
 @String{Crelle = "Crelle's J." } % didn't find in AMS MR.
%% When will they get up to date?
 @String{GiornaleMath = "Giornale di Mathematiche" }
 @String{GiornaleMath = "Giorn. Mat." } % didn't find in AMS MR., ibid.

 %IEEE
 @String{Computer = "{IEEE} Computer" }
 @String{Computer = "{IEEE} Computer" }
 @String{IEEETransComp = "{IEEE} Transactions on Computers" }
 @String{IEEETransComp = "{IEEE} Trans. Comput." }
 @String{IEEETransAC = "{IEEE} Transactions on Automatic Control" }
 @String{IEEETransAC = "{IEEE} Trans. Automat. Control" }
 @String{IEEESpec = "{IEEE} Spectrum" }
 @String{IEEESpec = "{IEEE} Spectrum" } % didn't find in AMS MR
 @String{ProcIEEE = "Proceedings of the {IEEE}" }
 @String{ProcIEEE = "Proc. {IEEE}" } % didn't find in AMS MR
 @String{IEEETransAeroElec = "{IEEE} Transactions on Aerospace and Electronic
     Systems" }
 @String{IEEETransAeroElec = "{IEEE} Trans. Aerospace Electron. Systems" }

 @String{IMANumerAna = "{IMA} Journal of Numerical Analysis" }
 @String{IMANumerAna = "{IMA} J. Numer. Anal." }
 @String{InfProcLet = "Information Processing Letters" }
 @String{InfProcLet = "Inform. Process. Lett." }
 @String{InstMathApp = "Journal of the Institute of Mathematics and
     its Applications" }
 @String{InstMathApp = "J. Inst. Math. Appl." }
 @String{IntControl = "International Journal of Control" }
 @String{IntControl = "Internat. J. Control" }
 @String{IntNumerEng = "International Journal for Numerical Methods in
     Engineering" }
 @String{IntNumerEng = "Internat. J. Numer. Methods Engrg." }
 @String{IntSuper = "International Journal of Supercomputing Applications" }
 @String{IntSuper = "Internat. J. Supercomputing Applic." } % didn't find
%% in AMS MR
 @String{Kibernetika = "Kibernetika" }
 @String{Kibernetika = "Kibernetika" }
 @String{JResNatBurStand = "Journal of Research of the National Bureau
     of Standards" }
 @String{JResNatBurStand = "J. Res. Nat. Bur. Standards" }
 @String{LinAlgApp = "Linear Algebra and its Applications" }
 @String{LinAlgApp = "Linear Algebra Appl." }
 @String{MathAnaAppl = "Journal of Mathematical Analysis and Applications" }
 @String{MathAnaAppl = "J. Math. Anal. Appl." }
 @String{MathAnnalen = "Mathematische Annalen" }
 @String{MathAnnalen = "Math. Ann." }
 @String{MathPhys = "Journal of Mathematical Physics" }
 @String{MathPhys = "J. Math. Phys." }
 @String{MathComp = "Mathematics of Computation" }
 @String{MathComp = "Math. Comp." }
 @String{MathScand = "Mathematica Scandinavica" }
 @String{MathScand = "Math. Scand." }
 @String{TablesAidsComp = "Mathematical Tables and Other Aids to Computation" }
 @String{TablesAidsComp = "Math. Tables Aids Comput." }
 @String{NumerMath = "Numerische Mathematik" }
 @String{NumerMath = "Numer. Math." }
 @String{PacificMath = "Pacific Journal of Mathematics" }
 @String{PacificMath = "Pacific J. Math." }
 @String{ParDistComp = "Journal of Parallel and Distributed Computing" }
 @String{ParDistComp = "J. Parallel and Distrib. Comput." } % didn't find
%% in AMS MR
 @String{ParComputing = "Parallel Computing" }
 @String{ParComputing = "Parallel Comput." }
 @String{PhilMag = "Philosophical Magazine" }
 @String{PhilMag = "Philos. Mag." }
 @String{ProcNAS = "Proceedings of the National Academy of Sciences
                    of the USA" }
 @String{ProcNAS = "Proc. Nat. Acad. Sci. U. S. A." }
 @String{Psychometrika = "Psychometrika" }
 @String{Psychometrika = "Psychometrika" }
 @String{QuartMath = "Quarterly Journal of Mathematics, Oxford, Series (2)" }
 @String{QuartMath = "Quart. J. Math. Oxford Ser. (2)" }
 @String{QuartApplMath = "Quarterly of Applied Mathematics" }
 @String{QuartApplMath = "Quart. Appl. Math." }
 @String{RevueInstStat = "Review of the International Statisical Institute" }
 @String{RevueInstStat = "Rev. Inst. Internat. Statist." }

 %SIAM
 @String{JSIAM = "Journal of the Society for Industrial and Applied
     Mathematics" }
 @String{JSIAM = "J. Soc. Indust. Appl. Math." }
 @String{JSIAMB = "Journal of the Society for Industrial and Applied
     Mathematics, Series B, Numerical Analysis" }
 @String{JSIAMB = "J. Soc. Indust. Appl. Math. Ser. B Numer. Anal." }
 @String{SIAMAlgMeth = "{SIAM} Journal on Algebraic and Discrete Methods" }
 @String{SIAMAlgMeth = "{SIAM} J. Algebraic Discrete Methods" }
 @String{SIAMAppMath = "{SIAM} Journal on Applied Mathematics" }
 @String{SIAMAppMath = "{SIAM} J. Appl. Math." }
 @String{SIAMComp = "{SIAM} Journal on Computing" }
 @String{SIAMComp = "{SIAM} J. Comput." }
 @String{SIAMMatrix = "{SIAM} Journal on Matrix Analysis and Applications" }
 @String{SIAMMatrix = "{SIAM} J. Matrix Anal. Appl." }
 @String{SIAMNumAnal = "{SIAM} Journal on Numerical Analysis" }
 @String{SIAMNumAnal = "{SIAM} J. Numer. Anal." }
 @String{SIAMReview = "{SIAM} Review" }
 @String{SIAMReview = "{SIAM} Rev." }
 @String{SIAMSciStat = "{SIAM} Journal on Scientific and Statistical
     Computing" }
 @String{SIAMSciStat = "{SIAM} J. Sci. Statist. Comput." }

 @String{SoftPracExp = "Software Practice and Experience" }
 @String{SoftPracExp = "Software Prac. Experience" } % didn't find in AMS MR
 @String{StatScience = "Statistical Science" }
 @String{StatScience = "Statist. Sci." }
 @String{Techno = "Technometrics" }
 @String{Techno = "Technometrics" }
 @String{USSRCompMathPhys = "{USSR} Computational Mathematics and Mathematical
     Physics" }
 @String{USSRCompMathPhys = "{U. S. S. R.} Comput. Math. and Math. Phys." }
 @String{VLSICompSys = "Journal of {VLSI} and Computer Systems" }
 @String{VLSICompSys = "J. {VLSI} Comput. Syst." }
 @String{ZAngewMathMech = "Zeitschrift fur Angewandte Mathematik und
     Mechanik" }
 @String{ZAngewMathMech = "Z. Angew. Math. Mech." }
 @String{ZAngewMathPhys = "Zeitschrift fur Angewandte Mathematik und Physik" }
 @String{ZAngewMathPhys = "Z. Angew. Math. Phys." }

% Publishers

 @String{Academic = "Academic Press" }
 @String{ACMPress = "{ACM} Press" }
 @String{AdamHilger = "Adam Hilger" }
 @String{AddisonWesley = "Addison-Wesley" }
 @String{AllynBacon = "Allyn and Bacon" }
 @String{AMS = "American Mathematical Society" }
 @String{Birkhauser = "Birkha{\"u}ser" }
 @String{CambridgePress = "Cambridge University Press" }
 @String{Chelsea = "Chelsea" }
 @String{ClaredonPress = "Claredon Press" }
 @String{DoverPub = "Dover Publications" }
 @String{Eyolles = "Eyolles" }
 @String{HoltRinehartWinston = "Holt, Rinehart and Winston" }
 @String{Interscience = "Interscience" }
 @String{JohnsHopkinsPress = "The Johns Hopkins University Press" }
 @String{JohnWileySons = "John Wiley and Sons" }
 @String{Macmillan = "Macmillan" }
 @String{MathWorks = "The Math Works Inc." }
 @String{McGrawHill = "McGraw-Hill" }
 @String{NatBurStd = "National Bureau of Standards" }
 @String{NorthHolland = "North-Holland" }
 @String{OxfordPress = "Oxford University Press" }  %address Oxford or London?
 @String{PergamonPress = "Pergamon Press" }
 @String{PlenumPress = "Plenum Press" }
 @String{PrenticeHall = "Prentice-Hall" }
 @String{SIAMPub = "{SIAM} Publications" }
 @String{Springer = "Springer-Verlag" }
 @String{TexasPress = "University of Texas Press" }
 @String{VanNostrand = "Van Nostrand" }
 @String{WHFreeman = "W. H. Freeman and Co." }

%Entries

@Article{Aas71,
  author =       "J. O. Aasen",
  year =         "1971",
  title =        "On the Reduction of a Symmetric Matrix to Tridiagonal
                 Form",
  journal =      BIT,
  volume =       "11",
  pages =        "233--242",
}

@Article{Abd71,
  author =       "N. N. Abdelmalek",
  year =         "1971",
  title =        "Roundoff Error Analysis for {Gram}-{Schmidt} Method
                 and Solution of Linear Least Squares Problems",
  journal =      BIT,
  volume =       "11",
  pages =        "1345--1368",
}

@Article{Ada85,
  author =       "L. Adams",
  year =         "1985",
  title =        "{m}-step Preconditioned Conjugate Gradient Methods",
  journal =      SIAMSciStat,
  volume =       "6",
  pages =        "452--463",
}

@Article{AdaC84,
  author =       "L. Adams and T. Crockett",
  year =         "1984",
  title =        "Modelling Algorithm Execution Time on Processor
                 Arrays",
  journal =      Computer,
  volume =       "17",
  pages =        "38--43",
}

@Article{AlePP88,
  author =       "S. T. Alexander and C. T. Pan and R. J. Plemmons",
  year =         "1988",
  title =        "Analysis of a Recursive Least Squares Hyperbolic
                 Rotation Algorithm for Signal Processing",
  journal =      LinAlgApp,
  volume =       "98",
  pages =        "3--40",
}

@Article{All73,
  author =       "E. L. Allgower",
  year =         "1973",
  title =        "Exact Inverses of Certain Band Matrices",
  journal =      NumerMath,
  volume =       "21",
  pages =        "279--284",
}

@Techreport{AmiM65,
  author =       "A. R. Amir-Moez",
  year =         "1965",
  title =        "Extremal Properties of Linear Transformations and
                 Geometry of Unitary Spaces",
  institution =  "Texas Tech University",
  type =         "Mathematics Series",
  number =       "243",
  address =      "Lubbock, TX, USA",
}

@Article{AndK75,
  author =       "N. Anderson and I. Karasalo",
  year =         "1975",
  title =        "On Computing Bounds for the Least Singular Value of a
                 Triangular Matrix",
  journal =      BIT,
  volume =       "15",
  pages =        "1--4",
}

@Article{AndL73,
  author =       "P. Anderson and G. Loizou",
  year =         "1973",
  title =        "On the Quadratic Convergence of an Algorithm that
                 Diagonalizes a Complex Symmetric Matrix",
  journal =      InstMathApp,
  volume =       "12",
  pages =        "261--271",
}

@Article{AndL76,
  author =       "P. Anderson and G. Loizou",
  year =         "1976",
  title =        "A {Jacobi}-Type Method for Complex Symmetric Matrices
                 ({Handbook})",
  journal =      NumerMath,
  volume =       "25",
  pages =        "347--363",
}

@Article{AndOU87,
  author =       "T. W. Anderson and I. Olkin and L. G. Underhill",
  year =         "1987",
  title =        "Generation of Random Orthogonal Matrices",
  journal =      SIAMSciStat,
  volume =       "8",
  pages =        "625--629",
}

@Article{AndS83,
  author =       "G. Andrews and F. B. Schneider",
  year =         "1983",
  title =        "Concepts and Notations for Concurrent Programming",
  journal =      CompServ,
  volume =       "15",
  pages =        "1--43",
}

@Article{Arn51,
  author =       "W. E. Arnoldi",
  year =         "1951",
  title =        "The Principle of Minimized Iterations in the Solution
                 of the Matrix Eigenvalue Problem",
  journal =      QuartApplMath,
  volume =       "9",
  pages =        "17--29",
}

@Techreport{ArbG87,
  author =       "P. Arbenz and G. H. Golub",
  year =         "1987",
  title =        "On the Spectral Decomposition of {Hermitian} Matrices
                 Subject to Indefinite Low Rank Perturbations with
                 Applications",
  number =       "NA 87-07",
  institution =  "Computer Science, Stanford University",
  address =      "Stanford, CA, USA",
}

@Article{ArbGG88,
  author =       "P. Arbenz and W. Gander and G. H. Golub",
  year =         "1988",
  title =        "Restricted Rank Modification of the Symmetric
                 Eigenvalue Problem: Theoretical Considerations",
  journal =      LinAlgApp,
  volume =       "104",
  pages =        "75--95",
}

@Article{ArbG88,
  author =       "P. Arbenz and G. H. Golub",
  year =         "1988",
  title =        "On the Spectral Decomposition of {Hermitian} Matrices
                 Subject to Indefinite Low Rank Perturbations with
                 Applications",
  journal =      SIAMMatrix,
  volume =       "9",
  pages =        "40--58",
}

@Techreport{AriDD88,
  author =       "M. Arioli and J. W. Demmel and I. S. Duff",
  year =         "1988",
  title =        "Solving Sparse Linear Systems with Sparse Backward
                 Error",
  number =       "CSS 214",
  institution =  "Computer Science and Systems Division, AERE Harwell",
  address =      "Didcot, UK",
}

@Article{AriR85,
  author =       "M. Arioli and F. Romani",
  year =         "1985",
  title =        "Relations Between Condition Numbers and the
                 Convergence of the {Jacobi} Method for Real Positive
                 Definite Matrices",
  journal =      NumerMath,
  volume =       "46",
  pages =        "31--42",
}

@Article{AriL85,
  author =       "M. Arioli and A. Laratta",
  year =         "1985",
  title =        "Error Analysis of an Algorithm for Solving an
                 Underdetermined System",
  journal =      NumerMath,
  volume =       "46",
  pages =        "255--268",
}

@Techreport{ArmC76,
  author =       "E. S. Armstrong and A. K. Caglayan",
  year =         "1976",
  title =        "An Algorithm for the Weighting Matrices in the
                 Sample-Data Optimal Linear Regulator Problem",
  number =       "TN D-8372",
  institution =  "NASA",
}

@Article{ArnL84,
  author =       "W. F. Arnold and A. J. Laub",
  year =         "1984",
  title =        "Generalized Eigenproblem Algorithms and Software for
                 Algebraic {Riccati} Equations",
  journal =      ProcIEEE,
  volume =       "72",
  pages =        "1746--1754",
}

@Phdthesis{Ash87,
  author =       "S. F. Ashby",
  year =         "1987",
  title =        "Polynomial Preconditioning for Conjugate Gradient
                 Methods",
  school =       "Computer Science, University of Illinois",
  address =      "ILL",
}

@Techreport{AshMS88,
  author =       "S. Ashby and T. A. Manteuffel and P. E. Saylor",
  year =         "1988",
  title =        "A Taxonomy for Conjugate Gradient Methods",
  number =       "UCRL-98508",
  institution =  "Lawrence Livermore National Laboratory",
  address =      "Livermore, CA, USA",
}

@Article{Asp59,
  author =       "E. Asplund",
  year =         "1959",
  title =        "Inverse of Matrices {$\{a_{ij}\}$} Which Satisfy
                 {$a_{ij} = 0$, $j > i+p$}",
  journal =      MathScand,
  volume =       "7",
  pages =        "57--60",
}

@Incollection{Axe77,
  author =       "O. Axelsson",
  year =         "1977",
  title =        "Solution of Linear Systems of Equations: Iterative
                 Methods",
  booktitle =    "Sparse Matrix Techniques: {Copenhagen}, 1976",
  editor =       "V. A. Barker",
  publisher =    Springer,
  address =      "Berlin, Germany",
}

@Article{Axe80,
  author =       "O. Axelsson",
  year =         "1980",
  title =        "Conjugate Gradient Type Methods for Unsymmetric and
                 Inconsistent Systems of Linear Equations",
  journal =      LinAlgApp,
  volume =       "29",
  pages =        "1--66",
}

@Article{Axe85,
  author =       "O. Axelsson",
  year =         "1985",
  title =        "A Survey of Preconditioned Iterative Methods for
                 Linear Systems of Equations",
  journal =      BIT,
  volume =       "25",
  pages =        "166--187",
}

@Article{AxeP86,
  author =       "O. Axelsson and B. Polman",
  year =         "1986",
  title =        "On Approximate Factorization Methods for Block
                 Matrices Suitable for Vector and Parallel Processors",
  journal =      LinAlgApp,
  volume =       "77",
  pages =        "3--26",
}

@Article{Bai88a,
  author =       "Z. Bai",
  year =         "1988",
  title =        "Note on the Quadratic Convergence of {Kogbetliantz}'s
                 Algorithm for Computing the Singular Value
                 Decomposition",
  journal =      LinAlgApp,
  volume =       "104",
  pages =        "131--140",
}

@Article{Bai88b,
  author =       "D. Bailey",
  year =         "1988",
  title =        "Extra High Speed Matrix Multiplication on the
                 {Cray}-2",
  journal =      SIAMSciStat,
  volume =       "9",
  pages =        "603--607",
}

@Article{BarI75,
  author =       "I. Y. Bar-Itzhack",
  year =         "1975",
  title =        "Iterative Optimal Orthogonalization of the Strapdown
                 Matrix",
  journal =      IEEETransAeroElec,
  volume =       "11",
  pages =        "30--37",
}

@Article{Bar87,
  author =       "J. L. Barlow",
  year =         "1987",
  title =        "On the Smallest Positive Singular Value of an
                 {$M$}-Matrix with Applications to Ergodic {Markov}
                 Chains",
  journal =      SIAMAlgMeth,
  volume =       "7",
  pages =        "414--424",
}

@Article{BarNP88,
  author =       "J. L. Barlow and N. K. Nichols and R. J. Plemmons",
  year =         "1988",
  title =        "Iterative Methods for Equality Constrained Least
                 Squares Problems",
  journal =      SIAMSciStat,
  volume =       "9",
  pages =        "892--906",
}

@Article{BarS68,
  author =       "S. Barnett and C. Storey",
  year =         "1968",
  title =        "Some Applications of the {Lyapunov} Matrix Equation",
  journal =      InstMathApp,
  volume =       "4",
  pages =        "33--42",
}

@Article{BarP75a,
  author =       "I. Barrodale and C. Phillips",
  year =         "1975",
  title =        "Algorithm~495: Solution of an Overdetermined System
                 of Linear Equations in the {Chebychev} Norm",
  journal =      ACMMathSoft,
  volume =       "1",
  pages =        "264--270",
}

@Article{BarR73,
  author =       "I. Barrodale and F. D. K. Roberts",
  year =         "1973",
  title =        "An Improved Algorithm for Discrete {$L_{1}$} Linear
                 Approximation",
  journal =      SIAMNumAnal,
  volume =       "10",
  pages =        "839--848",
}

@Article{Bar71,
  author =       "R. H. Bartels",
  year =         "1971",
  title =        "A Stabilization of the Simplex Method",
  journal =      NumerMath,
  volume =       "16",
  pages =        "414--434",
}

@Article{BarCC78,
  author =       "R. H. Bartels and A. R. Conn and C. Charalambous",
  year =         "1978",
  title =        "On {Cline}'s Direct Method for Solving Overdetermined
                 Linear Systems in the {$L_{\infty}$} Sense",
  journal =      SIAMNumAnal,
  volume =       "15",
  pages =        "255--270",
}

@Article{BarCS78,
  author =       "R. H. Bartels and A. R. Conn and J. W. Sinclair",
  year =         "1978",
  title =        "Minimization Techniques for Piecewise Differentiable
                 Functions: The {$L_{1}$} Solution to an Overdetermined
                 Linear System",
  journal =      SIAMNumAnal,
  volume =       "15",
  pages =        "224--241",
}

@Article{BarS72,
  author =       "R. H. Bartels and G. W. Stewart",
  year =         "1972",
  title =        "Solution of the Equation {$AX + XB = C$}",
  journal =      CACM,
  volume =       "15",
  pages =        "820--826",
}

@Article{BarMW67,
  author =       "W. Barth and R. S. Martin and J. H. Wilkinson",
  year =         "1967",
  title =        "Calculation of the Eigenvalues of a Symmetric
                 Tridiagonal Matrix by the Method of Bisection",
  journal =      NumerMath,
  volume =       "9",
  pages =        "386--393",
  note =         "Also in \cite[pages 249--256]{WilR71}",
}

@Article{BarG76,
  author =       "V. Barwell and J. A. George",
  year =         "1976",
  title =        "A Comparison of Algorithms for Solving Symmetric
                 Indefinite Systems of Linear Equations",
  journal =      ACMMathSoft,
  volume =       "2",
  pages =        "242--251",
}

@Article{BatW73,
  author =       "K. J. Bathe and E. L. Wilson",
  year =         "1973",
  title =        "Solution Methods for Eigenvalue Problems in
                 Structural Mechanics",
  journal =      IntNumerEng,
  volume =       "6",
  pages =        "213--226",
}

@Article{BauF60a,
  author =       "F. L. Bauer and C. T. Fike",
  year =         "1960",
  title =        "Norms and Exclusion Theorems",
  journal =      NumerMath,
  volume =       "2",
  pages =        "137--144",
}

@Article{Bau63,
  author =       "F. L. Bauer",
  year =         "1963",
  title =        "Optimally Scaled Matrices",
  journal =      NumerMath,
  volume =       "5",
  pages =        "73--87",
}

@Article{Bau65,
  author =       "F. L. Bauer",
  year =         "1965",
  title =        "Elimination with Weighted Row Combinations for
                 Solving Linear Equations and Least Squares Problems",
  journal =      NumerMath,
  volume =       "7",
  pages =        "338--352",
  note =         "Also in \cite[pages 119--133]{WilR71}",
}

@Article{BauF60b,
  author =       "F. L. Bauer and C. T. Fike",
  year =         "1960",
  title =        "Norms and Exclusion Theorems",
  journal =      NumerMath,
  volume =       "2",
  pages =        "137--144",
}

@Article{BauR68,
  author =       "F. L. Bauer and C. Reinsch",
  year =         "1968",
  title =        "Rational {QR} Transformation with {Newton} Shift for
                 Symmetric Tridiagonal Matrices",
  journal =      NumerMath,
  volume =       "11",
  pages =        "264--272",
  note =         "Also in \cite[pages 257--265]{WilR71}",
}

@Incollection{BauR70,
  author =       "F. L. Bauer and C. Reinsch",
  year =         "1970",
  title =        "Inversion of Positive Definite Matrices by the
                 {Gauss}-{Jordan} Methods",
  booktitle =    "Handbook for Automatic Computation Vol. 2: Linear
                 Algebra",
  editor =       "J. H. Wilkinson and C. Reinsch",
  publisher =    Springer,
  address =      "New York, NY, USA",
  pages =        "45--49",
}

@Article{BavS79,
  author =       "C. Bavely and G. W. Stewart",
  year =         "1979",
  title =        "An Algorithm for Computing Reducing Subspaces by
                 Block Diagonalization",
  journal =      SIAMNumAnal,
  volume =       "16",
  pages =        "359--367",
}

@Book{Bel70,
  author =       "R. Bellman",
  year =         "1970",
  title =        "Introduction to Matrix Analysis",
  edition =      "second",
  publisher =    McGrawHill,
  address =      "New York, NY, USA",
}

@Article{Bel73,
  author =       "E. Beltrami",
  year =         "1873",
  title =        "Sulle Funzioni Bilineari",
  journal =      GiornaleMath,
  volume =       "11",
  pages =        "98--106",
}

@Article{BenS70,
  author =       "C. F. Bender and I. Shavitt",
  year =         "1970",
  title =        "An Iterative Procedure for the Calculation of the
                 Lowest Real Eigenvalue and Eigenvector of a
                 Non-Symmetric Matrix",
  journal =      CompPhys,
  volume =       "6",
  pages =        "146--149",
}

@Article{BerBI71,
  author =       "A. Berman and A. Ben-Israel",
  year =         "1971",
  title =        "A Note on Pencils of {Hermitian} of Symmetric
                 Matrices",
  journal =      SIAMAppMath,
  volume =       "21",
  pages =        "51--54",
}

@Article{BerV68,
  author =       "M. J. M. Bernal and J. H. Verner",
  year =         "1968",
  title =        "On Generalizations of the Theory of Consistent
                 Orderings for Successive Over-Relaxation Methods",
  journal =      NumerMath,
  volume =       "12",
  pages =        "215--222",
}

@Inproceedings{BerS86,
  author =       "M. Berry and A. Sameh",
  year =         "1986",
  title =        "Multiprocessor {Jacobi} Algorithms for Dense
                 Symmetric Eigenvalue and Singular Value
                 Decompositions",
  booktitle =    "Proceedings International Conference on Parallel
                 Processing",
  pages =        "433--440",
}

@Incollection{Bis87,
  author =       "C. H. Bischof",
  year =         "1987",
  title =        "The Two-Sided Block {Jacobi} Method on Hypercube
                 Architectures",
  booktitle =    "Hypercube Multiprocessors",
  editor =       "M. T. Heath",
  publisher =    SIAMPub,
  address =      "Philadelphia, PA, USA",
}

@Techreport{Bis88a,
  author =       "C. H. Bischof",
  year =         "1988",
  title =        "Computing the Singular Value Decomposition on a
                 Distributed System of Vector Processors",
  number =       "87 869",
  institution =  "Computer Science, Cornell University",
  address =      "Ithaca, NY, USA",
}

@Phdthesis{Bis88b,
  author =       "C. H. Bischof",
  year =         "1988",
  title =        "{QR} Factorization Algorithms for Coarse Grain
                 Distributed Systems",
  school =       "Computer Science, Cornell University",
  address =      "Ithaca, NY, USA",
}

@Incollection{BisL86,
  author =       "C. H. Bischof and C. Van Loan",
  year =         "1986",
  title =        "Computing the {SVD} on a Ring of Array Processors",
  booktitle =    "Large Scale Eigenvalue Problems",
  editor =       "J. Cullum and R. Willoughby",
  publisher =    NorthHolland,
  pages =        "51--66",
}

@Article{BisL87,
  author =       "C. H. Bischof and C. Van Loan",
  year =         "1987",
  title =        "The {WY} Representation for Products of {Householder}
                 Matrices",
  journal =      SIAMSciStat,
  volume =       "8",
  pages =        "s2--s13",
}

@Article{Bjo67a,
  author =       "{\AA}. Bj{\"o}rck",
  year =         "1967",
  title =        "Iterative Refinement of Linear Least Squares
                 Solution~{I}",
  journal =      BIT,
  volume =       "7",
  pages =        "257--278",
}

@Article{Bjo67b,
  author =       "{\AA}. Bj{\"o}rck",
  year =         "1967",
  title =        "Solving Linear Least Squares Problems by
                 {Gram}-{Schmidt} Orthogonalization",
  journal =      BIT,
  volume =       "7",
  pages =        "1--21",
}

@Article{Bjo68,
  author =       "{\AA}. Bj{\"o}rck",
  year =         "1968",
  title =        "Iterative Refinement of Linear Least Squares Solution
                 {II}",
  journal =      BIT,
  volume =       "8",
  pages =        "8--30",
}

@Article{Bjo84,
  author =       "{\AA}. Bj{\"o}rck",
  year =         "1984",
  title =        "A General Updating Algorithm for Constrained Linear
                 Least Squares Problems",
  journal =      SIAMSciStat,
  volume =       "5",
  pages =        "394--402",
}

@Article{Bjo87,
  author =       "{\AA}. Bj{\"o}rck",
  year =         "1987",
  title =        "Stability Analysis of the Method of Seminormal
                 Equations",
  journal =      LinAlgApp,
  volume =       "88/89",
  pages =        "31--48",
}

@Book{Bjo88,
  author =       "{\AA}. Bj{\"o}rck",
  year =         "1988",
  title =        "Solution of Equations in {$R^N$}",
  series =       "Least Squares Methods: Handbook of Numerical
                 Analysis",
  volume =       "1",
  publisher =    NorthHolland,
}

@Article{BjoB71,
  author =       "{\AA}. Bj{\"o}rck and C. Bowie",
  year =         "1971",
  title =        "An Iterative Algorithm for Computing the Best
                 Estimate of an Orthogonal Matrix",
  journal =      SIAMNumAnal,
  volume =       "8",
  pages =        "358--364",
}

@Article{BjoE73,
  author =       "{\AA}. Bj{\"o}rck and T. Elfving",
  year =         "1973",
  title =        "Algorithms for Confluent {Vandermonde} Systems",
  journal =      NumerMath,
  volume =       "21",
  pages =        "130--137",
}

@Article{BjoG67,
  author =       "{\AA}. Bj{\"o}rck and G. H. Golub",
  year =         "1967",
  title =        "Iterative Refinement of Linear Least Squares
                 Solutions by {Householder} Transformation",
  journal =      BIT,
  volume =       "7",
  pages =        "322--337",
}

@Article{BjoG73,
  author =       "{\AA}. Bj{\"o}rck and G. H. Golub",
  year =         "1973",
  title =        "Numerical Methods for Computing Angles Between Linear
                 Subspaces",
  journal =      MathComp,
  volume =       "27",
  pages =        "579--594",
}

@Article{BjoP70,
  author =       "{\AA}. Bj{\"o}rck and V. Pereyra",
  year =         "1970",
  title =        "Solution of {Vandermonde} Systems of Equations",
  journal =      MathComp,
  volume =       "24",
  pages =        "893--903",
}

@Book{BjoPS81,
  author =       "{\AA}. Bj{\"o}rck and R. J. Plemmons and H. Schneider",
  year =         "1981",
  title =        "Large-Scale Matrix Problems",
  publisher =    NorthHolland,
  address =      "New York, NY, USA",
}

@Article{BjoH83,
  author =       "{\AA}. Bj{\"o}rck and S. Hammarling",
  year =         "1983",
  title =        "A {Schur} Method for the Square Root of a Matrix",
  journal =      LinAlgApp,
  volume =       "52/53",
  pages =        "127--140",
}

@Article{Blu78,
  author =       "J. M. Blue",
  year =         "1978",
  title =        "A Portable {Fortran} Program to Find the {Euclidean}
                 Norm of a Vector",
  journal =      ACMMathSoft,
  volume =       "4",
  pages =        "15--23",
}

@Article{Boh75,
  author =       "Z. Bohte",
  year =         "1975",
  title =        "Bounds for Rounding Errors in the {Gaussian}
                 Elimination for Band Systems",
  journal =      InstMathApp,
  volume =       "16",
  pages =        "133--142",
}

@Article{BojBdH86,
  author =       "A. W. Bojanczyk and R. P. Brent and F. R. de Hoog",
  year =         "1986",
  title =        "{QR} Factorization of {Toeplitz} Matrices",
  journal =      NumerMath,
  volume =       "49",
  pages =        "81--94",
}

@Article{BojBDdH87,
  author =       "A. W. Bojanczyk and R. P. Brent and P. Van Dooren and
                 F. R. de Hoog",
  year =         "1987",
  title =        "A Note on Downdating the {Cholesky} Factorization",
  journal =      SIAMSciStat,
  volume =       "8",
  pages =        "210--221",
}

@Inproceedings{BolG78,
  author =       "D. L. Boley and G. H. Golub",
  year =         "1978",
  title =        "The Matrix Inverse Eigenvalue Problem for Periodic
                 {Jacobi} Matrices",
  booktitle =    "Proceedings Fourth Symposium on Basic Problems of
                 Numerical Mathematics, {Prague}",
  pages =        "63--76",
}

@Article{BolG84a,
  author =       "D. Boley and G. H. Golub",
  year =         "1984",
  title =        "A Modified Method for Restructuring Periodic {Jacobi}
                 Matrices",
  journal =      MathComp,
  volume =       "42",
  pages =        "143--150",
}

@Article{BooE68,
  author =       "J. Boothroyd and P. J. Eberlein",
  year =         "1968",
  title =        "Solution to the Eigenproblem by a Norm-Reducing
                 {Jacobi}-Type Method (Handbook)",
  journal =      NumerMath,
  volume =       "11",
  pages =        "1--12",
  note =         "Also in \cite[pages 327--338]{WilR71}",
}

@Article{BowMPW66,
  author =       "H. J. Bowdler and R. S. Martin and G. Peters and J. H.
                 Wilkinson",
  year =         "1966",
  title =        "Solution of Real and Complex Systems of Linear
                 Equations",
  journal =      NumerMath,
  volume =       "8",
  pages =        "217--234",
  note =         "Also in \cite[pages 93--110]{WilR71}",
}

@Article{BowMRW68,
  author =       "H. Bowdler and R. S. Martin and C. Reinsch and J. H.
                 Wilkinson",
  year =         "1968",
  title =        "The {QR} and {QL} Algorithms for Symmetric Matrices",
  journal =      NumerMath,
  volume =       "11",
  pages =        "293--306",
  note =         "Also in \cite[pages 227--240]{WilR71}",
}

@Book{BoyBD+87,
  author =       "J. Boyle and R. Butler and T. Disz and B. Glickfield
                 and E. Lusk and R. Overbeek and J. Patterson and R.
                 Stevens",
  year =         "1987",
  title =        "Portable Programs for Parallel Processors",
  publisher =    HoltRinehartWinston,
}

@Article{BraPS86a,
  author =       "J. H. Bramble and J. E. Pasciak and A. H. Schatz",
  year =         "1986",
  title =        "The construction of Preconditioners for Elliptic
                 Problems by Substructuring {I}",
  journal =      MathComp,
  volume =       "47",
  pages =        "103--134",
}

@Article{BraPS86b,
  author =       "J. H. Bramble and J. E. Pasciak and A. H. Schatz",
  year =         "1986",
  title =        "The construction of Preconditioners for Elliptic
                 Problems by Substructuring {II}",
  journal =      MathComp,
  volume =       "49",
  pages =        "1--17",
}

@Article{Bre70,
  author =       "R. P. Brent",
  year =         "1970",
  title =        "Error Analysis of Algorithms for Matrix
                 Multiplication and Triangular Decomposition Using
                 {Winograd}'s Identity",
  journal =      NumerMath,
  volume =       "16",
  pages =        "145--156",
}

@Article{BreL85,
  author =       "R. P. Brent and F. T. Luk",
  year =         "1985",
  title =        "The Solution of Singular Value and Symmetric
                 Eigenvalue Problems on Multiprocessor Arrays",
  journal =      SIAMSciStat,
  volume =       "6",
  pages =        "69--84",
}

@Article{BreLL85,
  author =       "R. P. Brent and F. T. Luk and C. Van Loan",
  year =         "1985",
  title =        "Computation of the Singular Value Decomposition Using
                 Mesh Connected Processors",
  journal =      VLSICompSys,
  volume =       "1",
  pages =        "242--270",
}

@Article{BroP75b,
  author =       "K. W. Brodlie and M. J. D. Powell",
  year =         "1975",
  title =        "On the Convergence of Cyclic {Jacobi} Methods",
  journal =      InstMathApp,
  volume =       "15",
  pages =        "279--287",
}

@Article{Bro73,
  author =       "C. G. Broyden",
  year =         "1973",
  title =        "Some Condition Number Bounds for the {Gaussian}
                 Elimination Process",
  journal =      InstMathApp,
  volume =       "12",
  pages =        "273--286",
}

@Article{Buc74,
  author =       "A. Buckley",
  year =         "1974",
  title =        "A Note on Matrices {$A = 1 + H$}, {$H$}
                 Skew-Symmetric",
  journal =      ZAngewMathMech,
  volume =       "54",
  pages =        "125--126",
}

@Article{Buc77,
  author =       "A. Buckley",
  year =         "1977",
  title =        "On the Solution of Certain Skew-Symmetric Linear
                 Systems",
  journal =      SIAMNumAnal,
  volume =       "14",
  pages =        "566--570",
}

@Article{Bun71a,
  author =       "J. R. Bunch",
  year =         "1971",
  title =        "Analysis of the Diagonal Pivoting Method",
  journal =      SIAMNumAnal,
  volume =       "8",
  pages =        "656--680",
}

@Article{Bun71b,
  author =       "J. R. Bunch",
  year =         "1971",
  title =        "Equilibration of Symmetric Matrices in the Max-Norm",
  journal =      JACM,
  volume =       "18",
  pages =        "566--572",
}

@Article{Bun74,
  author =       "J. R. Bunch",
  year =         "1974",
  title =        "Partial Pivoting Strategies for Symmetric Matrices",
  journal =      SIAMNumAnal,
  volume =       "11",
  pages =        "521--528",
}

@Incollection{Bun76,
  author =       "J. R. Bunch",
  year =         "1976",
  title =        "Block Methods for Solving Sparse Linear Systems",
  booktitle =    "Sparse Matrix Computations",
  editor =       "J. R. Bunch and D. J. Rose",
  publisher =    Academic,
  address =      "New York, NY, USA",
}

@Article{BunK77,
  author =       "J. R. Bunch and K. Kaufman",
  year =         "1977",
  title =        "Some Stable Methods for Calculating Inertia and
                 Solving Symmetric Linear Systems",
  journal =      MathComp,
  volume =       "31",
  pages =        "162--179",
}

@Article{BunKP76,
  author =       "J. R. Bunch and K. Kaufman and B. N. Parlett",
  year =         "1976",
  title =        "Decomposition of a Symmetric Matrix",
  journal =      NumerMath,
  volume =       "27",
  pages =        "95--109",
}

@Article{BunNS78,
  author =       "J. R. Bunch and C. P. Nielsen and D. C. Sorensen",
  year =         "1978",
  title =        "Rank-One Modification of the Symmetric Eigenproblem",
  journal =      NumerMath,
  volume =       "31",
  pages =        "31--48",
}

@Article{BunP71,
  author =       "J. R. Bunch and B. N. Parlett",
  year =         "1971",
  title =        "Direct Methods for Solving Symmetric Indefinite
                 Systems of Linear Equations",
  journal =      SIAMNumAnal,
  volume =       "8",
  pages =        "639--655",
}

@Book{BunR76,
  editor =       "J. R. Bunch and D. J. Rose",
  year =         "1976",
  title =        "Sparse Matrix Computations",
  publisher =    Academic,
  address =      "New York, NY, USA",
}

@Article{Bun82,
  author =       "J. R. Bunch",
  year =         "1982",
  title =        "A Note on the Stable Decomposition of Skew Symmetric
                 Matrices",
  journal =      MathComp,
  volume =       "158",
  pages =        "475--480",
}

@Article{Bun85,
  author =       "J. R. Bunch",
  year =         "1985",
  title =        "Stability of Methods for Solving {Toeplitz} Systems
                 of Equations",
  journal =      SIAMSciStat,
  volume =       "6",
  pages =        "349--364",
}

@Article{Bun87,
  author =       "J. R. Bunch",
  year =         "1987",
  title =        "The Weak and Strong Stability of Algorithms in
                 Numerical Linear Algebra",
  journal =      LinAlgApp,
  volume =       "88/89",
  pages =        "49--66",
}

@Techreport{Bun69,
  author =       "O. Buneman",
  year =         "1969",
  title =        "A Compact Non-Iterative {Poisson} Solver",
  institution =  "Institute for Plasma Research",
  address =      "Stanford University, Stanford, CA, USA",
  number =       "294",
}

@Article{BunG84b,
  author =       "A. Bunse-Gerstner",
  year =         "1984",
  title =        "An Algorithm for the Symmetric Generalized Eigenvalue
                 Problem",
  journal =      LinAlgApp,
  volume =       "58",
  pages =        "43--68",
}

@Article{BunGG88,
  author =       "A. Bunse-Gerstner and W. B. Gragg",
  year =         "1988",
  title =        "Singular Value Decompositions of Complex Symmetric
                 Matrices",
  journal =      CompApplMath,
  volume =       "21",
  pages =        "41--54",
}

@Article{Bus68,
  author =       "P. A. Businger",
  year =         "1968",
  title =        "Matrices Which Can be Optimally Scaled",
  journal =      NumerMath,
  volume =       "12",
  pages =        "346--348",
}

@Article{Bus69,
  author =       "P. A. Businger",
  year =         "1969",
  title =        "Reducing a Matrix to {Hessenberg} Form",
  journal =      MathComp,
  volume =       "23",
  pages =        "819--821",
}

@Article{Bus71a,
  author =       "P. A. Businger",
  year =         "1971",
  title =        "Monitoring the Numerical Stability of {Gaussian}
                 Elimination",
  journal =      NumerMath,
  volume =       "16",
  pages =        "360--361",
}

@Article{Bus71b,
  author =       "P. A. Businger",
  year =         "1971",
  title =        "Numerically Stable Deflation of {Hessenberg} and
                 Symmetric Tridiagonal Matrices",
  journal =      BIT,
  volume =       "11",
  pages =        "262--270",
}

@Article{BusG65,
  author =       "P. A. Businger and G. H. Golub",
  year =         "1965",
  title =        "Linear Least Squares Solutions by {Householder}
                 Transformations",
  journal =      NumerMath,
  volume =       "7",
  pages =        "269--276",
  note =         "Also in \cite[pages 111--118]{WilR71}",
}

@Article{BusG69,
  author =       "P. A. Businger and G. H. Golub",
  year =         "1969",
  title =        "Algorithm~358: Singular Value Decomposition of a
                 Complex Matrix",
  journal =      CACM,
  volume =       "12",
  pages =        "564--565",
}

@Article{BuzD74,
  author =       "B. L. Buzbee and F. W. Dorr",
  year =         "1974",
  title =        "The Direct Solution of the Biharmonic Equation on
                 Rectangular Regions and the {Poisson} Equation on
                 Irregular Regions",
  journal =      SIAMNumAnal,
  volume =       "11",
  pages =        "753--763",
}

@Article{BuzDGG71,
  author =       "B. L. Buzbee and F. W. Dorr and J. A. George and G. H.
                 Golub",
  year =         "1971",
  title =        "The Direct Solution of the Discrete {Poisson}
                 Equation on Irregular Regions",
  journal =      SIAMNumAnal,
  volume =       "8",
  pages =        "722--736",
}

@Article{BuzGN70,
  author =       "B. L. Buzbee and G. H. Golub and C. W. Nielson",
  year =         "1970",
  title =        "On Direct Methods for Solving {Poisson}'s Equations",
  journal =      SIAMNumAnal,
  volume =       "7",
  pages =        "627--656",
}

@Article{Buz86,
  author =       "B. L. Buzbee",
  year =         "1986",
  title =        "A Strategy for Vectorization",
  journal =      ParComputing,
  volume =       "3",
  pages =        "187--192",
}

@Phdthesis{Bye83,
  author =       "R. Byers",
  year =         "1983",
  title =        "{Hamiltonian} and Symplectic Algorithms for the
                 Algebraic {Riccati} Equation",
  school =       "Center for Applied Mathematics, Cornell University",
  address =      "Ithaca, NY, USA",
}

@Article{Bye84,
  author =       "R. Byers",
  year =         "1984",
  title =        "A {Linpack}-Style Condition Estimator for the
                 Equation {$AX - XB^{T} = C$}",
  journal =      IEEETransAC,
  volume =       "AC-29",
  pages =        "926--928",
}

@Article{Bye86,
  author =       "R. Byers",
  year =         "1986",
  title =        "A {Hamiltonian} {QR} Algorithm",
  journal =      SIAMSciStat,
  volume =       "7",
  pages =        "212--229",
}

@Article{ByeN87,
  author =       "R. Byers and S. G. Nash",
  year =         "1987",
  title =        "On the Singular Vectors of the {Lyapunov} Operator",
  journal =      SIAMAlgMeth,
  volume =       "8",
  pages =        "59--66",
}

@Inproceedings{Cal86,
  author =       "D. A. Calihan",
  year =         "1986",
  title =        "Block-Oriented, Local-Memory-Based Linear Equation
                 Solution on the {Cray}-2: Uniprocessor Algorithms",
  booktitle =    "Proceedings of the 1986 Conference on Parallel
                 Processing",
  pages =        "375--378",
}

@Article{ChaP77,
  author =       "S. P. Chan and B. N. Parlett",
  year =         "1977",
  title =        "Algorithm~517: A Program for Computing the Condition
                 Numbers of Matrix Eigenvalues without Computing
                 Eigenvectors",
  journal =      ACMMathSoft,
  volume =       "3",
  pages =        "186--203",
}

@Article{Cha82b,
  author =       "T. F. Chan",
  year =         "1982",
  title =        "An Improved Algorithm for Computing the Singular
                 Value Decomposition",
  journal =      ACMMathSoft,
  volume =       "8",
  pages =        "72--83",
}

@Article{Cha82a,
  author =       "T. F. Chan",
  year =         "1982",
  title =        "Algorithm~581: An Improved Algorithm for Computing
                 the Singular Value Decomposition",
  journal =      ACMMathSoft,
  volume =       "8",
  pages =        "84--88",
}

@Article{Cha84,
  author =       "T. F. Chan",
  year =         "1984",
  title =        "Deflated Decomposition Solutions of Nearly Singular
                 Systems",
  journal =      SIAMNumAnal,
  volume =       "21",
  pages =        "738--754",
}

@Article{Cha85,
  author =       "T. F. Chan",
  year =         "1985",
  title =        "On the Existence and Computation of {LU}
                 Factorizations with small pivots",
  journal =      MathComp,
  volume =       "42",
  pages =        "535--548",
}

@Article{Cha87,
  author =       "T. F. Chan",
  year =         "1987",
  title =        "Rank-Revealing {QR} Factorizations",
  journal =      LinAlgApp,
  volume =       "88/89",
  pages =        "67--82",
}

@Article{Cha88,
  author =       "T. F. Chan",
  year =         "1988",
  title =        "An Optimal Circulant Preconditioner for {Toeplitz}
                 Systems",
  journal =      SIAMSciStat,
  volume =       "9",
  pages =        "766--771",
}

@Article{ChaJZ83,
  author =       "T. F. Chan and K. R. Jackson and B. Zhu",
  year =         "1983",
  title =        "Alternating Direction Incomplete Factorizations",
  journal =      SIAMNumAnal,
  volume =       "20",
  pages =        "239--257",
}

@Article{ChaM88,
  author =       "H. Y. Chang and M.Salama",
  year =         "1988",
  title =        "A Parallel {Householder} Tridiagonalization Stratagem
                 Using Scattered Square Decomposition",
  journal =      ParComputing,
  volume =       "6",
  pages =        "297--312",
}

@Article{ChaVD88,
  author =       "J. P. Charlier and M. Vanbegin and P. Van Dooren",
  year =         "1988",
  title =        "On Efficient Implementation of {Kogbetliantz}'s
                 Algorithm for Computing the Singular Value
                 Decomposition",
  journal =      NumerMath,
  volume =       "52",
  pages =        "279--300",
}

@Article{ChaD87,
  author =       "J. P. Charlier and P. Van Dooren",
  year =         "1987",
  title =        "On {Kogbetliantz}'s {SVD} Algorithm in the Presence
                 of Clusters",
  journal =      LinAlgApp,
  volume =       "95",
  pages =        "135--160",
}

@Article{CheDH84,
  author =       "S. Chen and J. Dongarra and C. Hsuing",
  title =        "Multiprocessing Linear Algebra Algorithms on the
                 {Cray X-MP-2}: Experiences with Small Granularity",
  year =         "1984",
  journal =      ParDistComp,
  volume =       "1",
  pages =        "22--31",
}

@Article{CheKS78,
  author =       "S. Chen and D. Kuck and A. Sameh",
  year =         "1978",
  title =        "Practical Parallel Band Triangular Systems Solvers",
  journal =      ACMMathSoft,
  volume =       "4",
  pages =        "270--277",
}

@Article{CheS87,
  author =       "K. H. Cheng and S. Sahni",
  year =         "1987",
  title =        "{VLSI} Systems for Band Matrix Multiplication",
  journal =      ParComputing,
  volume =       "4",
  pages =        "239--258",
}

@Article{ChiMdP84,
  author =       " R. C. Chin and T. A. Manteuffel and J. de Pillis",
  year =         "1984",
  title =        "{ADI} as a Preconditioning for Solving the
                 Convection-Diffusion Equation",
  journal =      SIAMSciStat,
  volume =       "5",
  pages =        "281--299",
}

@Article{Cli73,
  author =       "A. K. Cline",
  year =         "1973",
  title =        "An Elimination Method for the Solution of Linear
                 Least Squares Problems",
  journal =      SIAMNumAnal,
  volume =       "10",
  pages =        "283--289",
}

@Article{Cli76a,
  author =       "A. K. Cline",
  year =         "1976",
  title =        "A Descent Method for the Uniform Solution to
                 Overdetermined Systems of Equations",
  journal =      SIAMNumAnal,
  volume =       "13",
  pages =        "293--309",
}

@Techreport{Cli76b,
  author =       "A. K. Cline",
  year =         "1976",
  title =        "Several observations on the Use of Conjugate Gradient
                 Methods",
  type =         "report",
  number =       "76-22",
  institution =  "ICASE, NASA Langley Research Center",
  address =      "Hampton, VA, USA",
}

@Article{CliR83,
  author =       "A. K. Cline and R. K. Rew",
  year =         "1983",
  title =        "A Set of Counter examples to Three Condition Number
                 Estimators",
  journal =      SIAMSciStat,
  volume =       "4",
  pages =        "602--611",
}

@Incollection{CliCL82,
  author =       "A. K. Cline and A. R. Conn and C. Van Loan",
  year =         "1982",
  title =        "Generalizing the {LINPACK} Condition Estimator",
  booktitle =    "Numerical Analysis",
  editor =       "J. P. Hennart",
  series =       "Lecture Notes in Mathematics 909",
  publisher =    Springer,
  address =      "New York, NY, USA",
}

@Incollection{CliGP76,
  author =       "A. K. Cline and G. H. Golub and G. W. Platzman",
  year =         "1976",
  title =        "Calculation of Normal Modes of Oceans Using a
                 {Lanczos} Method",
  booktitle =    "Sparse Matrix Computations",
  editor =       "J. R. Bunch and D. J. Rose",
  publisher =    Academic,
  address =      "New York, NY, USA",
  pages =        "409--426",
}

@Article{CliMSW79,
  author =       "A. K. Cline and C. B. Moler and G. W. Stewart and J. H.
                 Wilkinson",
  year =         "1979",
  title =        "An Estimate for the Condition Number of a Matrix",
  journal =      SIAMNumAnal,
  volume =       "16",
  pages =        "368--375",
}

@Article{CliP76,
  author =       "R. E. Cline and R. J. Plemmons",
  year =         "1976",
  title =        "{$L_{1}$}-Solutions to Underdetermined Linear
                 Systems",
  journal =      SIAMReview,
  volume =       "18",
  pages =        "92--106",
}

@Article{CliJ70,
  author =       "M. Clint and A. Jennings",
  year =         "1970",
  title =        "The Evaluation of Eigenvalues and Eigenvectors of
                 Real Symmetric Matrix by Simultaneous Iteration",
  journal =      CompJour,
  volume =       "13",
  pages =        "76--80",
}

@Article{CliJ71,
  author =       "M. Clint and A. Jennings",
  year =         "1971",
  title =        "A Simultaneous Iteration Method for the Unsymmetric
                 Eigenvalue Problem",
  journal =      InstMathApp,
  volume =       "8",
  pages =        "111--121",
}

@Article{Coc68,
  author =       "W. G. Cochrane",
  year =         "1968",
  title =        "Errors of Measurement in Statistics",
  journal =      Techno,
  volume =       "10",
  pages =        "637--666",
}

@Article{Coh74,
  author =       "A. M. Cohen",
  year =         "1974",
  title =        "A Note on Pivot Size in {Gaussian} Elimination",
  journal =      LinAlgApp,
  volume =       "8",
  pages =        "361--368",
}

@Book{ColL88,
  author =       "T. Coleman and C. Van Loan",
  year =         "1988",
  title =        "Handbook for Matrix Computations",
  publisher =    SIAMPub,
  address =      "Philadelphia, PA, USA",
}

@Article{ConG73,
  author =       "P. Concus and G. H. Golub",
  year =         "1973",
  title =        "Use of Fast Direct Methods for the Efficient
                 Numerical Solution of Nonseparable Elliptic Equations",
  journal =      SIAMNumAnal,
  volume =       "10",
  pages =        "1103--1120",
}

@Article{ConGM85,
  author =       "P. Concus and G. H. Golub and G. Meurant",
  year =         "1985",
  title =        "Block Preconditioning for the Conjugate Gradient
                 Method",
  journal =      SIAMSciStat,
  volume =       "6",
  pages =        "220--252",
}

@Incollection{ConGO76,
  author =       "P. Concus and G. H. Golub and D. P. O'Leary",
  year =         "1976",
  title =        "A Generalized Conjugate Gradient Method for the
                 Numerical Solution of Elliptic Partial Differential
                 Equations",
  booktitle =    "Sparse Matrix Computations",
  editor =       "J. R. Bunch and D. J. Rose",
  publisher =    Academic,
  address =      "New York, NY, USA",
}

@Book{CdB80,
  author =       "S. D. Conte and C. de Boor",
  year =         "1980",
  title =        "Elementary Numerical Analysis: An Algorithmic
                 Approach",
  publisher =    McGrawHill,
  address =      "New York, NY, USA",
  edition =      "third",
}

@Article{CopR79,
  author =       "J. E. Cope and B. W. Rust",
  year =         "1979",
  title =        "Bounds on Solutions of Systems with Inaccurate Data",
  journal =      SIAMNumAnal,
  volume =       "16",
  pages =        "950--963",
}

@Article{CosMR86,
  author =       "M. Costnard and J. M. Muller and Y. Robert",
  year =         "1986",
  title =        "Parallel {QR} Decomposition of a Rectangular Matrix",
  journal =      NumerMath,
  volume =       "48",
  pages =        "239--250",
}

@Article{CosMR88,
  author =       "M. Costnard and M. Marrakchi and Y. Robert",
  year =         "1988",
  title =        "Parallel {Gaussian} Elimination on an {MIMD}
                 Computer",
  journal =      ParComputing,
  volume =       "6",
  pages =        "275--296",
}

@Article{Cot74,
  author =       "R. W. Cottle",
  year =         "1974",
  title =        "Manifestations of the {Schur} Complement",
  journal =      LinAlgApp,
  volume =       "8",
  pages =        "189--211",
}

@Article{Cox81,
  author =       "M. G. Cox",
  year =         "1981",
  title =        "The Least Squares Solution of Overdetermined Linear
                 Equations having Band or Augmented Band Structure",
  journal =      IMANumerAna,
  volume =       "1",
  pages =        "3--22",
}

@Article{Cra73,
  author =       "C. R. Crawford",
  year =         "1973",
  title =        "Reduction of a Band Symmetric Generalized Eigenvalue
                 Problem",
  journal =      CACM,
  volume =       "16",
  pages =        "41--44",
}

@Article{Cra76,
  author =       "C. R. Crawford",
  year =         "1976",
  title =        "A Stable Generalized Eigenvalue Problem",
  journal =      SIAMNumAnal,
  volume =       "13",
  pages =        "854--860",
}

@Article{Cra86,
  author =       "C. R. Crawford",
  year =         "1986",
  title =        "Algorithm~646 {PDFIND}: A Routine to Find a Positive
                 Definite Linear Combination of Two Real Symmetric
                 Matrices",
  journal =      ACMMathSoft,
  volume =       "12",
  pages =        "278--282",
}

@Article{CraM83,
  author =       "C. R. Crawford and Y. S. Moon",
  year =         "1983",
  title =        "Finding a Positive Definite Linear Combination of Two
                 {Hermitian} Matrices",
  journal =      LinAlgApp,
  volume =       "51",
  pages =        "37--48",
}

@Article{Cry68,
  author =       "C. W. Cryer",
  year =         "1968",
  title =        "Pivot Size in {Gaussian} Elimination",
  journal =      NumerMath,
  volume =       "12",
  pages =        "335--345",
}

@Article{Cul78,
  author =       "J. Cullum",
  year =         "1978",
  title =        "The Simultaneous Computation of a Few of the
                 Algebraically Largest and Smallest Eigenvalues of a
                 Large Sparse Symmetric Matrix",
  journal =      BIT,
  volume =       "18",
  pages =        "265--275",
}

@Inproceedings{CulD74,
  author =       "J. Cullum and W. E. Donath",
  year =         "1974",
  title =        "A Block {Lanczos} Algorithm for Computing the {Q}
                 Algebraically Largest Eigenvalues and a Corresponding
                 Eigenspace of Large, Sparse Real Symmetric Matrices",
  booktitle =    "Proceedings of the 1974 IEEE Conference on Decision
                 and Control, {Phoenix, AZ}",
  pages =        "505--509",
}

@Techreport{CulW77,
  author =       "J. Cullum and R. A. Willoughby",
  year =         "1977",
  title =        "The Equivalence of the {Lanczos} and the Conjugate
                 Gradient Algorithms",
  number =       "RC-6903",
  institution =  "IBM",
  address =      "Yorktown Heights, NY, USA",
}

@Inproceedings{CulW79,
  author =       "J. Cullum and R. A. Willoughby",
  year =         "1979",
  title =        "{Lanczos} and the Computation in Specified Intervals
                 of the Spectrum of Large, Sparse Real Symmetric
                 Matrices",
  booktitle =    "Sparse Matrix Proceedings 1978",
  editor =       "I. S. Duff and G. W. Stewart",
  publisher =    SIAMPub,
  address =      "Philadelphia, PA, USA",
}

@Article{CulW80,
  author =       "J. Cullum and R. A. Willoughby",
  year =         "1980",
  title =        "The {Lanczos} Phenomena: An Interpretation Based on
                 Conjugate Gradient Optimization",
  journal =      LinAlgApp,
  volume =       "29",
  pages =        "63--90",
}

@Book{CulW85b,
  author =       "J. Cullum and R. A. Willoughby",
  year =         "1985",
  title =        "{Lanczos} Algorithms for Large Symmetric Eigenvalue
                 Computations, Volume 1: Theory",
  publisher =    Birkhauser,
  address =      "Boston, MA, USA",
}

@Book{CulW85a,
  author =       "J. Cullum and R. A. Willoughby",
  year =         "1985",
  title =        "{Lanczos} Algorithms for Large Symmetric Eigenvalue
                 Computations, Volume 2: Programs",
  publisher =    Birkhauser,
  address =      "Boston, MA, USA",
}

@Book{CulW86,
  editor =       "J. Cullum and R. A. Willoughby",
  year =         "1986",
  title =        "Large Scale Eigenvalue Problems",
  publisher =    NorthHolland,
}

@Article{CulWL83,
  author =       "J. Cullum and R. A. Willoughby and M. Lake",
  year =         "1983",
  title =        "A {Lanczos} Algorithm for Computing Singular Values
                 and Vectors of Large Matrices",
  journal =      SIAMSciStat,
  volume =       "4",
  pages =        "197--215",
}

@Article{Cup81,
  author =       "J. J. M. Cuppen",
  year =         "1981",
  title =        "A Divide and Conquer Method for the Symmetric
                 Eigenproblem",
  journal =      NumerMath,
  volume =       "36",
  pages =        "177--195",
}

@Article{Cup83,
  author =       "J. J. M. Cuppen",
  year =         "1983",
  title =        "The Singular Value Decomposition in Product Form",
  journal =      SIAMSciStat,
  volume =       "4",
  pages =        "216--222",
}

@Article{Cup84,
  author =       "J. J. M. Cuppen",
  year =         "1984",
  title =        "On Updating Triangular Products of {Householder}
                 Matrices",
  journal =      NumerMath,
  volume =       "45",
  pages =        "403--410",
}

@Incollection{Cut72,
  author =       "E. Cuthill",
  year =         "1972",
  title =        "Several Strategies for Reducing the Bandwidth of
                 Matrices",
  booktitle =    "Sparse Matrices and Their Applications",
  editor =       "D. J. Rose and R. A. Willoughby",
  publisher =    PlenumPress,
  address =      "New York, NY, USA",
}

@Phdthesis{Cyb78,
  author =       "G. Cybenko",
  year =         "1978",
  title =        "Error Analysis of Some Signal Processing Algorithms",
  school =       "Princeton University",
  address =      "Princeton, NJ, USA",
}

@Article{Cyb80,
  author =       "G. Cybenko",
  year =         "1980",
  title =        "The Numerical Stability of the {Levinson}-{Durbin}
                 Algorithm for {Toeplitz} Systems of Equations",
  journal =      SIAMSciStat,
  volume =       "1",
  pages =        "303--310",
}

@Article{Cyb84,
  author =       "G. Cybenko",
  year =         "1984",
  title =        "The Numerical Stability of the Lattice Algorithm for
                 Least Squares Linear Prediction Problems",
  journal =      BIT,
  volume =       "24",
  pages =        "441--455",
}

@Article{CybL86,
  author =       "G. Cybenko and C. Van Loan",
  year =         "1986",
  title =        "Computing the Minimum Eigenvalue of a Symmetric
                 Positive Definite {Toeplitz} Matrix",
  journal =      SIAMSciStat,
  volume =       "7",
  pages =        "123--131",
}

@Article{DanGKS76,
  author =       "J. Daniel and W. B. Gragg and L. Kaufman and G. W.
                 Stewart",
  year =         "1976",
  title =        "Reorthogonalization and Stable Algorithms for
                 Updating the {Gram}-{Schmidt} {QR} Factorization",
  journal =      MathComp,
  volume =       "30",
  pages =        "772--795",
}

@Article{Dav73,
  author =       "C. Davis",
  year =         "1973",
  title =        "Explicit Functional Calculus",
  journal =      LinAlgApp,
  volume =       "6",
  pages =        "193--199",
}

@Book{DatJK+88,
  author =       "B. N. Datta and C. R. Johnson and M. A. Kaashoek and R.
                 Plemmons and E. D. Sontag",
  year =         "1988",
  title =        "Linear Algebra in Signals, Systems, and Control",
  publisher =    SIAMPub,
  address =      "Philadelphia, PA, USA",
}

@Article{Dav86,
  author =       "G. J. Davis",
  year =         "1986",
  title =        "Column {LU} Pivoting on a Hypercube Multiprocessor",
  journal =      SIAMAlgMeth,
  volume =       "7",
  pages =        "538--550",
}

@Article{DavK70,
  author =       "C. Davis and W. M. Kahan",
  year =         "1970",
  title =        "The Rotation of Eigenvectors by a Perturbation {III}",
  journal =      SIAMNumAnal,
  volume =       "7",
  pages =        "1--46",
}

@Article{DaxK77,
  author =       "A. Dax and S. Kaniel",
  year =         "1977",
  title =        "Pivoting Techniques for Symmetric {Gaussian}
                 Elimination",
  journal =      NumerMath,
  volume =       "28",
  pages =        "221--242",
}

@Article{DayP88,
  author =       "J. Day and B. Peterson",
  year =         "1988",
  title =        "Growth in {Gaussian} Elimination",
  journal =      AmerMathMonthly,
  volume =       "95",
  pages =        "489--513",
}

@Techreport{DayD88,
  author =       "M. J. Dayde and I. S. Duff",
  year =         "1988",
  title =        "Use of Level-3 {BLAS} in {LU} Factorization on the
                 {Cray}-2, the {ETA-10P}, and the {IBM 3090-200/VF}",
  number =       "CSS-229",
  institution =  "Computer Science and Systems Division, Harwell
                 Laboratory",
  address =      "Oxon OX11 ORA, UK",
}

@Article{dBooP77,
  author =       "C. de Boor and A. Pinkus",
  year =         "1977",
  title =        "A Backward Error Analysis for Totally Positive Linear
                 Systems",
  journal =      NumerMath,
  volume =       "27",
  pages =        "485--490",
}

@Article{DeiNT83,
  author =       "P. Deift and T. Nande and C. Tome",
  year =         "1983",
  title =        "Ordinary Differential Equations and the Symmetric
                 Eigenvalue Problem",
  journal =      SIAMNumAnal,
  volume =       "20",
  pages =        "1--22",
}

@Article{DekT71,
  author =       "T. J. Dekker and J. F. Traub",
  year =         "1971",
  title =        "The Shifted {QR} Algorithm for {Hermitian} Matrices",
  journal =      LinAlgApp,
  volume =       "4",
  pages =        "137--154",
}

@Article{DelI86,
  author =       "J. M. Delosme and I. C. F. Ipsen",
  year =         "1986",
  title =        "Parallel Solution of Symmetric Positive Definite
                 Systems with Hyperbolic Rotations",
  journal =      LinAlgApp,
  volume =       "77",
  pages =        "75--112",
}

@Phdthesis{Dem83b,
  author =       "J. W. Demmel",
  year =         "1983",
  title =        "A Numerical Analyst's {Jordan} Canonical Form",
  school =       "Univ. of California at Berkeley",
  address =      "Berkeley, CA, USA",
}

@Article{Dem83a,
  author =       "J. W. Demmel",
  year =         "1983",
  title =        "The Condition Number of Equivalence Transformations
                 that Block Diagonalize Matrix Pencils",
  journal =      SIAMNumAnal,
  volume =       "20",
  pages =        "599--610",
}

@Article{Dem84,
  author =       "J. W. Demmel",
  year =         "1984",
  title =        "Underflow and the Reliability of Numerical Software",
  journal =      SIAMSciStat,
  volume =       "5",
  pages =        "887--919",
}

@Article{Dem87b,
  author =       "J. W. Demmel",
  year =         "1987",
  title =        "On the Distance to the Nearest Ill-Posed Problem",
  journal =      NumerMath,
  volume =       "51",
  pages =        "251--289",
}

@Article{Dem87a,
  author =       "J. W. Demmel",
  year =         "1987",
  title =        "A Counterexample for two Conjectures About Stability",
  journal =      IEEETransAC,
  volume =       "AC-32",
  pages =        "340--342",
}

@Article{Dem87d,
  author =       "J. W. Demmel",
  year =         "1987",
  title =        "Three Methods for Refining Estimates of Invariant
                 Subspaces",
  journal =      Computing,
  volume =       "38",
  pages =        "43--57",
}

@Article{Dem87c,
  author =       "J. W. Demmel",
  year =         "1987",
  title =        "The smallest perturbation of a submatrix which lowers
                 the rank and constrained total least squares problems",
  journal =      SIAMNumAnal,
  volume =       "24",
  pages =        "199--206",
}

@Article{Dem88,
  author =       "J. W. Demmel",
  year =         "1988",
  title =        "The Probability that a Numerical Analysis Problem is
                 Difficult",
  journal =      MathComp,
  volume =       "50",
  pages =        "449--480",
}

@Article{DemK87,
  author =       "J. W. Demmel and B. K{\aa}gstr{\"o}m",
  year =         "1987",
  title =        "Computing Stable Eigendecompositions of Matrix
                 Pencils",
  journal =      LinAlgApp,
  volume =       "88/89",
  pages =        "139--186",
}

@Article{DemK88,
  author =       "J. W. Demmel and B. K{\aa}gstr{\"o}m",
  year =         "1988",
  title =        "Accurate Solutions of Ill-Posed Problems in Control
                 Theory",
  journal =      SIAMMatrix,
  pages =        "126--145",
}

@Book{DenS83,
  author =       "J. E. Dennis and R. Schnabel",
  year =         "1983",
  title =        "Numerical Methods for Unconstrained Optimization and
                 Nonlinear Equations",
  publisher =    PrenticeHall,
  address =      "Englewood Cliffs, NJ, USA",
}

@Article{DenT87,
  author =       "J. E. Dennis Jr and K. Turner",
  year =         "1987",
  title =        "Generalized Conjugate Directions",
  journal =      LinAlgApp,
  volume =       "88/89",
  pages =        "187--209",
}

@Article{Des63,
  author =       "J. Descloux",
  year =         "1963",
  title =        "Bounds for the Spectral Norm of Functions of
                 Matrices",
  journal =      NumerMath,
  volume =       "5",
  pages =        "185--190",
}

@Article{DiaF76,
  author =       "M. A. Diamond and D. L. V. Ferreira",
  year =         "1976",
  title =        "On a Cyclic Reduction Method for the Solution of
                 {Poisson}'s Equation",
  journal =      SIAMNumAnal,
  volume =       "13",
  pages =        "54--70",
}

@Article{Don83,
  author =       "J. J. Dongarra",
  year =         "1983",
  title =        "Improving the Accuracy of Computed Singular Values",
  journal =      SIAMSciStat,
  volume =       "4",
  pages =        "712--719",
}

@Manual{DonBMS78,
  author =       "J. J. Dongarra and J. R. Bunch and C. B. Moler and G. W.
                 Stewart",
  year =         "1978",
  title =        "{LINPACK} Users Guide",
  publisher =    SIAMPub,
  address =      "Philadelphia, PA, USA",
}

@Techreport{DonCDH88,
  author =       "J. J. Dongarra and J. Du Croz and I. S. Duff and S.
                 Hammarling",
  year =         "1988",
  title =        "A Set of Level 3 {Basic} {Linear} {Algebra}
                 {Subprograms}",
  number =       "ANL-MCS-TM-88",
  institution =  "Argonne National Laboratory",
  address =      "Argonne, ILL",
}

@Article{DonCHH88b,
  author =       "J. J. Dongarra and J. Du Croz and S. Hammarling and
                 R. J. Hanson",
  year =         "1988",
  title =        "An Extended Set of {Fortran} {Basic} {Linear}
                 {Algebra} {Subprograms}",
  journal =      ACMMathSoft,
  volume =       "14",
  pages =        "1--17",
}

@Article{DonCHH88a,
  author =       "J. J. Dongarra and J. Du Croz and S. Hammarling and
                 R. J. Hanson",
  year =         "1988",
  title =        "Algorithm~656: An Extended Set of {Fortran} Basic
                 Linear Algebra Subprograms: Model Implementation and
                 Test Programs",
  journal =      ACMMathSoft,
  volume =       "14",
  pages =        "18--32",
}

@Article{DonE84,
  author =       "J. J. Dongarra and S. Eisenstat",
  year =         "1984",
  title =        "Squeezing the Most Out of an Algorithm in {Cray}
                 {Fortran}",
  journal =      ACMMathSoft,
  volume =       "10",
  pages =        "221--230",
}

@Article{DonGK84,
  author =       "J. J. Dongarra and F. G. Gustavson and A. Karp",
  year =         "1984",
  title =        "Implementing Linear Algebra Algorithms for Dense
                 Matrices on a Vector Pipeline Machine",
  journal =      SIAMReview,
  volume =       "26",
  pages =        "91--112",
}

@Techreport{DonHS87,
  author =       "J. J. Dongarra and S. Hammarling and D. C. Sorensen",
  year =         "1987",
  title =        "Block Reduction of Matrices to Condensed form for
                 Eigenvalue Computations",
  number =       "ANL-MCS-TM 99",
  institution =  "Argonne National Laboratory",
  address =      "Argonne, IL, USA",
}

@Article{DonH86,
  author =       "J. Dongarra and T. Hewitt",
  year =         "1986",
  title =        "Implementing Dense Linear Algebra Algorithms Using
                 Multitasking on the {Cray X-MP-4} (or Approaching the
                 Gigaflop)",
  journal =      SIAMSciStat,
  volume =       "7",
  pages =        "347--350",
}

@Article{DonH79,
  author =       "J. Dongarra and A. Hinds",
  year =         "1979",
  title =        "Unrolling Loops in {Fortran}",
  journal =      SoftPracExp,
  volume =       "9",
  pages =        "219--229",
}

@Article{DonH84,
  author =       "J. J. Dongarra and R. E. Hiromoto",
  year =         "1984",
  title =        "A Collection of Parallel Linear Equation Routines for
                 the {Denelcor} {HEP}",
  journal =      ParComputing,
  volume =       "1",
  pages =        "133--142",
}

@Article{DonKH86,
  author =       "J. J. Dongarra and L. Kaufman and S. Hammarling",
  year =         "1986",
  title =        "Squeezing the Most Out of Eigenvalue Solvers on High
                 Performance Computers",
  journal =      LinAlgApp,
  volume =       "77",
  pages =        "113--136",
}

@Article{DonMW83,
  author =       "J. J. Dongarra and C. B. Moler and J. H. Wilkinson",
  year =         "1983",
  title =        "Improving the Accuracy of Computed Eigenvalues and
                 Eigenvectors",
  journal =      SIAMNumAnal,
  volume =       "20",
  pages =        "23--46",
}

@Article{DonS84,
  author =       "J. J. Dongarra and A. H. Sameh",
  year =         "1984",
  title =        "On Some Parallel Banded System Solvers",
  journal =      ParComputing,
  volume =       "1",
  pages =        "223--235",
}

@Article{DonSS86,
  author =       "J. J. Dongarra and A. Sameh and D. Sorensen",
  year =         "1986",
  title =        "Implementation of Some Concurrent Algorithms for
                 Matrix Factorization",
  journal =      ParComputing,
  volume =       "3",
  pages =        "25--34",
}

@Article{DonS86,
  author =       "J. J. Dongarra and D. C. Sorensen",
  year =         "1986",
  title =        "Linear Algebra on High Performance Computers",
  journal =      ApplMathComp,
  volume =       "20",
  pages =        "57--88",
}

@Article{DonS87a,
  author =       "J. J. Dongarra and D. C. Sorensen",
  year =         "1987",
  title =        "A Fully Parallel Algorithm for the Symmetric
                 Eigenvalue Problem",
  journal =      SIAMSciStat,
  volume =       "8",
  pages =        "s139-s154",
}

@Article{DonS87b,
  author =       "J. J. Dongarra and D. C. Sorensen",
  year =         "1987",
  title =        "A Portable Environment for Developing Parallel
                 Programs",
  journal =      ParComputing,
  volume =       "5",
  pages =        "175--186",
}

@Article{Dor70,
  author =       "F. W. Dorr",
  year =         "1970",
  title =        "The Direct Solution of the Discrete {Poisson}
                 Equation on a Rectangle",
  journal =      SIAMReview,
  volume =       "12",
  pages =        "248--263",
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@Article{Dor73,
  author =       "F. W. Dorr",
  year =         "1973",
  title =        "The Direct Solution of the Discrete {Poisson}
                 Equation in {$O(n^{2})$} Operations",
  journal =      SIAMReview,
  volume =       "15",
  pages =        "412--415",
}

@Article{DubGR79,
  author =       "P. F. Dubois and A. Greenbaum and G. H. Rodrigue",
  year =         "1979",
  title =        "Approximating the Inverse of a Matrix for Use on
                 Iterative Algorithms on Vector Processors",
  journal =      Computing,
  volume =       "22",
  pages =        "257--268",
}

@Article{Dub70,
  author =       "A. Dubrulle",
  year =         "1970",
  title =        "A Short Note on the Implicit {QL} Algorithm for
                 Symmetric Tridiagonal Matrices",
  journal =      NumerMath,
  volume =       "15",
  pages =        "450",
}

@Article{DubMW68,
  author =       "A. Dubrulle and R. S. Martin and J. H. Wilkinson",
  year =         "1968",
  title =        "The Implicit {QL} Algorithm",
  journal =      NumerMath,
  volume =       "12",
  pages =        "377--383",
  note =         "Also in \cite[pages 241--248]{WilR71}",
}

@Article{Duf74,
  author =       "I. S. Duff",
  year =         "1974",
  title =        "Pivot Selection and Row Ordering in {Givens}
                 Reduction on Sparse Matrices",
  journal =      Computing,
  volume =       "13",
  pages =        "239--248",
}

@Article{Duf77,
  author =       "I. S. Duff",
  year =         "1977",
  title =        "A Survey of Sparse Matrix Research",
  journal =      ProcIEEE,
  volume =       "65",
  pages =        "500--535",
}

@Article{DufR75,
  author =       "I. S. Duff and J. K. Reid",
  year =         "1975",
  title =        "On the Reduction of Sparse Matrices to Condensed
                 Forms by Similarity Transformations",
  journal =      InstMathApp,
  volume =       "15",
  pages =        "217--224",
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@Article{DufR76,
  author =       "I. S. Duff and J. K. Reid",
  year =         "1976",
  title =        "A Comparison of Some Methods for the Solution of
                 Sparse Over-Determined Systems of Linear Equations",
  journal =      InstMathApp,
  volume =       "17",
  pages =        "267--280",
}

@Proceedings{DufS78,
  editor =       "I. S. Duff and G. W. Stewart",
  year =         "1978",
  title =        "Sparse Matrix Proceedings",
  publisher =    SIAMPub,
  address =      "Philadelphia, PA, USA",
}

@Book{DufER86,
  author =       "I. S. Duff and A. M. Erisman and J. K. Reid",
  year =         "1986",
  title =        "Direct Methods for Sparse Matrices",
  publisher =    OxfordPress,
}

@Book{DunS58,
  author =       "N. Dunford and J. Schwartz",
  year =         "1958",
  title =        "Linear Operators, Part {I}",
  publisher =    Interscience,
  address =      "New York, NY, USA",
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@Article{Dur60,
  author =       "J. Durbin",
  year =         "1960",
  title =        "The Fitting of Time Series Models",
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@Article{Ebe65,
  author =       "P. J. Eberlein",
  year =         "1965",
  title =        "On Measures of Non-normality for Matrices",
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  volume =       "72",
  pages =        "995--996",
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@Article{Ebe70,
  author =       "P. J. Eberlein",
  year =         "1970",
  title =        "Solution to the Complex Eigenproblem by a
                 Norm-Reducing {Jacobi}-Type Method",
  journal =      NumerMath,
  volume =       "14",
  pages =        "232--245",
  note =         "Also in \cite[pages 404--417]{WilR71}",
}

@Article{Ebe71,
  author =       "P. J. Eberlein",
  year =         "1971",
  title =        "On the Diagonalization of Complex Symmetric Matrices",
  journal =      InstMathApp,
  volume =       "7",
  pages =        "377--383",
}

@Incollection{Ebe87,
  author =       "P. J. Eberlein",
  year =         "1987",
  title =        "On Using the {Jacobi} Method on a Hypercube",
  booktitle =    "Hypercube Multiprocessors",
  editor =       "M. T. Heath",
  publisher =    SIAMPub,
  address =      "Philadelphia, PA, USA",
}

@Article{EckY39,
  author =       "C. Eckart and G. Young",
  year =         "1939",
  title =        "A Principal Axis Transformation for Non-{Hermitian}
                 Matrices",
  journal =      BullAMS,
  volume =       "45",
  pages =        "118--121",
}

@Article{EieN83,
  author =       "M. Eiermann and W. Niethammer",
  year =         "1983",
  title =        "On the Construction of Semi-iterative Methods",
  journal =      SIAMNumAnal,
  volume =       "20",
  pages =        "1153--1160",
}

@Article{Eis84,
  author =       "S. C. Eisenstat",
  year =         "1984",
  title =        "Efficient Implementation of a Class of Preconditioned
                 Conjugate Gradient Methods",
  journal =      SIAMSciStat,
  volume =       "2",
  pages =        "1--4",
}

@Article{EisHHR88,
  author =       "S.C Eisenstat and M. T. Heath and C. S. Henkel and C. H.
                 Romine",
  year =         "1988",
  title =        "Modified Cyclic Algorithms for Solving Triangular
                 Systems on Distributed Memory Multiprocessors",
  journal =      SIAMSciStat,
  volume =       "9",
  pages =        "589--600",
}

@Article{Eld77a,
  author =       "L. Eld{\`e}n",
  year =         "1977",
  title =        "Algorithms for the Regularization of Ill-Conditioned
                 Least Squares Problems",
  journal =      BIT,
  volume =       "17",
  pages =        "134--145",
}

@Phdthesis{Eld77b,
  author =       "L. Eld{\`e}n",
  year =         "1977",
  title =        "Numerical Analysis of Regularization and Constrained
                 Least Square Methods",
  number =       "20",
  school =       "Linkoping Studies in Science and Technology",
  address =      "Linkoping, Sweden",
}

@Article{Eld80,
  author =       "L. Eld{\`e}n",
  year =         "1980",
  title =        "Perturbation Theory for the Least Squares Problem
                 with Linear Equality Constraints",
  journal =      SIAMNumAnal,
  volume =       "17",
  pages =        "338--350",
}

@Article{Eld83,
  author =       "L. Eld{\`e}n",
  year =         "1983",
  title =        "A Weighted Pseudoinverse, Generalized Singular
                 Values, and Constrained Least Squares Problems",
  journal =      BIT,
  volume =       "22",
  pages =        "487--502",
}

@Article{Eld84,
  author =       "L. Eld{\`e}n",
  year =         "1984",
  title =        "An Algorithm for the Regularization of
                 Ill-Conditioned, Banded Least Squares Problems",
  journal =      SIAMSciStat,
  volume =       "5",
  pages =        "237--254",
}

@Article{Eld85,
  author =       "L. Eld{\`e}n",
  year =         "1985",
  title =        "A Note on the Computation of the Generalized
                 Cross-Validation Function for Ill-Conditioned Least
                 Squares Problems",
  journal =      BIT,
  volume =       "24",
  pages =        "467--472",
}

@Techreport{Eld88,
  author =       "L. Eld{\`e}n",
  year =         "1988",
  title =        "A Parallel {QR} Decomposition Algorithm",
  number =       "LiTh Mat R 1988-02",
  institution =  "Mathematics, Linkoping University",
  address =      "Sweden",
}

@Article{EldS86,
  author =       "L. Eld{\`e}n and R. Schreiber",
  year =         "1986",
  title =        "An Application of Systolic Arrays to Linear Discrete
                 Ill-Posed Problems",
  journal =      SIAMSciStat,
  volume =       "7",
  pages =        "892--903",
}

@Article{Elm86,
  author =       "H. Elman",
  year =         "1986",
  title =        "A Stability Analysis of Incomplete {LU}
                 Factorization",
  journal =      MathComp,
  volume =       "47",
  pages =        "191--218",
}

@Article{ElsS82,
  author =       "L. Elsner and J. Guang Sun",
  year =         "1982",
  title =        "Perturbation Theorems for the Generalized Eigenvalue
                 Problem",
  journal =      LinAlgApp,
  volume =       "48",
  pages =        "341--357",
}

@Inproceedings{ElsR88,
  author =       "A. Elster and A. P. Reeves",
  year =         "1988",
  title =        "Block Matrix Operations Using Orthogonal Trees",
  booktitle =    "The Third Conference on Hypercube Concurrent
                 Computers and Applications, Vol. {II}, Applications",
  editor =       "G. Fox",
  publisher =    ACMPress,
  address =      "New York, NY, USA",
  pages =        "1554--1561",
}

@Article{Enr79,
  author =       "W. Enright",
  year =         "1979",
  title =        "On the Efficient and Reliable Numerical Solution of
                 Large Linear Systems of {O. D. E.}'s",
  journal =      IEEETransAC,
  volume =       "AC-24",
  pages =        "905--908",
}

@Article{Erd67,
  author =       "I. Erdelyi",
  year =         "1967",
  title =        "On the Matrix Equation {$Ax = \lambda Bx$}",
  journal =      MathAnaAppl,
  volume =       "17",
  pages =        "119--132",
}

@Article{EriR80,
  author =       "T. Ericsson and A. Ruhe",
  year =         "1980",
  title =        "The Spectral Transformation {Lanczos} Method for the
                 Numerical Solution of Large Sparse Generalized
                 Symmetric Eigenvalue Problems",
  journal =      MathComp,
  volume =       "35",
  pages =        "1251--1268",
}

@Article{EriR74,
  author =       "A. M. Erisman and J. K. Reid",
  year =         "1974",
  title =        "Monitoring the Stability of the Triangular
                 Factorization of a Sparse Matrix",
  journal =      NumerMath,
  volume =       "22",
  pages =        "183--186",
}

@Article{Eva84,
  author =       "D. J. Evans",
  year =         "1984",
  title =        "Parallel {SOR} Iterative Methods",
  journal =      ParComputing,
  volume =       "1",
  pages =        "3--18",
}

@Article{EvaD83,
  author =       "D. J. Evans and R. Dunbar",
  year =         "1983",
  title =        "The Parallel Solution of Triangular Systems of
                 Equations",
  journal =      IEEETransComp,
  volume =       "C-32",
  pages =        "201--204",
}

@Article{FabM84,
  author =       "V. Faber and T. Manteuffel",
  year =         "1984",
  title =        "Necessary and Sufficient Conditions for the Existence
                 of a Conjugate Gradient Method",
  journal =      SIAMNumAnal,
  volume =       "21",
  pages =        "352--362",
}

@Book{FadF63,
  author =       "D. K. Faddeev and V. N. Faddeva",
  year =         "1963",
  title =        "Computational Methods of Linear Algebra",
  publisher =    WHFreeman,
  address =      "San Francisco, CA, USA",
}

@Article{FadF77,
  author =       "V. N. Fadeeva and D. K. Fadeev",
  year =         "1977",
  title =        "Parallel Calculations in Linear Algebra",
  journal =      Kibernetika,
  volume =       "6",
  pages =        "28--40",
}

@Article{FaiL70,
  author =       "W. Fair and Y. Luke",
  year =         "1970",
  title =        "{Pad}{\'e} Approximations to the Operator
                 Exponential",
  journal =      NumerMath,
  volume =       "14",
  pages =        "379--382",
}

@Article{FeiV62,
  author =       "D. G. Feingold and R. S. Varga",
  year =         "1962",
  title =        "Block Diagonally Dominant Matrices and
                 Generalizations of the {Gershgorin} Circle Theorem",
  journal =      "Pacific J. Math.",
  volume =       "12",
  pages =        "1241--1250",
}

@Article{FenL74,
  author =       "T. Fenner and G. Loizou",
  year =         "1974",
  title =        "Some New Bounds on the Condition Numbers of Optimally
                 Scaled Matrices",
  journal =      JACM,
  volume =       "1",
  pages =        "514--524",
}

@Article{FisU69,
  author =       "C. Fischer and R. A. Usmani",
  year =         "1969",
  title =        "Properties of Some Tridiagonal Matrices and Their
                 Application to Boundary Value Problems",
  journal =      SIAMNumAnal,
  volume =       "6",
  pages =        "127--142",
}

@Article{FixH72,
  author =       "G. Fix and R. Heiberger",
  year =         "1972",
  title =        "An Algorithm for the Ill-Conditioned Generalized
                 Eigenvalue Problem",
  journal =      SIAMNumAnal,
  volume =       "9",
  pages =        "78--88",
}

@Article{Fle76,
  author =       "R. Fletcher",
  year =         "1976",
  title =        "Factorizing Symmetric Indefinite Matrices",
  journal =      LinAlgApp,
  volume =       "14",
  pages =        "257--272",
}

@Article{For60,
  author =       "G. E. Forsythe",
  year =         "1960",
  title =        "Crout with Pivoting",
  journal =      CACM,
  volume =       "3",
  pages =        "507--508",
}

@Article{ForG65,
  author =       "G. E. Forsythe and G. H. Golub",
  year =         "1965",
  title =        "On the Stationary Values of a Second-Degree
                 Polynomial on the Unit Sphere",
  journal =      SIAMAppMath,
  volume =       "13",
  pages =        "1050--1068",
}

@Article{ForH60,
  author =       "G. E. Forsythe and P. Henrici",
  year =         "1960",
  title =        "The Cyclic {Jacobi} Method for Computing the
                 Principal Values of a Complex Matrix",
  journal =      "Trans. Amer. Math. Soc.",
  volume =       "94",
  pages =        "1--23",
}

@Book{ForMM77,
  author =       "G. E. Forsythe and M. A. Malcolm and C. B. Moler",
  year =         "1977",
  title =        "Computer Methods for Mathematical Computations",
  publisher =    PrenticeHall,
  address =      "Englewood Cliffs, NJ, USA",
}

@Book{ForM67,
  author =       "G. E. Forsythe and C. B. Moler",
  year =         "1967",
  title =        "Computer Solution of Linear Algebraic Systems",
  publisher =    PrenticeHall,
  address =      "Englewood Cliffs, NJ, USA",
}

@Article{Fos86,
  author =       "L. V. Foster",
  year =         "1986",
  title =        "Rank and Null Space Calculations Using Matrix
                 Decomposition without Column Interchanges",
  journal =      LinAlgApp,
  volume =       "74",
  pages =        "47--71",
}

@Article{Fou84,
  author =       "R. Fourer",
  year =         "1984",
  title =        "Staircase Matrices and Systems",
  journal =      SIAMReview,
  volume =       "26",
  pages =        "1--71",
}

@Book{Fox64,
  author =       "L. Fox",
  year =         "1964",
  title =        "An Introduction to Numerical Linear Algebra",
  publisher =    OxfordPress,
  address =      "Oxford, UK",
}

@Proceedings{Fox88,
  editor =       "G. Fox",
  year =         "1988",
  title =        "Applications",
  series =       "The Third Conference on Hypercube Concurrent
                 Computers and Applications",
  volume =       "2",
  publisher =    ACMPress,
  address =      "New York, NY, USA",
}

@Article{FoxOH87,
  author =       "G. Fox and S. W. Otto and A. J. Hey",
  year =         "1987",
  title =        "Matrix Algorithms on a Hypercube {I}: Matrix
                 Multiplication",
  journal =      ParComputing,
  volume =       "4",
  pages =        "17--31",
}

@Book{FoxJL+88,
  author =       "G. Fox and M. Johnson and G. Lyzenga and S. Otto and
                 J. Salmon and D. Walker",
  year =         "1988",
  title =        "On Concurrent Processors Vol {I}: General Techniques
                 and Regular Problems",
  publisher =    PrenticeHall,
  address =      "Englewood Cliffs, NJ, USA",
}

@Article{Fra64a,
  author =       "J. S. Frame",
  year =         "1964",
  title =        "Matrix Functions and Applications, Part {II}",
  journal =      IEEESpec,
  volume =       "1",
  month =        apr,
  pages =        "102--108",
}

@Article{Fra64b,
  author =       "J. S. Frame",
  year =         "1964",
  title =        "Matrix Functions and Applications, Part {IV}",
  journal =      IEEESpec,
  volume =       "1",
  month =        jun,
  pages =        "123--131",
}

@Article{Fra61,
  author =       "J. G. F. Francis",
  year =         "1961",
  title =        "The {QR} Transformation: A Unitary Analogue to the
                 {LR} Transformation, Parts~{I} and~{II}",
  journal =      CompJour,
  volume =       "4",
  pages =        "265--272, 332--345",
}

@Article{Fri75,
  author =       "S. Friedland",
  year =         "1975",
  title =        "On Inverse Multiplicative Eigenvalue Problems for
                 Matrices",
  journal =      LinAlgApp,
  volume =       "12",
  pages =        "127--138",
}

@Article{Fri77,
  author =       "S. Friedland",
  year =         "1977",
  title =        "Inverse Eigenvalue Problems",
  journal =      LinAlgApp,
  volume =       "17",
  pages =        "15--52",
}

@Article{FriNO87,
  author =       "S. Friedland and J. Nocedal and M. L. Overton",
  year =         "1987",
  title =        "The Formulation and Analysis of Numerical Methods for
                 Inverse Eigenvalue Problems",
  journal =      SIAMNumAnal,
  volume =       "24",
  pages =        "634--667",
}

@Article{Fro65,
  author =       "C. E. Froberg",
  year =         "1965",
  title =        "On Triangularization of Complex Matrices by
                 Two-Dimen\-sional Unitary Transformations",
  journal =      BIT,
  volume =       "5",
  pages =        "230--234",
}

@Article{FunG86,
  author =       "R. E. Funderlic and A. Geist",
  year =         "1986",
  title =        "Torus Data Flow for Parallel Computation of Missized
                 Matrix Problems",
  journal =      LinAlgApp,
  volume =       "77",
  pages =        "149--164",
}

@Article{FunNP82,
  author =       "R. E. Funderlic and M. Neuman and R. J. Plemmons",
  year =         "1982",
  title =        "Generalized Diagonally Dominant Matrices",
  journal =      NumerMath,
  volume =       "40",
  pages =        "57--70",
}

@Article{GalP70,
  author =       "G. Galimberti and V. Pereyra",
  year =         "1970",
  title =        "Numerical Differentiation and the Solution of
                 Multidimensional {Vandermonde} Systems",
  journal =      MathComp,
  volume =       "24",
  pages =        "357--364",
}

@Article{GalP71,
  author =       "G. Galimberti and V. Pereyra",
  year =         "1971",
  title =        "Solving Confluent {Vandermonde} Systems of {Hermite}
                 Type",
  journal =      NumerMath,
  volume =       "18",
  pages =        "44--60",
}

@Article{GalJM87,
  author =       "K. Gallivan and W. Jalby and U. Meier",
  year =         "1987",
  title =        "The Use of {BLAS3} in Linear Algebra on a Parallel
                 Processor with a Hierarchical Memory",
  journal =      SIAMSciStat,
  volume =       "8",
  pages =        "1079--1084",
}

@Article{GalJMS88,
  author =       "K. Gallivan and W. Jalby and U. Meier and A. H. Sameh",
  year =         "1988",
  title =        "Impact of Hierarchical Memory Systems on Linear
                 Algebra Algorithm Design",
  journal =      IntSuper,
  volume =       "2",
  pages =        "12--48",
}

@Article{Gan81,
  author =       "W. Gander",
  year =         "1981",
  title =        "Least Squares with a Quadratic Constraint",
  journal =      NumerMath,
  volume =       "36",
  pages =        "291--307",
}

@Article{GanR84,
  author =       "D. Gannon and J. Van Rosendale",
  year =         "1984",
  title =        "On the Impact of Communication Complexity on the
                 Design of Parallel Numerical Algorithms",
  journal =      IEEETransComp,
  volume =       "C-33",
  pages =        "1180--1194",
}

@Book{Gan59a,
  author =       "F. R. Gantmacher",
  year =         "1959",
  title =        "The Theory of Matrices",
  publisher =    Chelsea,
  address =      "New York, NY, USA",
  volume =       "1",
}

@Book{Gan59b,
  author =       "F. R. Gantmacher",
  year =         "1959",
  title =        "The Theory of Matrices",
  publisher =    Chelsea,
  address =      "New York, NY, USA",
  volume =       "2",
}

@Manual{GarBDM72,
  author =       "B. S. Garbow and J. M. Boyle and J. J. Dongarra and C. B.
                 Moler",
  year =         "1972",
  title =        "Matrix Eigensystem Routines: {EISPACK} Guide
                 Extension",
  publisher =    Springer,
  address =      "New York, NY, USA",
}

@Article{Gau75a,
  author =       "W. Gautschi",
  year =         "1975",
  title =        "Norm Estimates for Inverses of {Vandermonde}
                 Matrices",
  journal =      NumerMath,
  volume =       "23",
  pages =        "337--347",
}

@Article{Gau75b,
  author =       "W. Gautschi",
  year =         "1975",
  title =        "Optimally Conditioned {Vandermonde} Matrices",
  journal =      NumerMath,
  volume =       "24",
  pages =        "1--12",
}

@Techreport{GeiH85,
  author =       "G. A. Geist and M. T. Heath",
  year =         "1985",
  title =        "Parallel {Cholesky} Factorization on a Hypercube
                 Multiprocessor",
  number =       "ORNL 6190",
  institution =  "Oak Ridge Laboratory",
  address =      "Oak Ridge, TN, USA",
}

@Incollection{GeiH86,
  author =       "G. A. Geist and M. T. Heath",
  year =         "1986",
  title =        "Matrix Factorization on a Hypercube",
  booktitle =    "Hypercube Multiprocessors",
  editor =       "M. T. Heath",
  publisher =    SIAMPub,
  pages =        "161--180",
}

@Inproceedings{GeiWDF88,
  author =       "G. A. Geist and R. C. Ward and G. J. Davis and R. E.
                 Funderlic",
  year =         "1988",
  title =        "Finding Eigenvalues and Eigenvectors of Unsymmetric
                 Matrices Using a Hypercube Multiprocessor",
  booktitle =    "The Third Conference on Hypercube Concurrent
                 Computers and Applications, Vol. {II}, Applications",
  editor =       "G. Fox",
  publisher =    ACMPress,
  address =      "New York, NY, USA",
  pages =        "1577--1582",
}

@Article{Gen73a,
  author =       "W. M. Gentleman",
  year =         "1973",
  title =        "Error Analysis of {QR} Decompositions by {Givens}
                 Transformations",
  journal =      LinAlgApp,
  volume =       "10",
  pages =        "189--197",
}

@Article{Gen73b,
  author =       "W. M. Gentleman",
  year =         "1973",
  title =        "Least Squares Computations by {Givens}
                 Transformations Without Square Roots",
  journal =      InstMathApp,
  volume =       "12",
  pages =        "329--336",
}

@Inproceedings{GenK82,
  author =       "W. M. Gentleman and H. T. Kung",
  year =         "1982",
  title =        "Matrix Triangularization by Systolic Arrays",
  booktitle =    "{SPIE} Proceedings",
  volume =       "298",
  pages =        "19--26",
}

@Article{Geo73,
  author =       "J. A. George",
  year =         "1973",
  title =        "Nested Dissection of a Regular Finite Element Mesh",
  journal =      SIAMNumAnal,
  volume =       "10",
  pages =        "345--363",
}

@Article{Geo74,
  author =       "J. A. George",
  year =         "1974",
  title =        "On Block Elimination for Sparse Linear Systems",
  journal =      SIAMNumAnal,
  volume =       "11",
  pages =        "585--603",
}

@Article{GeoH80,
  author =       "J. A. George and M. T. Heath",
  year =         "1980",
  title =        "Solution of Sparse Linear Least Squares Problems
                 Using {Givens} Rotations",
  journal =      LinAlgApp,
  volume =       "34",
  pages =        "69--83",
}

@Article{GeoHL86,
  author =       "J. A. George and M. T. Heath and J. Liu",
  year =         "1986",
  title =        "Parallel {Cholesky} Factorization on a Shared Memory
                 Multiprocessor",
  journal =      LinAlgApp,
  volume =       "77",
  pages =        "165--187",
}

@Book{GeoL81a,
  author =       "J. A. George and J. W. Liu",
  year =         "1981",
  title =        "Computer Solution of Large Sparse Positive Definite
                 Systems",
  publisher =    PrenticeHall,
  address =      "Englewood Cliffs, NJ, USA",
}

@Article{GibWP74,
  author =       "N. E. Gibbs and W. G. {Poole, Jr}",
  year =         "1974",
  title =        "Tridiagonalization by Permutations",
  journal =      CACM,
  volume =       "17",
  pages =        "20--24",
}

@Article{GibPS76b,
  author =       "N. E. Gibbs and W. G. Poole and P. K. Stockmeyer",
  year =         "1976",
  title =        "A Comparison of Several Bandwidth and Profile
                 Reduction Algorithms",
  journal =      ACMMathSoft,
  volume =       "2",
  pages =        "322--330",
}

@Article{GibPS76a,
  author =       "N. E. Gibbs and W. G. Poole and P. K. Stockmeyer",
  year =         "1976",
  title =        "An Algorithm for Reducing the Bandwidth and Profile
                 of a Sparse Matrix",
  journal =      SIAMNumAnal,
  volume =       "13",
  pages =        "236--250",
}

@Article{GilGMS74,
  author =       "P. E. Gill and G. H. Golub and W. Murray and M. A.
                 Saunders",
  year =         "1974",
  title =        "Methods for Modifying Matrix Factorizations",
  journal =      MathComp,
  volume =       "28",
  pages =        "505--535",
}

@Incollection{GilM76,
  author =       "P. E. Gill and W. Murray",
  year =         "1976",
  title =        "The Orthogonal Factorization of a Large Sparse
                 Matrix",
  booktitle =    "Sparse Matrix Computations",
  editor =       "J. R. Bunch and D. J. Rose",
  publisher =    Academic,
  address =      "New York, NY, USA",
  pages =        "177--200",
}

@Article{GilMS75,
  author =       "P. E. Gill and W. Murray and M. A. Saunders",
  year =         "1975",
  title =        "Methods for Computing and Modifying the {LDV} Factors
                 of a Matrix",
  journal =      MathComp,
  volume =       "29",
  pages =        "1051--1077",
}

@Incollection{Gin71,
  author =       "T. Ginsburg",
  year =         "1971",
  title =        "The Conjugate Gradient Method",
  booktitle =    "Handbook for Automatic Computation Vol. 2: Linear
                 Algebra",
  editor =       "J. H. Wilkinson and C. Reinsch",
  publisher =    Springer,
  address =      "New York, NY, USA",
  pages =        "57--69",
}

@Article{Giv58,
  author =       "W. Givens",
  year =         "1958",
  title =        "Computation of Plane Unitary Rotations Transforming a
                 General Matrix to Triangular Form",
  journal =      SIAMAppMath,
  volume =       "6",
  pages =        "26--50",
}

@Book{GohK69,
  author =       "I. C. Gohberg and M. G. Krein",
  year =         "1969",
  title =        "Introduction to the Theory of Linear Non-Self-Adjoint
                 Operators",
  publisher =    AMS,
  address =      "Providence, RI, USA",
}

@Book{GohLR86,
  author =       "I. C. Gohberg and P. Lancaster and L. Rodman",
  year =         "1986",
  title =        "Invariant Subspaces of Matrices With Applications",
  publisher =    JohnWileySons,
  address =      "New York, NY, USA",
}

@Article{GolH59,
  author =       "H. H. Goldstine and L. P. Horowitz",
  year =         "1959",
  title =        "A Procedure for the Diagonalization of Normal
                 Matrices",
  journal =      JACM,
  volume =       "6",
  pages =        "176--195",
}

@Article{Gol76,
  author =       "D. Goldfarb",
  year =         "1976",
  title =        "Factorized Variable Metric Methods for Unconstrained
                 Optimization",
  journal =      MathComp,
  volume =       "30",
  pages =        "796--811",
}

@Article{Gol65,
  author =       "G. H. Golub",
  year =         "1965",
  title =        "Numerical Methods for Solving Linear Least Squares
                 Problems",
  journal =      NumerMath,
  volume =       "7",
  pages =        "206--216",
}

@Incollection{Gol69,
  author =       "G. H. Golub",
  year =         "1969",
  title =        "Matrix Decompositions and Statistical Computation",
  booktitle =    "Statistical Computation",
  editor =       "R. C. Milton and J. A. Nelder",
  publisher =    Academic,
  address =      "New York, NY, USA",
  pages =        "365--397",
}

@Article{Gol73,
  author =       "G. H. Golub",
  year =         "1973",
  title =        "Some Modified Matrix Eigenvalue Problems",
  journal =      SIAMReview,
  volume =       "15",
  pages =        "318--344",
}

@Incollection{Gol74,
  author =       "G. H. Golub",
  year =         "1974",
  title =        "Some Uses of the {Lanczos} Algorithm in Numerical
                 Linear Algebra",
  booktitle =    "Topics in Numerical Analysis",
  editor =       "J. J. H. Miller",
  publisher =    Academic,
  address =      "New York, NY, USA",
}

@Article{GolHW79,
  author =       "G. H. Golub and M. Heath and G. Wahba",
  year =         "1979",
  title =        "Generalized Cross-Validation as a Method for Choosing
                 a Good Ridge Parameter",
  journal =      Techno,
  volume =       "21",
  pages =        "215--223",
}

@Article{GolHS88,
  author =       "G. H. Golub and A. Hoffman and G. W. Stewart",
  year =         "1988",
  title =        "A Generalization of the {Eckart}-{Young}-{Mirsky}
                 Approximation Theorem",
  journal =      LinAlgApp,
  volume =       "88/89",
  pages =        "317--328",
}

@Article{GolK65,
  author =       "G. H. Golub and W. Kahan",
  year =         "1965",
  title =        "Calculating the Singular Values and Pseudo-Inverse of
                 a Matrix",
  journal =      JSIAMB,
  volume =       "2",
  pages =        "205--224",
}

@Techreport{GolKS76,
  author =       "G. H. Golub and V. Klema and G. W. Stewart",
  year =         "1976",
  title =        "Rank Degeneracy and Least Squares Problems",
  number =       "TR-456",
  institution =  "Computer Science, University of Maryland",
  address =      "College Park, MD, USA",
}

@Article{GolLO81,
  author =       "G. H. Golub and F. T. Luk and M. Overton",
  year =         "1981",
  title =        "A Block {Lanczos} Method for Computing the Singular
                 Values and Corresponding Singular Vectors of a Matrix",
  journal =      ACMMathSoft,
  volume =       "7",
  pages =        "149--169",
}

@Book{GolM83,
  author =       "G. H. Golub and G. Meurant",
  year =         "1983",
  title =        "R{\'e}solution Num{\'e}rique des Grands Syst{\`e}mes
                 Lin{\'e}aires",
  series =       "Collection de la Direction des Etudes et Recherches
                 de l'Electricit\'e de France",
  volume =       "49",
  publisher =    Eyolles,
  address =      "Paris, France",
}

@Article{GolM86,
  author =       "G. H. Golub and C. D. Meyer",
  year =         "1986",
  title =        "Using the {QR} Factorization and Group Inversion to
                 Compute, Differentiate, and estimate the Sensitivity
                 of Stationary Probabilities for {Markov} Chains",
  journal =      SIAMAlgMeth,
  volume =       "7",
  pages =        "273--281",
}

@Article{GolNL79,
  author =       "G. H. Golub and S. Nash and C. Van Loan",
  year =         "1979",
  title =        "A {Hessenberg}-{Schur} Method for the Matrix Problem
                 {$AX + XB = C$}",
  journal =      IEEETransAC,
  volume =       "AC-24",
  pages =        "909--913",
}

@Article{GolO88,
  author =       "G. H. Golub and M. Overton",
  year =         "1988",
  title =        "The Convergence of Inexact {Chebychev} and
                 {Richardson} Iterative Methods for Solving Linear
                 Systems",
  journal =      NumerMath,
  volume =       "53",
  pages =        "571--594",
}

@Article{GolP73,
  author =       "G. H. Golub and V. Pereyra",
  year =         "1973",
  title =        "The Differentiation of Pseudo-Inverses and Nonlinear
                 Least Squares Problems Whose Variables Separate",
  journal =      SIAMNumAnal,
  volume =       "10",
  pages =        "413--432",
}

@Incollection{GolP76,
  author =       "G. H. Golub and V. Pereyra",
  year =         "1976",
  title =        "Differentiation of Pseudo-Inverses, Separable
                 Nonlinear Least Squares Problems and Other Tales",
  booktitle =    "Generalized Inverses and Applications",
  editor =       "M. Z. Nashed",
  publisher =    Academic,
  address =      "New York, NY, USA",
  pages =        "303--324",
}

@Article{GolR70,
  author =       "G. H. Golub and C. Reinsch",
  year =         "1970",
  title =        "Singular Value Decomposition and Least Squares
                 Solutions",
  journal =      NumerMath,
  volume =       "14",
  pages =        "403--420",
  note =         "Also in \cite[pages 134--151]{WilR71}",
}

@Article{GolT81,
  author =       "G. H. Golub and W. P. Tang",
  year =         "1981",
  title =        "The Block Decomposition of a {Vandermonde} Matrix and
                 Its Applications",
  journal =      BIT,
  volume =       "21",
  pages =        "505--517",
}

@Article{GolU70,
  author =       "G. H. Golub and R. Underwood",
  year =         "1970",
  title =        "Stationary Values of the Ratio of Quadratic Forms
                 Subject to Linear Constraints",
  journal =      ZAngewMathPhys,
  volume =       "21",
  pages =        "318--326",
}

@Incollection{GolU77,
  author =       "G. H. Golub and R. Underwood",
  year =         "1977",
  title =        "The Block {Lanczos} Method for Computing Eigenvalues",
  booktitle =    "Mathematical Software {III}",
  editor =       "J. Rice",
  publisher =    Academic,
  address =      "New York, NY, USA",
  pages =        "364--377",
}

@Techreport{GolUW72,
  author =       "G. H. Golub and R. Underwood and J. H. Wilkinson",
  year =         "1972",
  title =        "The {Lanczos} Algorithm for the Symmetric {$Ax =
                 \lambda Bx$} Problem",
  number =       "STAN-CS-72-270",
  institution =  "Computer Science, Stanford University",
  address =      "Stanford, CA, USA",
}

@Article{GolL79,
  author =       "G. H. Golub and C. F. Van Loan",
  year =         "1979",
  title =        "Unsymmetric Positive Definite Linear Systems",
  journal =      LinAlgApp,
  volume =       "28",
  pages =        "85--98",
}

@Article{GolL80,
  author =       "G. H. Golub and C. F. Van Loan",
  year =         "1980",
  title =        "An Analysis of the Total Least Squares Problem",
  journal =      SIAMNumAnal,
  volume =       "17",
  pages =        "883--893",
}

@Book{GolL89,
  author =       "G. H. Golub and C. F. Van Loan",
  year =         "1989",
  title =        "Matrix Computations",
  edition =      "second",
  publisher =    JohnsHopkinsPress,
  address =      "Baltimore, MD, USA",
}

@Article{GolV74,
  author =       "G. H. Golub and J. M. Varah",
  year =         "1974",
  title =        "On a Characterization of the Best {$L_{2}$}-Scaling
                 of a Matrix",
  journal =      SIAMNumAnal,
  volume =       "11",
  pages =        "472--479",
}

@Article{GolV61,
  author =       "G. H. Golub and R. S. Varga",
  year =         "1961",
  title =        "{Chebychev} Semi-Iterative Methods, Successive
                 Over-Relaxation Iterative Methods, and Second-Order
                 {Richardson} Iterative Methods, Parts {I} and {II}",
  journal =      NumerMath,
  volume =       "3",
  pages =        "147--156, 157--168",
}

@Article{GolW69,
  author =       "G. H. Golub and J. H. Welsch",
  year =         "1969",
  title =        "Calculation of {Gauss} Quadrature Rules",
  journal =      MathComp,
  volume =       "23",
  pages =        "221--230",
}

@Article{GolW66,
  author =       "G. H. Golub and J. H. Wilkinson",
  year =         "1966",
  title =        "Note on the Iterative Refinement of Least Squares
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@Article{GolW76,
  author =       "G. H. Golub and J. H. Wilkinson",
  year =         "1976",
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  author =       "A. R. Gourlay",
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@Article{Gra86,
  author =       "W. B. Gragg",
  year =         "1986",
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  volume =       "16",
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@Article{GraH84,
  author =       "W. B. Gragg and W. J. Harrod",
  year =         "1984",
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  journal =      NumerMath,
  volume =       "44",
  pages =        "317--336",
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@Article{Gre52,
  author =       "B. Green",
  year =         "1952",
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  volume =       "17",
  pages =        "429--440",
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@Techreport{Gre81,
  author =       "A. Greenbaum",
  year =         "1981",
  title =        "Behavior of the Conjugate Gradient Algorithm in
                 Finite Precision Arithmetic",
  number =       "UCRL 85752",
  institution =  "Lawrence Livermore Laboratory",
  address =      "Livermore, CA, USA",
}

@Article{GriL81b,
  author =       "R. G. Grimes and J. G. Lewis",
  year =         "1981",
  title =        "Condition Number Estimation for Sparse Matrices",
  journal =      SIAMSciStat,
  volume =       "2",
  pages =        "384--388",
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@Article{GunWM76,
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  year =         "1976",
  title =        "A Comparison of Least Squares and Latent Root
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  journal =      Techno,
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  year =         "1972",
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@Book{HagY81,
  author =       "L. A. Hageman and D. M. Young",
  year =         "1981",
  title =        "Applied Iterative Methods",
  publisher =    Academic,
  address =      "New York, NY, USA",
}

@Article{Hag84,
  author =       "W. Hager",
  year =         "1984",
  title =        "Condition Estimates",
  journal =      SIAMSciStat,
  volume =       "5",
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@Book{Hag88,
  author =       "W. Hager",
  year =         "1988",
  title =        "Applied Numerical Linear Algebra",
  publisher =    PrenticeHall,
  address =      "Englewood Cliffs, NJ, USA",
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@Book{Hal58,
  author =       "P. Halmos",
  year =         "1958",
  title =        "Finite Dimensional Vector Spaces",
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  author =       "S. Hammarling",
  year =         "1974",
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  volume =       "13",
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@Article{Ham85,
  author =       "S. J. Hammarling",
  year =         "1985",
  title =        "The Singular Value Decomposition in Multivariate
                 Statistics",
  journal =      SIGNUM,
  volume =       "20",
  pages =        "2--25",
}

@Article{Han62,
  author =       "E. R. Hansen",
  year =         "1962",
  title =        "On Quasicyclic {Jacobi} Methods",
  journal =      JACM,
  volume =       "9",
  pages =        "118--135",
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@Article{Han63,
  author =       "E. R. Hanson",
  year =         "1963",
  title =        "On Cyclic {Jacobi} Methods",
  journal =      SIAMAppMath,
  volume =       "11",
  pages =        "448--459",
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@Article{Han87,
  author =       "P. C. Hansen",
  year =         "1987",
  title =        "The Truncated {SVD} as a Method for Regularization",
  journal =      BIT,
  volume =       "27",
  pages =        "534--553",
}

@Incollection{Han88,
  author =       "P. C. Hansen",
  year =         "1988",
  title =        "Reducing the Number of Sweeps in {Hestenes} Method",
  booktitle =    "Singular Value Decomposition and Signal Processing",
  editor =       "E. F. Deprettere",
  publisher =    NorthHolland,
}

@Article{HanL69,
  author =       "R. J. Hanson and C. L. Lawson",
  year =         "1969",
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  volume =       "23",
  pages =        "787--812",
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@Article{HanN81,
  author =       "R. J. Hanson and M. J. Norris",
  year =         "1981",
  title =        "Analysis of Measurements Based on the Singular Value
                 Decomposition",
  journal =      SIAMSciStat,
  volume =       "2",
  pages =        "363--374",
}

@Article{Har82,
  author =       "V. Hari",
  year =         "1982",
  title =        "On the Global Convergence of the {Eberlein} Method
                 for Real Matrices",
  journal =      NumerMath,
  volume =       "39",
  pages =        "361--370",
}

@Phdthesis{Hea78,
  author =       "M. T. Heath",
  year =         "1978",
  title =        "Numerical Algorithms for Nonlinearly Constrained
                 Optimization",
  number =       "STAN-CS-78-656",
  school =       "Computer Science, Stanford University",
  address =      "Stanford, CA, USA",
}

@Proceedings{Hea86,
  editor =       "M. T. Heath",
  year =         "1986",
  title =        "Proceedings of First {SIAM} Conference on Hypercube
                 Multiprocessors",
  publisher =    SIAMPub,
  address =      "Philadelphia, PA, USA",
}

@Proceedings{Hea87,
  editor =       "M. T. Heath",
  year =         "1987",
  title =        "Hypercube Multiprocessors",
  publisher =    SIAMPub,
  address =      "Philadelphia, PA, USA",
}

@Article{HeaLPW86,
  author =       "M. T. Heath and A. J. Laub and C. C. Paige and R. C.
                 Ward",
  year =         "1986",
  title =        "Computing the {SVD} of a Product of Two Matrices",
  journal =      SIAMSciStat,
  volume =       "7",
  pages =        "1147--1159",
}

@Article{HeaR88,
  author =       "M. T. Heath and C. H. Romine",
  year =         "1988",
  title =        "Parallel Solution of Triangular Systems on
                 Distributed Memory Multiprocessors",
  journal =      SIAMSciStat,
  volume =       "9",
  pages =        "558--588",
}

@Article{HeaS86,
  author =       "M. T. Heath and D. C. Sorensen",
  year =         "1986",
  title =        "A Pipelined Method for Computing the {QR}
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  volume =       "77",
  pages =        "189--203",
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@Article{Hel76,
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  year =         "1976",
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  volume =       "13",
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@Article{Hel78,
  author =       "D. Heller",
  year =         "1978",
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  journal =      SIAMReview,
  volume =       "20",
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@Article{HelI83,
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  volume =       "4",
  pages =        "261--269",
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@Article{Hel68,
  author =       "B. W. Helton",
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@Inproceedings{HenHP88,
  author =       "C. S. Henkel and M. T. Heath and R. J. Plemmons",
  year =         "1988",
  title =        "{Cholesky} Downdating on a Hypercube",
  booktitle =    "The Third Conference on Hypercube Concurrent
                 Computers and Applications, Vol. {II}, Applications",
  editor =       "G. Fox",
  publisher =    ACMPress,
  address =      "New York, NY, USA",
  pages =        "1592--1598",
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@Article{Hen58,
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  year =         "1958",
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  pages =        "144--162",
  bibdate =      "Tue Mar 14 19:21:50 1995",
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@Article{Hen62,
  author =       "P. Henrici",
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@Article{HenZ68,
  author =       "P. Henrici and K. Zimmermann",
  year =         "1968",
  title =        "An Estimate for the Norms of Certain cyclic {Jacobi}
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  journal =      LinAlgApp,
  volume =       "1",
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@Book{Hes80,
  author =       "M. R. Hestenes",
  year =         "1980",
  title =        "Conjugate Direction Methods in Optimization",
  publisher =    Springer,
  address =      "Berlin, Germany",
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@Article{HesS52,
  author =       "M. R. Hestenes and E. Stiefel",
  year =         "1952",
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@Phdthesis{Hig85,
  author =       "N. J. Higham",
  year =         "1985",
  title =        "Nearness Problems in Numerical Linear Algebra",
  school =       "University of Manchester",
  address =      "UK",
}

@Article{Hig86c,
  author =       "N. J. Higham",
  year =         "1986",
  title =        "{Newton}'s Method for the Matrix Square Root",
  journal =      MathComp,
  volume =       "46",
  pages =        "537--550",
}

@Article{Hig86a,
  author =       "N. J. Higham",
  year =         "1986",
  title =        "Computing the Polar Decomposition with Applications",
  journal =      SIAMSciStat,
  volume =       "7",
  pages =        "1160--1174",
}

@Article{Hig86b,
  author =       "N. J. Higham",
  year =         "1986",
  title =        "Efficient Algorithms for computing the condition
                 number of a tridiagonal matrix",
  journal =      SIAMSciStat,
  volume =       "7",
  pages =        "150--165",
}

@Article{Hig87c,
  author =       "N. J. Higham",
  year =         "1987",
  title =        "A Survey of Condition Number Estimation for
                 Triangular Matrices",
  journal =      SIAMReview,
  volume =       "29",
  pages =        "575--596",
}

@Article{Hig87b,
  author =       "N. J. Higham",
  year =         "1987",
  title =        "Error Analysis of the {Bj}{\"o}rck-{Pereyra}
                 Algorithms for Solving {Vandermonde} Systems",
  journal =      NumerMath,
  volume =       "50",
  pages =        "613--632",
}

@Article{Hig87a,
  author =       "N. J. Higham",
  year =         "1987",
  title =        "Computing Real Square Roots of a Real Matrix",
  journal =      LinAlgApp,
  volume =       "88/89",
  pages =        "405--430",
}

@Techreport{Hig88f,
  author =       "N. J. Higham",
  year =         "1988",
  title =        "Matrix Nearness Problems and Applications",
  number =       "161",
  institution =  "Mathematics, University of Manchester",
  address =      "UK",
  note =         "To appear in Proceedings of the IMA Conference on
                 Applications of Matrix Theory, eds. S. Barnett and
                 M. J. C. Gover",
}

@Article{Hig88e,
  author =       "N. J. Higham",
  year =         "1988",
  title =        "{Fortran} Codes for Estimating the One-Norm of a Real
                 or Complex Matrix, with Applications to Condition
                 Estimation",
  journal =      ACMMathSoft,
  volume =       "14",
  pages =        "381--396",
}

@Article{Hig88d,
  author =       "N. J. Higham",
  year =         "1988",
  title =        "The Symmetric {Procrustes} Problem",
  journal =      BIT,
  volume =       "28",
  pages =        "133--143",
}

@Article{Hig88c,
  author =       "N. J. Higham",
  year =         "1988",
  title =        "Fast Solution of {Vandermonde}-like Systems Involving
                 Orthogonal Polynomials",
  journal =      IMANumerAna,
  volume =       "8",
  pages =        "473--486",
}

@Article{Hig88b,
  author =       "N. J. Higham",
  year =         "1988",
  title =        "Computing a Nearest Symmetric Positive Semidefinite
                 Matrix",
  journal =      LinAlgApp,
  volume =       "103",
  pages =        "103--118",
}

@Techreport{Hig88a,
  author =       "N. J. Higham",
  year =         "1988",
  title =        "The Accuracy of Solutions to Triangular Systems",
  number =       "158",
  institution =  "Mathematics, University of Manchester",
  address =      "UK",
}

@Incollection{Hig89,
  author =       "N. J. Higham",
  year =         "1989",
  title =        "Analysis of the {Cholesky} Decomposition of a
                 Semi-definite Matrix",
  booktitle =    "Reliable Numerical Computation",
  editor =       "M. G. Cox and S. J. Hammarling",
  publisher =    OxfordPress,
}

@Article{HigH89,
  author =       "N. J. Higham and D. J. Higham",
  year =         "1989",
  title =        "Large Growth Factors in {Gaussian} Elimination with
                 Pivoting",
  journal =      SIAMMatrix,
  volume =       "10",
  pages =        "155--164",
}

@Techreport{HigS88,
  author =       "N. J. Higham and R. S. Schreiber",
  year =         "1988",
  title =        "Fast Polar Decomposition of an Arbitrary Matrix",
  number =       "88-942",
  institution =  "Computer Science, Cornell University",
  address =      "Ithaca, NY 14853",
}

@Incollection{Hoa77,
  author =       "D. Hoaglin",
  year =         "1977",
  title =        "Mathematical Software and Exploratory Data Analysis",
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  editor =       "John Rice",
  publisher =    Academic,
  address =      "New York, NY, USA",
  pages =        "139--159",
}

@Article{Hoc65,
  author =       "R. W. Hockney",
  year =         "1965",
  title =        "A Fast Direct Solution of {Poisson}'s Equation Using
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  journal =      JACM,
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@Article{Hoc83,
  author =       "R. Hockney",
  year =         "1983",
  title =        "Characterizing Computers and Optimizing the
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  journal =      IEEETransComp,
  volume =       "C-32",
  pages =        "933--941",
}

@Book{HocJ88,
  author =       "R. W. Hockney and C. R. Jesshope",
  year =         "1988",
  title =        "Parallel Computers 2",
  publisher =    AdamHilger,
  address =      "Bristol and Philadelphia",
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@Article{HofP78,
  author =       "W. Hoffmann and B. N. Parlett",
  year =         "1978",
  title =        "A New Proof of Global Convergence for the Tridiagonal
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@Article{Hot57,
  author =       "H. Hotelling",
  year =         "1957",
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@Article{Hou58,
  author =       "A. S. Householder",
  year =         "1958",
  title =        "Unitary Triangularization of a Nonsymmetric Matrix",
  journal =      JACM,
  volume =       "5",
  pages =        "339--342",
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@Article{Hou68,
  author =       "A. S. Householder",
  year =         "1968",
  title =        "Moments and Characteristic Roots {II}",
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@Book{Hou74,
  author =       "A. S. Householder",
  year =         "1974",
  title =        "The Theory of Matrices in Numerical Analysis",
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  author =       "C. P. Huang",
  year =         "1975",
  title =        "A {Jacobi}-Type Method for Triangularizing an
                 Arbitrary Matrix",
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@Article{Hua81,
  author =       "C. P. Huang",
  year =         "1981",
  title =        "On the Convergence of the {QR} Algorithm with Origin
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  author =       "T. E. Hull and J. R. Swenson",
  year =         "1966",
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@Article{Ike79,
  author =       "Y. Ikebe",
  year =         "1979",
  title =        "On Inverses of {Hessenberg} Matrices",
  journal =      LinAlgApp,
  volume =       "24",
  pages =        "93--97",
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@Article{IpsSS86,
  author =       "I. C. F. Ipsen and Y. Saad and M. Schultz",
  year =         "1986",
  title =        "Dense Linear Systems on a Ring of Processors",
  journal =      LinAlgApp,
  volume =       "77",
  pages =        "205--239",
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@Book{IseP87,
  editor =       "A. Iserles and M. J. D. Powell",
  year =         "1987",
  title =        "The State of the Art in Numerical Analysis",
  publisher =    OxfordPress,
}

@Article{Jac46,
  author =       "C. G. J. Jacobi",
  year =         "1846",
  title =        "{\"U}ber ein leichtes Verfahren die in der Theorie
                 der S{\"a}cul{\"a}rst{\"o}rungen vorkommenden
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  journal =      Crelle,
  volume =       "30",
  pages =        "51--94",
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@Article{JanW77,
  author =       "M. Jankowski and M. Wozniakowski",
  year =         "1977",
  title =        "Iterative Refinement Implies Numerical Stability",
  journal =      BIT,
  volume =       "17",
  pages =        "303--311",
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@Article{JeaY83,
  author =       "K. C. Jea and D. M. Young",
  year =         "1983",
  title =        "On the Simplification of Generalized Conjugate
                 Gradient Methods for Nonsymmetrizable Linear Systems",
  journal =      LinAlgApp,
  volume =       "52/53",
  pages =        "399--417",
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@Article{Jen77a,
  author =       "A. Jennings",
  year =         "1977",
  title =        "Influence of the Eigenvalue Spectrum on the
                 Convergence Rate of the Conjugate Gradient Method",
  journal =      InstMathApp,
  volume =       "20",
  pages =        "61--72",
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@Book{Jen77b,
  author =       "A. Jennings",
  year =         "1977",
  title =        "Matrix Computation for Engineers and Scientists",
  publisher =    JohnWileySons,
  address =      "New York, NY, USA",
}

@Article{JenO71,
  author =       "A. Jennings and D. R. L. Orr",
  year =         "1971",
  title =        "Application of the Simultaneous Iteration Method to
                 Undamped Vibration Problems",
  journal =      IntNumerEng,
  volume =       "3",
  pages =        "13--24",
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@Article{JenO77,
  author =       "A. Jennings and M. R. Osborne",
  year =         "1977",
  title =        "Generalized Eigenvalue Problems for Certain
                 Unsymmetric Band Matrices",
  journal =      LinAlgApp,
  volume =       "29",
  pages =        "139--150",
}

@Article{JenS75,
  author =       "A. Jennings and W. J. Stewart",
  year =         "1975",
  title =        "Simultaneous Iteration for the Partial Eigensolution
                 of Real Matrices",
  journal =      InstMathApp,
  volume =       "15",
  pages =        "351--362",
}

@Article{JenO74,
  author =       "L. S. Jennings and M. R. Osborne",
  year =         "1974",
  title =        "A Direct Error Analysis for Least Squares",
  journal =      NumerMath,
  volume =       "22",
  pages =        "322--332",
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@Article{Jen72,
  author =       "P. S. Jenson",
  year =         "1972",
  title =        "The Solution of Large Symmetric Eigenproblems by
                 Sectioning",
  journal =      SIAMNumAnal,
  volume =       "9",
  pages =        "534--545",
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@Article{JohP71,
  author =       "J. Johnson and C. L. Phillips",
  year =         "1971",
  title =        "An Algorithm for the Computation of the Integral of
                 the State Transition Matrix",
  journal =      IEEETransAC,
  volume =       "AC-16",
  pages =        "204--205",
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@Article{JohMP83,
  author =       "O. G. Johnson and C. A. Micchelli and G. Paul",
  year =         "1983",
  title =        "Polynomial Preconditioners for Conjugate Gradient
                 Calculations",
  journal =      SIAMNumAnal,
  volume =       "20",
  pages =        "362--376",
}

@Techreport{Joh84,
  author =       "S. L. Johnsson",
  year =         "1984",
  title =        "Odd-Even Cyclic Reduction on Ensemble Architectures
                 and the Solution of Tridiagonal Systems of Equations",
  number =       "YALEU DCS RR-339",
  institution =  "Computer Science, Yale University",
  address =      "New Haven, CT, USA",
}

@Article{Joh85,
  author =       "S. L. Johnsson",
  year =         "1985",
  title =        "Solving Narrow Banded Systems on Ensemble
                 Architectures",
  journal =      ACMMathSoft,
  volume =       "11",
  pages =        "271--288",
}

@Incollection{Joh86,
  author =       "S. L. Johnsson",
  year =         "1986",
  title =        "Band Matrix System Solvers on Ensemble Architectures",
  booktitle =    "Supercomputers: Algorithms, Architectures, and
                 Scientific Computation",
  editor =       "F. A. Matsen and T. Tajima",
  publisher =    TexasPress,
  address =      "Austin, TX, USA",
  pages =        "196--216",
}

@Article{Joh87b,
  author =       "S. L. Johnsson",
  year =         "1987",
  title =        "Solving Tridiagonal Systems on Ensemble
                 Architectures",
  journal =      SIAMSciStat,
  volume =       "8",
  pages =        "354--392",
}

@Article{Joh87a,
  author =       "S. L. Johnsson",
  year =         "1987",
  title =        "Communication Efficient Basic Linear Algebra
                 Computations on Hypercube Multiprocessors",
  journal =      ParDistComp,
  volume =       "4",
  pages =        "133--172",
}

@Techreport{JohH87c,
  author =       "S. L. Johnsson and C. T. Ho",
  year =         "1987",
  title =        "Multiple Tridiagonal Systems, the Alternating
                 Direction Methods, and {Boolean} Cube Configured
                 Multiprocessors",
  number =       "YALEU DCS RR-532",
  institution =  "Computer Science, Yale University",
  address =      "New Haven, CT, USA",
}

@Techreport{JohH87,
  author =       "S. L. Johnsson and C. T. Ho",
  year =         "1987",
  title =        "Algorithms for Multiplying Matrices of Arbitrary
                 Shapes Using Shared Memory Primatives on a {Boolean}
                 Cube",
  number =       "YALEU DCS RR-569",
  institution =  "Computer Science, Yale University",
  address =      "New Haven, CT, USA",
}

@Article{JohH88,
  author =       "S. L. Johnsson and C. T. Ho",
  year =         "1988",
  title =        "Algorithms for Matrix Transposition on {Boolean}
                 {$N$}-Cube Configured Ensemble Architectures",
  journal =      SIAMMatrix,
  volume =       "9",
  pages =        "419--454",
}

@Article{Joh71,
  author =       "R. L. Johnston",
  year =         "1971",
  title =        "{Gershgorin} Theorems for Partitioned Matrices",
  journal =      LinAlgApp,
  volume =       "4",
  pages =        "205--220",
}

@Article{Jor87,
  author =       "H. Jordan",
  year =         "1987",
  title =        "Interpreting Parallel Processor Performance
                 Measurements",
  journal =      SIAMSciStat,
  volume =       "8",
  pages =        "s220--s226",
}

@Inproceedings{Jor84,
  author =       "T. Jordan",
  year =         "1984",
  title =        "Conjugate Gradient Preconditioners for Vector and
                 Parallel Processors",
  booktitle =    "Proceedings of the Conference on Elliptic Problem
                 Solvers",
  editor =       "G. Birkoff and A. Schoenstadt",
  publisher =    Academic,
  address =      "New York, NY, USA",
}

@Article{Kag77a,
  author =       "B. K{\aa}gstr{\"o}m",
  year =         "1977",
  title =        "Bounds and Perturbation Bounds for the Matrix
                 Exponential",
  journal =      BIT,
  volume =       "17",
  pages =        "39--57",
}

@Techreport{Kag77b,
  author =       "B. K{\aa}gstr{\"o}m",
  year =         "1977",
  title =        "Numerical Computation of Matrix Functions",
  number =       "UMINF-58.77",
  institution =  "Information Processing, University of Ume{\aa}",
  address =      "Ume{\aa}, Sweden",
}

@Article{KagR80b,
  author =       "B. K{\aa}gstr{\"o}m and A. Ruhe",
  year =         "1980",
  title =        "An Algorithm for Numerical Computation of the
                 {Jordan} Normal Form of a Complex Matrix",
  journal =      ACMMathSoft,
  volume =       "6",
  pages =        "398--419",
}

@Article{KagR80a,
  author =       "B. K{\aa}gstr{\"o}m and A. Ruhe",
  year =         "1980",
  title =        "Algorithm~560~{JNF}: An Algorithm for Numerical
                 Computation of the {Jordan} Normal Form of a Complex
                 Matrix",
  journal =      ACMMathSoft,
  volume =       "6",
  pages =        "437--443",
}

@Article{Kag85,
  author =       "B. K{\aa}gstr{\"o}m",
  year =         "1985",
  title =        "The Generalized Singular Value Decomposition and the
                 General {$A - \lambda B$} Problem",
  journal =      BIT,
  volume =       "24",
  pages =        "568--583",
}

@Article{Kag86,
  author =       "B. K{\aa}gstr{\"o}m",
  year =         "1986",
  title =        "{RGSVD}: An Algorithm for Computing the {Kronecker}
                 Structure and Reducing Subspaces of Singular {$A -
                 \lambda B$} Pencils",
  journal =      SIAMSciStat,
  volume =       "7",
  pages =        "185--211",
}

@Techreport{KagL88,
  author =       "B. K{\aa}gstr{\"o}m and P. Ling",
  year =         "1988",
  title =        "Level 2 and 3 {BLAS} Routines for the {IBM 3090
                 VF/400}: Implementation and Experiences",
  number =       "UMINF-154.88",
  institution =  "Information Processing, University of Ume{\aa}",
  address =      "S-901 87 Ume{\aa}, Sweden",
}

@Techreport{KagNP87,
  author =       "B. K{\aa}gstr{\"o}m and L. Nystr{\"o}m and P.
                 Poromaa",
  year =         "1987",
  title =        "Parallel Algorithms for Solving the Triangular
                 {Sylvester} Equation on a Hypercube Multiprocessor",
  number =       "UMINF-136.87",
  institution =  "Information Processing, University of Ume{\aa}",
  address =      "S-901 87 Ume{\aa}, Sweden",
}

@Techreport{KagNP88,
  author =       "B. K{\aa}gstr{\"o}m and L. Nystr{\"o}m and P.
                 Poromaa",
  year =         "1988",
  title =        "Parallel Shared Memory Algorithms for Solving the
                 Triangular {Sylvester} Equation",
  number =       "UMINF-155.88",
  institution =  "Information Processing, University of Ume{\aa}",
  address =      "S-901 87 Ume{\aa}, Sweden",
}

@Proceedings{KagR83,
  editor =       "B. K{\aa}gstr{\"o}m and A. Ruhe",
  year =         "1983",
  title =        "Proceedings of the Conference on Matrix Pencils,
                 {Pite} {Havsbad} 1982",
  series =       "Lecture Notes in Mathematics",
  volume =       "973",
  publisher =    Springer,
  address =      "New York and Berlin",
}

@Techreport{KagW87,
  author =       "B. K{\aa}gstr{\"o}m and L. Westin",
  year =         "1987",
  title =        "{GSYLV}- {Fortran} Routines for the Generalized
                 {Schur} Method with dif$^{-1}$ estimators for Solving
                 the Generalized {Sylvester} Equation",
  number =       "UMINF-132.86",
  institution =  "Information Processing, University of Ume{\aa}",
  address =      "S-901 87 Ume{\aa}, Sweden",
}

@Article{Kah66,
  author =       "W. Kahan",
  year =         "1966",
  title =        "Numerical Linear Algebra",
  journal =      CanMathBull,
  volume =       "9",
  pages =        "757--801",
}

@Techreport{Kah67,
  author =       "W. Kahan",
  year =         "1967",
  title =        "Inclusion Theorems for Clusters of Eigenvalues of
                 {Hermitian} Matrices",
  type =         "report",
  institution =  "Computer Science, University of Toronto",
  address =      "Toronto, Canada",
}

@Article{Kah75,
  author =       "W. Kahan",
  year =         "1975",
  title =        "Spectra of Nearly {Hermitian} Matrices",
  journal =      ProcAMS,
  volume =       "48",
  pages =        "11--17",
}

@Techreport{KahP74,
  author =       "W. Kahan and B. N. Parlett",
  year =         "1974",
  title =        "An Analysis of {Lanczos} Algorithms for Symmetric
                 Matrices",
  number =       "ERL-M467",
  institution =  "University of California, Berkeley",
  address =      "Berkeley, CA, USA",
}

@Incollection{KahP76,
  author =       "W. Kahan and B. N. Parlett",
  year =         "1976",
  title =        "How Far Should You Go with the {Lanczos} Process?",
  booktitle =    "Sparse Matrix Computations",
  editor =       "J. Bunch and D. Rose",
  publisher =    Academic,
  address =      "New York, NY, USA",
  pages =        "131--144",
}

@Article{KahPJ82,
  author =       "W. Kahan and B. N. Parlett and E. Jiang",
  year =         "1982",
  title =        "Residual Bounds on Approximate Eigensystems of
                 Nonnormal Matrices",
  journal =      SIAMNumAnal,
  volume =       "19",
  pages =        "470--484",
}

@Book{KahMN88,
  author =       "D. Kahaner and C. B. Moler and S. Nash",
  year =         "1988",
  title =        "Numerical Methods and Software",
  publisher =    PrenticeHall,
  address =      "Englewood Cliffs, NJ, USA",
}

@Article{Kan66,
  author =       "S. Kaniel",
  year =         "1966",
  title =        "Estimates for Some Computational Techniques in Linear
                 Algebra",
  journal =      MathComp,
  volume =       "20",
  pages =        "369--378",
}

@Article{KapB84,
  author =       "R. N. Kapur and J. C. Browne",
  year =         "1984",
  title =        "Techniques for Solving Block Tridiagonal Systems on
                 Reconfigurable Array Computers",
  journal =      SIAMSciStat,
  volume =       "5",
  pages =        "701--719",
}

@Article{Kar74,
  author =       "I. Karasalo",
  year =         "1974",
  title =        "A Criterion for Truncation of the {QR} Decomposition
                 Algorithm for the Singular Linear Least Squares
                 Problem",
  journal =      BIT,
  volume =       "14",
  pages =        "156--166",
}

@Book{Kat66,
  author =       "T. Kato",
  year =         "1966",
  title =        "Perturbation Theory for Linear Operators",
  publisher =    Springer,
  address =      "New York, NY, USA",
}

@Article{Kau74,
  author =       "L. Kaufman",
  year =         "1974",
  title =        "The {LZ} Algorithm to Solve the Generalized
                 Eigenvalue Problem",
  journal =      SIAMNumAnal,
  volume =       "11",
  pages =        "997--1024",
}

@Article{Kau77,
  author =       "L. Kaufman",
  year =         "1977",
  title =        "Some Thoughts on the {QZ} Algorithm for Solving the
                 Generalized Eigenvalue Problem",
  journal =      ACMMathSoft,
  volume =       "3",
  pages =        "65--75",
}

@Article{Kau79,
  author =       "L. Kaufman",
  year =         "1979",
  title =        "Application of Dense {Householder} Transformations to
                 a Sparse Matrix",
  journal =      ACMMathSoft,
  volume =       "5",
  pages =        "442--450",
}

@Article{Kau83,
  author =       "L. Kaufman",
  year =         "1983",
  title =        "Matrix Methods for Queueing Problems",
  journal =      SIAMSciStat,
  volume =       "4",
  pages =        "525--552",
}

@Article{Kau87,
  author =       "L. Kaufman",
  year =         "1987",
  title =        "The Generalized {Householder} Transformation and
                 Sparse Matrices",
  journal =      LinAlgApp,
  volume =       "90",
  pages =        "221--234",
}

@Article{KauG83,
  author =       "J. Kautsky and G. H. Golub",
  year =         "1983",
  title =        "On the Calculation of {Jacobi} Matrices",
  journal =      LinAlgApp,
  volume =       "52/53",
  pages =        "439--456",
}

@Incollection{Ker82,
  author =       "D. Kershaw",
  year =         "1982",
  title =        "Solution of Single Tridiagonal Linear Systems and
                 Vectorization of the {ICCG} Algorithm on the {Cray}-1",
  booktitle =    "Parallel Computation",
  editor =       "G. Roderigue",
  publisher =    Academic,
  address =      "New York, NY, USA",
}

@Article{Kie87,
  author =       "A. Kielbasinski",
  year =         "1987",
  title =        "A Note on Rounding Error Analysis of {Cholesky}
                 Factorization",
  journal =      LinAlgApp,
  volume =       "88/89",
  pages =        "487--494",
}

@Book{Knu81,
  author =       "D. Knuth",
  year =         "1981",
  title =        "Seminumerical-Algorithms",
  edition =      "second",
  publisher =    AddisonWesley,
  address =      "Reading, MA, USA",
  volume =       "2",
  series =       "The Art of Computer Programming",
}

@Article{Kog55,
  author =       "E. G. Kogbetliantz",
  year =         "1955",
  title =        "Solution of Linear Equations by Diagonalization of
                 Coefficient Matrix",
  journal =      QuartApplMath,
  volume =       "13",
  pages =        "123--132",
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@Article{KouP81,
  author =       "S. Kourouklis and C. C. Paige",
  year =         "1981",
  title =        "A Constrained Least Squares Approach to the General
                 {Gauss}-{Markov} Linear Model",
  journal =      AmerStatAssoc,
  volume =       "76",
  pages =        "620--625",
}

@Article{KriM86a,
  author =       "A. S. Krishnakuma and M. Morf",
  year =         "1986",
  title =        "Eigenvalues of a Symmetric Tridiagonal Matrix: A
                 Divide and Conquer Approach",
  journal =      NumerMath,
  volume =       "48",
  pages =        "349--368",
}

@Article{Kub61,
  author =       "V. N. Kublanovskaya",
  year =         "1961",
  title =        "On Some Algorithms for the Solution of the Complete
                 Eigenvalue Problem",
  journal =      USSRCompMathPhys,
  volume =       "3",
  pages =        "637--657",
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@Article{KubF64,
  author =       "V. N. Kublanovskaya and V. N. Fadeeva",
  year =         "1964",
  title =        "Computational Methods for the Solution of a
                 Generalized Eigenvalue Problem",
  journal =      AMSTrans,
  volume =       "2",
  pages =        "271--290",
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@Article{KulM86b,
  author =       "U. W. Kulisch and W. L. Miranker",
  year =         "1986",
  title =        "The Arithmetic of the Digital Computer",
  journal =      SIAMReview,
  volume =       "28",
  pages =        "1--40",
}

@Article{Kun82,
  author =       "H. T. Kung",
  year =         "1982",
  title =        "Why Systolic Architectures?",
  journal =      Computer,
  volume =       "15",
  pages =        "37--46",
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@Article{Bud64,
  author =       "C. D. La Budde",
  year =         "1964",
  title =        "Two Classes of Algorithms for Finding the Eigenvalues
                 and Eigenvectors of Real Symmetric Matrices",
  journal =      JACM,
  volume =       "11",
  pages =        "53--58",
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@Article{LamV75,
  author =       "J. Lambiotte and R. G. Voigt",
  year =         "1975",
  title =        "The Solution of Tridiagonal Linear Systems on the
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  journal =      ACMMathSoft,
  volume =       "1",
  pages =        "308--329",
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@Article{Lan70,
  author =       "P. Lancaster",
  year =         "1970",
  title =        "Explicit Solution of Linear Matrix Equations",
  journal =      SIAMReview,
  volume =       "12",
  pages =        "544--566",
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@Book{LanT85,
  author =       "P. Lancaster and M. Tismenetsky",
  year =         "1985",
  title =        "The Theory of Matrices",
  edition =      "second",
  publisher =    Academic,
  address =      "New York, NY, USA",
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@Article{Lan50,
  author =       "C. Lanczos",
  year =         "1950",
  title =        "An Iteration Method for the Solution of the
                 Eigenvalue Problem of Linear Differential and Integral
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  journal =      JResNatBurStand,
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  pages =        "255--282",
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@Article{LarS78,
  author =       "J. Larson and A. Sameh",
  year =         "1978",
  title =        "Efficient Calculation of the Effects of Roundoff
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  journal =      ACMMathSoft,
  volume =       "4",
  pages =        "228--236",
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@Article{Lau81,
  author =       "A. Laub",
  year =         "1981",
  title =        "Efficient Multivariable Frequency Response
                 Computations",
  journal =      IEEETransAC,
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@Article{Lau85,
  author =       "A. Laub",
  year =         "1985",
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  journal =      IEEETransAC,
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  pages =        "97--108",
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@Article{LawH69,
  author =       "C. L. Lawson and R. J. Hanson",
  year =         "1969",
  title =        "Extensions and Applications of the {Householder}
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  journal =      MathComp,
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@Book{LawH74,
  author =       "C. L. Lawson and R. J. Hanson",
  year =         "1974",
  title =        "Solving Least Squares Problems",
  publisher =    PrenticeHall,
  address =      "Englewood Cliffs, NJ, USA",
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@Article{LawHKK79b,
  author =       "C. L. Lawson and R. J. Hanson and D. R. Kincaid and F. T.
                 Krogh",
  year =         "1979",
  title =        "Basic Linear Algebra Subprograms for {Fortran} Usage",
  journal =      ACMMathSoft,
  volume =       "5",
  pages =        "308--323",
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@Article{LawHKK79a,
  author =       "C. L. Lawson and R. J. Hanson and D. R. Kincaid and F. T.
                 Krogh",
  year =         "1979",
  title =        "Algorithm~539: Basic Linear Algebra Subprograms for
                 {Fortran} Usage",
  journal =      ACMMathSoft,
  volume =       "5",
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@Article{Leh63,
  author =       "N. J. Lehmann",
  year =         "1963",
  title =        "Optimale {Eigenwerteinschliessungen}",
  journal =      NumerMath,
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@Article{Lem73,
  author =       "F. Lemeire",
  year =         "1973",
  title =        "Bounds for Condition Numbers of Triangular and
                 Trapezoid Matrices",
  journal =      BIT,
  volume =       "15",
  pages =        "58--64",
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@Book{Leo80,
  author =       "S. J. Leon",
  year =         "1980",
  title =        "Linear Algebra with Applications.",
  publisher =    Macmillan,
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@Article{Lev47,
  author =       "N. Levinson",
  year =         "1947",
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@Techreport{Lew77,
  author =       "J. Lewis",
  year =         "1977",
  title =        "Algorithms for Sparse Matrix Eigenvalue Problems",
  number =       "STAN-CS-77-595",
  institution =  "Department of Computer Science, Stanford University",
  address =      "Stanford, CA, USA",
}

@Article{LiC88,
  author =       "G. Li and T. Coleman",
  year =         "1988",
  title =        "A Parallel Triangular Solver for a Distributed-Memory
                 Multiprocessor",
  journal =      SIAMSciStat,
  volume =       "9",
  pages =        "485--502",
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@Book{Lin61,
  author =       "I. Linnik",
  year =         "1961",
  title =        "Method of Least Squares and Principles of the Theory
                 of Observation",
  publisher =    PergamonPress,
  address =      "New York, NY, USA",
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@Article{LoPS87,
  author =       "S. Lo and B. Philippe and A. Sameh",
  year =         "1987",
  title =        "A Multiprocessor Algorithm for the Symmetric
                 Tridiagonal Eigenvalue Problem",
  journal =      SIAMSciStat,
  volume =       "8",
  pages =        "s155--s165",
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@Article{Loi69,
  author =       "G. Loizou",
  year =         "1969",
  title =        "Nonnormality and {Jordan} Condition Numbers of
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@Article{Loi72,
  author =       "G. Loizou",
  year =         "1972",
  title =        "On the Quadratic Convergence of the {Jacobi} Method
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  volume =       "15",
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@Article{Lot56,
  author =       "M. Lotkin",
  year =         "1956",
  title =        "Characteristic Values of Arbitrary Matrices",
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  volume =       "14",
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@Book{Lue73,
  author =       "D. G. Luenberger",
  year =         "1973",
  title =        "Introduction to Linear and Nonlinear Programming",
  publisher =    AddisonWesley,
  address =      "New York, NY, USA",
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@Phdthesis{Luk78,
  author =       "F. T. Luk",
  year =         "1978",
  title =        "Sparse and Parallel Matrix Computations",
  number =       "STAN-CS-78-685",
  school =       "Computer Science, Stanford University",
  address =      "Stanford, CA, USA",
}

@Article{Luk80,
  author =       "F. T. Luk",
  year =         "1980",
  title =        "Computing the Singular Value Decomposition on the
                 {ILLIAC IV}",
  journal =      ACMMathSoft,
  volume =       "6",
  pages =        "524--539",
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@Article{Luk86a,
  author =       "F. T. Luk",
  year =         "1986",
  title =        "A Rotation Method for Computing the {QR}
                 Factorization",
  journal =      SIAMSciStat,
  volume =       "7",
  pages =        "452--459",
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@Article{Luk86b,
  author =       "F. T. Luk",
  year =         "1986",
  title =        "A Triangular Processor Array for Computing Singular
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  journal =      LinAlgApp,
  volume =       "77",
  pages =        "259--274",
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@Techreport{LusO83,
  author =       "E. Lusk and R. Overbeek",
  year =         "1983",
  title =        "Implementation of Monitors with Macros: A Programming
                 Aid for the {HEP} and other Parallel Processors",
  number =       "83-97",
  institution =  "Argonne National Laboratory",
  address =      "Argonne, ILL",
}

@Article{McCS73a,
  author =       "C. McCarthy and G. Strang",
  year =         "1973",
  title =        "Optimal Conditioning of Matrices",
  journal =      SIAMNumAnal,
  volume =       "10",
  pages =        "370--388",
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@Article{McC72,
  author =       "S. F. McCormick",
  year =         "1972",
  title =        "A General Approach to One-Step Iterative Methods with
                 Application to Eigenvalue Problems",
  journal =      CompSysSci,
  volume =       "6",
  pages =        "354--372",
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@Article{McK62,
  author =       "W. M. McKeeman",
  year =         "1962",
  title =        "Crout with Equilibration and Iteration",
  journal =      CACM,
  volume =       "5",
  pages =        "553--555",
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@Article{Mad59,
  author =       "A. Madansky",
  year =         "1959",
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  volume =       "54",
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@Article{MadRK76,
  author =       "N. Madsen and G. Roderigue and J. Karush",
  year =         "1976",
  title =        "Matrix Multiplication by Diagonals of a Vector
                 Parallel Processor",
  journal =      InfProcLet,
  pages =        "41--45",
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@Article{Mah79,
  author =       "K. N. Mahindar",
  year =         "1979",
  title =        "Linear Combinations of {Hermitian} and Real Symmetric
                 Matrices",
  journal =      LinAlgApp,
  volume =       "25",
  pages =        "95--105",
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@Article{Mak75,
  author =       "J. Makhoul",
  year =         "1975",
  title =        "Linear Prediction: A Tutorial Review",
  journal =      ProcIEEE,
  volume =       "63(4)",
  pages =        "561--580",
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@Article{MalP74,
  author =       "M. A. Malcolm and J. Palmer",
  year =         "1974",
  title =        "A Fast Method For Solving a Class of Tridiagonal
                 Systems of Linear Equations",
  journal =      CACM,
  volume =       "17",
  pages =        "14--17",
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@Article{Man77,
  author =       "T. A. Manteuffel",
  year =         "1977",
  title =        "The {Tchebychev} Iteration for Nonsymmetric Linear
                 Systems",
  journal =      NumerMath,
  volume =       "28",
  pages =        "307--327",
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@Inproceedings{Man79,
  author =       "T. A. Manteuffel",
  year =         "1979",
  title =        "Shifted Incomplete {Cholesky} Factorization",
  booktitle =    "Sparse Matrix Proceedings 1978",
  editor =       "I. S. Duff and G. W. Stewart",
  publisher =    SIAMPub,
  address =      "Philadelphia, PA, USA",
}

@Book{MarM64,
  author =       "M. Marcus and H. Minc",
  year =         "1964",
  title =        "A Survey of Matrix Theory and Matrix Inequalities",
  publisher =    AllynBacon,
  address =      "Boston, MA, USA",
}

@Book{MarG76,
  author =       "J. Markel and A. Gray",
  year =         "1976",
  title =        "Linear Prediction of Speech",
  publisher =    Springer,
  address =      "Berlin and New York",
}

@Article{MarPW65,
  author =       "R. S. Martin and G. Peters and J. H. Wilkinson",
  year =         "1965",
  title =        "Symmetric Decomposition of a Positive Definite
                 Matrix",
  journal =      NumerMath,
  volume =       "7",
  pages =        "362--383",
  note =         "Also in \cite[pages 9--30]{WilR71}",
}

@Article{MarPW66,
  author =       "R. S. Martin and G. Peters and J. H. Wilkinson",
  year =         "1966",
  title =        "Iterative Refinement of the Solution of a Positive
                 Definite System of Equations",
  journal =      NumerMath,
  volume =       "8",
  pages =        "203--216",
  note =         "Also in \cite[pages 31--44]{WilR71}",
}

@Article{MarPW70,
  author =       "R. S. Martin and G. Peters and J. H. Wilkinson",
  year =         "1970",
  title =        "The {QR} Algorithm for Real {Hessenberg} Matrices",
  journal =      NumerMath,
  volume =       "14",
  pages =        "219--231",
  note =         "Also in \cite[pages 359--371]{WilR71}",
}

@Article{MarRW70,
  author =       "R. S. Martin and C. Reinsch and J. H. Wilkinson",
  year =         "1970",
  title =        "The {QR} Algorithm for Band Symmetric Matrices",
  journal =      NumerMath,
  volume =       "16",
  pages =        "85--92",
  note =         "Also in \cite[pages 266--272]{WilR71}",
}

@Article{MarW65,
  author =       "R. S. Martin and J. H. Wilkinson",
  year =         "1965",
  title =        "Symmetric Decomposition of Positive Definite Band
                 Matrices",
  journal =      NumerMath,
  volume =       "7",
  pages =        "355--361",
  note =         "Also in \cite[pages 50--56]{WilR71}",
}

@Article{MarW67,
  author =       "R. S. Martin and J. H. Wilkinson",
  year =         "1967",
  title =        "Solution of Symmetric and Unsymmetric Band Equations
                 and the Calculation of Eigenvalues of Band Matrices",
  journal =      NumerMath,
  volume =       "9",
  pages =        "279--301",
  note =         "Also in \cite[pages 70--92]{WilR71}",
}

@Article{MarW68a,
  author =       "R. S. Martin and J. H. Wilkinson",
  year =         "1968",
  title =        "{Householder}'s Tridiagonalization of a Symmetric
                 Matrix",
  journal =      NumerMath,
  volume =       "11",
  pages =        "181--195",
  note =         "Also in \cite[pages 212--226]{WilR71}",
}

@Article{MarW68b,
  author =       "R. S. Martin and J. H. Wilkinson",
  year =         "1968",
  title =        "The Modified {LR} Algorithm for Complex {Hessenberg}
                 Matrices",
  journal =      NumerMath,
  volume =       "12",
  pages =        "369--376",
  note =         "Also in \cite[pages 396--403]{WilR71}",
}

@Article{MarW68c,
  author =       "R. S. Martin and J. H. Wilkinson",
  year =         "1968",
  title =        "Reduction of the Symmetric Eigenproblem {$Ax =
                 \lambda Bx$} and Related Problems to Standard Form",
  journal =      NumerMath,
  volume =       "11",
  pages =        "99--110",
}

@Article{MarW68d,
  author =       "R. S. Martin and J. H. Wilkinson",
  year =         "1968",
  title =        "Similarity Reduction of a General Matrix to
                 {Hessenberg} Form",
  journal =      NumerMath,
  volume =       "12",
  pages =        "349--368",
  note =         "Also in \cite[pages 339--358]{WilR71}",
}

@Article{MvdV87,
  author =       "O. McBryan and E. F. van de Velde",
  year =         "1987",
  title =        "Hypercube Algorithms and Implementations",
  journal =      SIAMSciStat,
  volume =       "8",
  pages =        "s227--s287",
}

@Article{MdV77,
  author =       "J. A. Meijerink and H. A. Van der Vorst",
  year =         "1977",
  title =        "An Iterative Solution Method for Linear Equations
                 Systems of Which the Coefficient Matrix is a Symmetric
                 {$M$}-Matrix",
  journal =      MathComp,
  volume =       "31",
  pages =        "148--162",
}

@Article{Mei83,
  author =       "J. Meinguet",
  year =         "1983",
  title =        "Refined Error Analyses of {Cholesky} Factorization",
  journal =      SIAMNumAnal,
  volume =       "20",
  pages =        "1243--1250",
}

@Article{Mel87,
  author =       "R. Melhem",
  year =         "1987",
  title =        "Toward efficient Implementation of Preconditioned
                 Conjugate Gradient Methods on Vector Supercomputers",
  journal =      IntSuper,
  volume =       "1",
  pages =        "70--98",
}

@Article{Mer85,
  author =       "M. L. Merriam",
  year =         "1985",
  title =        "On the Factorization of Block Tridiagonals With
                 Storage Constraints",
  journal =      SIAMSciStat,
  volume =       "6",
  pages =        "182--192",
}

@Article{Meu84,
  author =       "G. Meurant",
  year =         "1984",
  title =        "The Block Preconditioned Conjugate Gradient Method on
                 Vector Computers",
  journal =      BIT,
  volume =       "24",
  pages =        "623--633",
}

@Article{Meu89,
  author =       "G. Meurant",
  year =         "1989",
  title =        "Domain Decomposition Methods for Partial Differential
                 Equations on Parallel Computers",
  journal =      IntSuper,
  note =         "To appear",
}

@Article{Mil75,
  author =       "W. Miller",
  year =         "1975",
  title =        "Computational Complexity and Numerical Stability",
  journal =      SIAMComp,
  volume =       "4",
  pages =        "97--107",
}

@Article{MilS78,
  author =       "W. Miller and D. Spooner",
  year =         "1978",
  title =        "Software for Roundoff Analysis, {II}",
  journal =      ACMMathSoft,
  volume =       "4",
  pages =        "369--390",
}

@Article{MimP82,
  author =       "G. Miminis and C. C. Paige",
  year =         "1982",
  title =        "An Algorithm for Pole Assignment of Time Invariant
                 Linear Systems",
  journal =      IntControl,
  volume =       "35",
  pages =        "341--354",
}

@Book{Mir55,
  author =       "L. Mirsky",
  year =         "1955",
  title =        "An Introduction to Linear Algebra",
  publisher =    OxfordPress,
  address =      "London, UK",
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@Article{Mir60,
  author =       "L. Mirsky",
  year =         "1960",
  title =        "Symmetric Gauge Functions and Unitarily Invariant
                 Norms",
  journal =      QuartMath,
  volume =       "11",
  pages =        "50--59",
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@Book{Mod88,
  author =       "J. J. Modi",
  year =         "1988",
  title =        "Parallel Algorithms and Matrix Computation",
  publisher =    OxfordPress,
  address =      "Oxford, UK",
}

@Article{ModC86,
  author =       "J. J. Modi and M. R. B. Clarke",
  year =         "1986",
  title =        "An Alternative {Givens} Ordering",
  journal =      NumerMath,
  volume =       "43",
  pages =        "83--90",
}

@Article{ModP85,
  author =       "J. J. Modi and J. D. Pryce",
  year =         "1985",
  title =        "Efficient Implementation of {Jacobi}'s
                 Diagonalization Method on the {DAP}",
  journal =      NumerMath,
  volume =       "46",
  pages =        "443--454",
}

@Article{Mol67,
  author =       "C. B. Moler",
  year =         "1967",
  title =        "Iterative Refinement in Floating Point",
  journal =      JACM,
  volume =       "14",
  pages =        "316--371",
}

@Techreport{Mol80,
  author =       "C. B. Moler",
  year =         "1980",
  title =        "{MATLAB} User's Guide",
  number =       "CS81-1",
  institution =  "Computer Science, University of New Mexico",
  address =      "Albuquerque, NM, USA",
  bibdate =      "Tue Mar 14 19:21:58 1995",
}

@Incollection{Mol86,
  author =       "C. B. Moler",
  year =         "1986",
  title =        "Matrix Computations on Distributed Memory
                 Multiprocessors",
  booktitle =    "Hypercube Multiprocessors",
  editor =       "M. T. Heath",
  publisher =    SIAMPub,
  address =      "Philadelphia, PA, USA",
}

@Manual{MolLB87,
  author =       "C. B. Moler and J. N. Little and S. Bangert",
  year =         "1987",
  title =        "{PC}-{Matlab} Users Guide",
  publisher =    MathWorks,
  address =      "20 N. Main St., Sherborn, MA, USA",
}

@Article{MolM83,
  author =       "C. B. Moler and D. Morrison",
  year =         "1983",
  title =        "Singular Value Analysis of Cryptograms",
  journal =      AmerMathMonthly,
  volume =       "90",
  pages =        "78--87",
}

@Article{MolS73b,
  author =       "C. B. Moler and G. W. Stewart",
  year =         "1973",
  title =        "An Algorithm for Generalized Matrix Eigenvalue
                 Problems",
  journal =      SIAMNumAnal,
  volume =       "10",
  pages =        "241--256",
}

@Article{MolL78,
  author =       "C. B. Moler and C. F. Van Loan",
  year =         "1978",
  title =        "Nineteen Dubious Ways to Compute the Exponential of a
                 Matrix",
  journal =      SIAMReview,
  volume =       "20",
  pages =        "801--836",
}

@Article{MonL82,
  author =       "R. Montoye and D. Laurie",
  year =         "1982",
  title =        "A Practical Algorithm for the Solution of Triangular
                 Systems on a Parallel Processing System",
  journal =      IEEETransComp,
  volume =       "C-31",
  pages =        "1076--1082",
}

@Article{Mue66,
  author =       "D. Mueller",
  year =         "1966",
  title =        "{Householder}'s Method for Complex Matrices and
                 {Hermitian} Matrices",
  journal =      NumerMath,
  volume =       "8",
  pages =        "72--92",
}

@Article{MurW31,
  author =       "F. D. Murnaghan and A. Wintner",
  year =         "1931",
  title =        "A Canonical Form for Real Matrices Under Orthogonal
                 Transformations",
  journal =      ProcNAS,
  volume =       "17",
  pages =        "417--420",
}

@Article{Nan85,
  author =       "T. Nanda",
  year =         "1985",
  title =        "Differential Equations and the {QR} Algorithm",
  journal =      SIAMNumAnal,
  volume =       "22",
  pages =        "310--321",
}

@Article{Nas75,
  author =       "J. C. Nash",
  year =         "1975",
  title =        "A One-Sided Transformation Method for the Singular
                 Value Decomposition and Algebraic Eigenproblem",
  journal =      CompJour,
  volume =       "18",
  pages =        "74--76",
}

@Book{Nas76,
  author =       "M. Z. Nashed",
  year =         "1976",
  title =        "Generalized Inverses and Applications",
  publisher =    Academic,
  address =      "New York, NY, USA",
}

@Article{Nic74,
  author =       "R. A. Nicolaides",
  year =         "1974",
  title =        "On a Geometrical Aspect of {SOR} and the Theory of
                 Consistent Ordering for Positive Definite Matrices",
  journal =      NumerMath,
  volume =       "23",
  pages =        "99--104",
}

@Article{NieV83,
  author =       "W. Niethammer and R. S. Varga",
  year =         "1983",
  title =        "The Analysis of {$k$}-step Iterative Methods for
                 Linear Systems from Summability Theory",
  journal =      NumerMath,
  volume =       "41",
  pages =        "177--206",
}

@Book{NobD77,
  author =       "B. Noble and J. W. Daniel",
  year =         "1977",
  title =        "Applied Linear Algebra",
  publisher =    PrenticeHall,
  address =      "Englewood Cliffs, NJ, USA",
}

@Article{NooV75,
  author =       "A. Noor and R. Voigt",
  year =         "1975",
  title =        "Hypermatrix Scheme for the {STAR-100} Computer",
  journal =      CompStruct,
  volume =       "5",
  pages =        "287--296",
}

@Article{OetP64,
  author =       "W. Oettli and W. Prager",
  year =         "1964",
  title =        "Compatibility of Approximate Solutions of Linear
                 Equations with Given Error Bounds for Coefficients and
                 Right Hand Sides",
  journal =      NumerMath,
  volume =       "6",
  pages =        "405--409",
}

@Phdthesis{OLe76,
  author =       "D. P. O'Leary",
  year =         "1976",
  title =        "Hybrid Conjugate Gradient Algorithms",
  number =       "STAN-CS-76-548",
  school =       "Computer Science, Stanford University",
  address =      "Stanford, CA, USA",
}

@Article{OLe80a,
  author =       "D. P. O'Leary",
  year =         "1980",
  title =        "The Block Conjugate Gradient Algorithm and Related
                 Methods",
  journal =      LinAlgApp,
  volume =       "29",
  pages =        "293--322",
}

@Article{OLe80b,
  author =       "D. P. O'Leary",
  year =         "1980",
  title =        "Estimating Matrix Condition Numbers",
  journal =      SIAMSciStat,
  volume =       "1",
  pages =        "205--209",
}

@Article{OLeS81,
  author =       "D. P. O'Leary and J. A. Simmons",
  year =         "1981",
  title =        "A Bidiagonalization - Regularization Procedure for
                 Large Scale Discretizations of Ill-Posed Problems",
  journal =      SIAMSciStat,
  volume =       "2",
  pages =        "474--489",
}

@Article{OLeS85,
  author =       "D. P. O'Leary and G. W. Stewart",
  year =         "1985",
  title =        "Data Flow Algorithms for Parallel Matrix
                 Computations",
  journal =      CACM,
  volume =       "28",
  pages =        "841--853",
}

@Article{OLeS86,
  author =       "D. P. O'Leary and G. W. Stewart",
  year =         "1986",
  title =        "Assignment and Scheduling in Parallel Matrix
                 Factorization",
  journal =      LinAlgApp,
  volume =       "77",
  pages =        "275--300",
}

@Book{Opp78,
  author =       "A. V. Oppenheim",
  year =         "1978",
  title =        "Applications of Digital Signal Processing",
  publisher =    PrenticeHall,
  address =      "Englewood Cliffs, NJ, USA",
}

@Book{Ort72,
  author =       "J. M. Ortega",
  year =         "1972",
  title =        "Numerical Analysis: A Second Course",
  publisher =    Academic,
  address =      "New York, NY, USA",
}

@Book{Ort88,
  author =       "J. M. Ortega",
  year =         "1988",
  title =        "Matrix Theory: A Second Course",
  publisher =    PlenumPress,
  address =      "New York, NY, USA",
}

@Article{OrtR88,
  author =       "J. M. Ortega and C. H. Romine",
  year =         "1988",
  title =        "The {$ijk$} Forms of Factorization Methods {II}:
                 Parallel Systems",
  journal =      ParComputing,
  volume =       "7",
  pages =        "149--162",
}

@Article{OrtV85,
  author =       "J. M. Ortega and R. G. Voigt",
  year =         "1985",
  title =        "Solution of Partial Differential Equations on Vector
                 and Parallel Computers",
  journal =      SIAMReview,
  volume =       "27",
  pages =        "149--240",
}

@Article{Osb60,
  author =       "E. E. Osborne",
  year =         "1960",
  title =        "On Preconditioning of Matrices",
  journal =      JACM,
  volume =       "7",
  pages =        "338--345",
}

@Article{Paa71,
  author =       "M. H. C. Paardekooper",
  year =         "1971",
  title =        "An Eigenvalue Algorithm for Skew Symmetric Matrices",
  journal =      NumerMath,
  volume =       "17",
  pages =        "189--202",
}

@Article{Pai70,
  author =       "C. C. Paige",
  year =         "1970",
  title =        "Practical Use of the Symmetric {Lanczos} Process with
                 Reorthogonalization",
  journal =      BIT,
  volume =       "10",
  pages =        "183--195",
}

@Phdthesis{Pai71,
  author =       "C. C. Paige",
  year =         "1971",
  title =        "The Computation of Eigenvalues and Eigenvectors of
                 Very Large Sparse Matrices",
  school =       "London University",
  address =      "London, UK",
}

@Article{Pai73,
  author =       "C. C. Paige",
  year =         "1973",
  title =        "An Error Analysis of a Method for Solving Matrix
                 Equations",
  journal =      MathComp,
  volume =       "27",
  pages =        "355--359",
}

@Article{Pai74a,
  author =       "C. C. Paige",
  year =         "1974",
  title =        "Bidiagonalization of Matrices and Solution of Linear
                 Equations",
  journal =      SIAMNumAnal,
  volume =       "11",
  pages =        "197--209",
}

@Article{Pai74b,
  author =       "C. C. Paige",
  year =         "1974",
  title =        "Eigenvalues of Perturbed {Hermitian} Matrices",
  journal =      LinAlgApp,
  volume =       "8",
  pages =        "1--10",
}

@Article{Pai76,
  author =       "C. C. Paige",
  year =         "1976",
  title =        "Error Analysis of the {Lanczos} Algorithm for
                 Tridiagonalizing a Symmetric Matrix",
  journal =      InstMathApp,
  volume =       "18",
  pages =        "341--349",
}

@Article{Pai79a,
  author =       "C. C. Paige",
  year =         "1979",
  title =        "Computer Solution and Perturbation Analysis of
                 Generalized Least Squares Problems",
  journal =      MathComp,
  volume =       "33",
  pages =        "171--184",
}

@Article{Pai79b,
  author =       "C. C. Paige",
  year =         "1979",
  title =        "Fast Numerically Stable Computations for Generalized
                 Linear Least Squares Problems",
  journal =      SIAMNumAnal,
  volume =       "16",
  pages =        "165--171",
}

@Article{Pai80,
  author =       "C. C. Paige",
  year =         "1980",
  title =        "Accuracy and Effectiveness of the {Lanczos} Algorithm
                 for the Symmetric Eigenproblem",
  journal =      LinAlgApp,
  volume =       "34",
  pages =        "235--258",
}

@Article{Pai81,
  author =       "C. C. Paige",
  year =         "1981",
  title =        "Properties of Numerical Algorithms Related to
                 Computing Controllability",
  journal =      IEEETransAC,
  volume =       "AC-26",
  pages =        "130--138",
}

@Article{Pai84,
  author =       "C. C. Paige",
  year =         "1984",
  title =        "A Note on a Result of {Sun} {J}.-{Guang}: Sensitivity
                 of the {CS} and {GSV} Decompositions",
  journal =      SIAMNumAnal,
  volume =       "21",
  pages =        "186--191",
}

@Article{Pai85,
  author =       "C. C. Paige",
  year =         "1985",
  title =        "The General Linear Model and the Generalized Singular
                 Value Decomposition",
  journal =      LinAlgApp,
  volume =       "70",
  pages =        "269--284",
}

@Article{Pai86,
  author =       "C. C. Paige",
  year =         "1986",
  title =        "Computing the Generalized Singular Value
                 Decomposition",
  journal =      SIAMSciStat,
  volume =       "7",
  pages =        "1126--1146",
}

@Article{PaiD86,
  author =       "C. C. Paige and P. Van Dooren",
  year =         "1986",
  title =        "On the Quadratic Convergence of {Kogbetliantz}'s
                 Algorithm for Computing the Singular Value
                 Decomposition",
  journal =      LinAlgApp,
  volume =       "77",
  pages =        "301--313",
}

@Article{PaiS75,
  author =       "C. C. Paige and M. A. Saunders",
  year =         "1975",
  title =        "Solution of Sparse Indefinite Systems of Linear
                 Equations",
  journal =      SIAMNumAnal,
  volume =       "12",
  pages =        "617--629",
}

@Techreport{PaiS78,
  author =       "C. C. Paige and M. A. Saunders",
  year =         "1978",
  title =        "A Bidiagonalization Algorithm for Sparse Linear
                 Equations and Least Squares Problems",
  number =       "SOL 78-19",
  institution =  "Operations Research, Stanford University",
  address =      "Stanford, CA, USA",
}

@Article{PaiS81,
  author =       "C. C. Paige and M. Saunders",
  year =         "1981",
  title =        "Towards A Generalized Singular Value Decomposition",
  journal =      SIAMNumAnal,
  volume =       "18",
  pages =        "398--405",
}

@Article{PaiS82b,
  author =       "C. C. Paige and M. A. Saunders",
  year =         "1982",
  title =        "{LSQR}: An Algorithm for Sparse Linear Equations and
                 Sparse Least Squares",
  journal =      ACMMathSoft,
  volume =       "8",
  pages =        "43--71",
}

@Article{PaiS82a,
  author =       "C. C. Paige and M. A. Saunders",
  year =         "1982",
  title =        "Algorithm~583~{LSQR}: Sparse Linear Equations and
                 Least Squares Problems",
  journal =      ACMMathSoft,
  volume =       "8",
  pages =        "195--209",
}

@Article{PaiL81,
  author =       "C. C. Paige and C. Van Loan",
  year =         "1981",
  title =        "A {Schur} Decomposition for {Hamiltonian} Matrices",
  journal =      LinAlgApp,
  volume =       "41",
  pages =        "11--32",
}

@Article{Pan84,
  author =       "V. Pan",
  year =         "1984",
  title =        "How Can We Speed Up Matrix Multiplication?",
  journal =      SIAMReview,
  volume =       "26",
  pages =        "393--416",
}

@Article{Par65,
  author =       "B. N. Parlett",
  year =         "1965",
  title =        "Convergence of the {QR} Algorithm",
  journal =      NumerMath,
  volume =       "7",
  pages =        "187--193",
  note =         "Correction in Numerische Mathematik 10, pp. 163--164",
}

@Article{Par66,
  author =       "B. N. Parlett",
  year =         "1966",
  title =        "Singular and Invariant Matrices Under the {QR}
                 Algorithm",
  journal =      MathComp,
  volume =       "20",
  pages =        "611--615",
}

@Article{Par67,
  author =       "B. N. Parlett",
  year =         "1967",
  title =        "Canonical Decomposition of {Hessenberg} Matrices",
  journal =      MathComp,
  volume =       "21",
  pages =        "223--227",
}

@Article{Par68,
  author =       "B. N. Parlett",
  year =         "1968",
  title =        "Global Convergence of the Basic {QR} Algorithm on
                 {Hessenberg} Matrices",
  journal =      MathComp,
  volume =       "22",
  pages =        "803--817",
}

@Article{Par71,
  author =       "B. N. Parlett",
  year =         "1971",
  title =        "Analysis of Algorithms for Reflections in Bisectors",
  journal =      SIAMReview,
  volume =       "13",
  pages =        "197--208",
}

@Techreport{Par74a,
  author =       "B. N. Parlett",
  year =         "1974",
  title =        "Computation of Functions of Triangular Matrices",
  type =         "Memorandum",
  number =       "ERL-M481",
  institution =  "Electronics Research Laboratory, College of
                 Engineering, University of California, Berkeley",
  address =      "Berkeley, CA, USA",
}

@Article{Par74b,
  author =       "B. N. Parlett",
  year =         "1974",
  title =        "The {Rayleigh} Quotient Iteration and Some
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  volume =       "28",
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  year =         "1976",
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@Article{Par80a,
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@Book{Par80b,
  author =       "B. N. Parlett",
  year =         "1980",
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  volume =       "10",
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  year =         "1981",
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  volume =       "1",
  pages =        "135--155",
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@Article{ParR69,
  author =       "B. N. Parlett and C. Reinsch",
  year =         "1969",
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@Article{ParS79,
  author =       "B. N. Parlett and D. S. Scott",
  year =         "1979",
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  year =         "1982",
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  year =         "1969",
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@Article{PetW70a,
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  year =         "1970",
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@Article{PetW70b,
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  year =         "1970",
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  author =       "G. Peters and J. H. Wilkinson",
  year =         "1971",
  title =        "The Calculation of Specified Eigenvectors by Inverse
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  booktitle =    "Handbook for Automatic Computation Vol. 2: Linear
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  editor =       "J. H. Wilkinson and C. Reinsch",
  publisher =    Springer,
  address =      "New York, NY, USA",
  pages =        "418--439",
}

@Article{PetW79,
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  year =         "1979",
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  volume =       "21",
  pages =        "339--360",
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  volume =       "25",
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  year =         "1974",
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@Article{Ple86,
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  year =         "1986",
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@Article{PooO87,
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  year =         "1987",
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@Article{PopT57,
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  year =         "1987",
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  booktitle =    "Hypercube Multiprocessors",
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  year =         "1968",
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  year =         "1984",
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  year =         "1985",
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  author =       "W. Rath",
  year =         "1982",
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@Article{Rei67,
  author =       "J. K. Reid",
  year =         "1967",
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@Article{Rei71a,
  author =       "J. K. Reid",
  year =         "1971",
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@Incollection{Rei71b,
  author =       "J. K. Reid",
  year =         "1971",
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  editor =       "J. K. Reid",
  publisher =    Academic,
  address =      "New York, NY, USA",
  pages =        "231--254",
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@Article{Rei72,
  author =       "J. K. Reid",
  year =         "1972",
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  pages =        "325--332",
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@Article{ReiB68,
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  year =         "1968",
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  note =         "Also in \cite[pages 257--265]{WilR71}",
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@Article{Ric66b,
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@Book{Ric81,
  author =       "J. R. Rice",
  year =         "1981",
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  editor =       "G. Roderigue",
  year =         "1982",
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  editor =       "D. J. Rose and R. A. Willoughby",
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@Article{RodW84b,
  author =       "G. Roderigue and D. Wolitzer",
  year =         "1984",
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  volume =       "42",
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@Book{Rod82b,
  editor =       "G. Roderigue",
  year =         "1982",
  title =        "Parallel Computations",
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@Article{Ruh67,
  author =       "A. Ruhe",
  year =         "1967",
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                 for Normal Matrices",
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  volume =       "7",
  pages =        "305--313",
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@Article{Ruh68,
  author =       "A. Ruhe",
  year =         "1968",
  title =        "On the Quadratic Convergence of a Generalization of
                 the {Jacobi} Method to Arbitrary Matrices",
  journal =      BIT,
  volume =       "8",
  pages =        "210--231",
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@Article{Ruh69b,
  author =       "A. Ruhe",
  year =         "1969",
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@Article{Ruh69a,
  author =       "A. Ruhe",
  year =         "1969",
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  volume =       "10",
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@Article{Ruh70a,
  author =       "A. Ruhe",
  year =         "1970",
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                 Invariant Subspaces",
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@Article{Ruh70b,
  author =       "A. Ruhe",
  year =         "1970",
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@Article{Ruh74,
  author =       "A. Ruhe",
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@Article{Ruh75,
  author =       "A. Ruhe",
  year =         "1975",
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@Article{Ruh78,
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@Article{Ruh83,
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@Article{Ruh87,
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  author =       "W. Sch{\"o}nauer",
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  year =         "1986",
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@Article{SchL89,
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@Article{Sch09,
  author =       "I. Schur",
  year =         "1909",
  title =        "On the Characteristic Roots of a Linear Substitution
                 with an Application to the Theory of Integral
                 Equations",
  journal =      MathAnnalen,
  volume =       "66",
  pages =        "488--510",
  note =         "German",
}

@Article{Sch68,
  author =       "H. R. Schwartz",
  year =         "1968",
  title =        "Tridiagonalization of a Symmetric Band Matrix",
  journal =      NumerMath,
  volume =       "12",
  pages =        "231--241",
  note =         "Also in \cite[pages 273--283]{WilR71}",
}

@Article{Sch74,
  author =       "H. R. Schwartz",
  year =         "1974",
  title =        "The Method of Coordinate Relaxation for {$(A -
                 \lambda B)x = 0$}",
  journal =      NumerMath,
  volume =       "23",
  pages =        "135--152",
}

@Techreport{Sco78,
  author =       "D. S. Scott",
  year =         "1978",
  title =        "Analysis of the Symmetric {Lanczos} Process",
  number =       "M78/40",
  institution =  "UCB-ERL, University of California, Berkeley",
  address =      "Berkeley, CA, USA",
}

@Techreport{Sco79a,
  author =       "D. S. Scott",
  year =         "1979",
  title =        "Block {Lanczos} Software for Symmetric Eigenvalue
                 Problems",
  number =       "ORNL/CSD-48",
  institution =  "Oak Ridge National Laboratory",
  address =      "Oak Ridge, TN, USA",
}

@Article{Sco79b,
  author =       "D. S. Scott",
  year =         "1979",
  title =        "How to Make the {Lanczos} Algorithm Converge Slowly",
  journal =      MathComp,
  volume =       "33",
  pages =        "239--247",
}

@Article{Sco84,
  author =       "D. S. Scott",
  year =         "1984",
  title =        "Computing a Few Eigenvalues and Eigenvectors of a
                 Symmetric Band Matrix",
  journal =      SIAMSciStat,
  volume =       "5",
  pages =        "658--666",
}

@Article{Sco85,
  author =       "D. S. Scott",
  year =         "1985",
  title =        "On the Accuracy of the {Gershgorin} Circle Theorem
                 for Bounding the Spread of a Real Symmetric Matrix",
  journal =      LinAlgApp,
  volume =       "65",
  pages =        "147--155",
}

@Article{ScoHW86,
  author =       "D. S. Scott and M. T. Heath and R. C. Ward",
  year =         "1986",
  title =        "Parallel Block {Jacobi} Eigenvalue Algorithms Using
                 Systolic Arrays",
  journal =      LinAlgApp,
  volume =       "77",
  pages =        "345--356",
}

@Article{Sea86,
  author =       "M. K. Seager",
  year =         "1986",
  title =        "Parallelizing Conjugate Gradient for the {Cray X-MP}",
  journal =      ParComputing,
  volume =       "3",
  pages =        "35--47",
}

@Article{Sea69,
  author =       "J. J. Seaton",
  year =         "1969",
  title =        "Diagonalization of Complex Symmetric Matrices Using a
                 Modified {Jacobi} Method",
  journal =      CompJour,
  volume =       "12",
  pages =        "156--157",
}

@Article{Ser80,
  author =       "S. Serbin",
  year =         "1980",
  title =        "On Factoring a Class of Complex Symmetric Matrices
                 Without Pivoting",
  journal =      MathComp,
  volume =       "35",
  pages =        "1231--1234",
}

@Article{SerB79,
  author =       "S. Serbin and S. Blalock",
  year =         "1979",
  title =        "An Algorithm for Computing the Matrix Cosine",
  journal =      SIAMSciStat,
  volume =       "1",
  pages =        "198--204",
}

@Article{She55,
  author =       "J. W. Sheldon",
  year =         "1955",
  title =        "On the Numerical Solution of Elliptic Difference
                 Equations",
  journal =      TablesAidsComp,
  volume =       "9",
  pages =        "101--112",
}

@Techreport{ShrS87,
  author =       "G. Shroff and R. Schreiber",
  year =         "1987",
  title =        "Convergence of Block {Jacobi} Methods",
  number =       "87-25",
  institution =  "Computer Science, Rensselaer Polytechnic Institute",
  address =      "Troy, NY, USA",
}

@Article{Sim84,
  author =       "H. Simon",
  year =         "1984",
  title =        "Analysis of the Symmetric {Lanczos} Algorithm with
                 Reorthogonalization Methods",
  journal =      LinAlgApp,
  volume =       "61",
  pages =        "101--132",
}

@Article{SinS76,
  author =       "B. Singer and S. Spilerman",
  year =         "1976",
  title =        "The Representation of Social Processes by {Markov}
                 Models",
  journal =      AmerSocio,
  volume =       "82",
  pages =        "1--54",
}

@Article{Ske79,
  author =       "R. D. Skeel",
  year =         "1979",
  title =        "Scaling for Numerical Stability in {Gaussian}
                 Elimination",
  journal =      JACM,
  volume =       "26",
  pages =        "494--526",
}

@Article{Ske80,
  author =       "R. D. Skeel",
  year =         "1980",
  title =        "Iterative Refinement Implies Numerical Stability for
                 {Gaussian} Elimination",
  journal =      MathComp,
  volume =       "35",
  pages =        "817--832",
}

@Article{Ske81,
  author =       "R. D. Skeel",
  year =         "1981",
  title =        "Effect of Equilibration on Residual Size for Partial
                 Pivoting",
  journal =      SIAMNumAnal,
  volume =       "18",
  pages =        "449--455",
}

@Book{SmiBI+70,
  author =       "B. T. Smith and J. M. Boyle and Y. Ikebe and V. C. Klema
                 and C. B. Moler",
  year =         "1970",
  title =        "Matrix Eigensystem Routines: {EISPACK} Guide",
  edition =      "second",
  publisher =    Springer,
  address =      "New York, NY, USA",
}

@Article{Smi67,
  author =       "R. A. Smith",
  year =         "1967",
  title =        "The Condition Numbers of the Matrix Eigenvalue
                 Problem",
  journal =      NumerMath,
  volume =       "10",
  pages =        "232--240",
}

@Book{Smi70,
  author =       "F. Smithies",
  year =         "1970",
  title =        "Integral Equations",
  publisher =    CambridgePress,
  address =      "Cambridge, UK",
}

@Article{Sor85,
  author =       "D. Sorensen",
  year =         "1985",
  title =        "Analysis of Pairwise Pivoting in {Gaussian}
                 Elimination",
  journal =      IEEETransComp,
  volume =       "C-34",
  pages =        "274--278",
}

@Article{Ste81a,
  author =       "D. Stevenson",
  year =         "1981",
  title =        "A Proposed Standard for Binary Floating Point
                 Arithmetic",
  journal =      Computer,
  volume =       "14",
  month =        mar,
  pages =        "51--62",
}

@Article{Ste69,
  author =       "G. W. Stewart",
  year =         "1969",
  title =        "Accelerating the Orthogonal Iteration for the
                 Eigenvectors of a {Hermitian} Matrix",
  journal =      NumerMath,
  volume =       "13",
  pages =        "362--376",
}

@Article{Ste70,
  author =       "G. W. Stewart",
  year =         "1970",
  title =        "Incorporating Origin Shifts into the {QR} Algorithm
                 for Symmetric Tridiagonal Matrices",
  journal =      CACM,
  volume =       "13",
  pages =        "365--367",
}

@Article{Ste71,
  author =       "G. W. Stewart",
  year =         "1971",
  title =        "Error Bounds for Approximate Invariant Subspaces of
                 Closed Linear Operators",
  journal =      SIAMNumAnal,
  volume =       "8",
  pages =        "796--808",
}

@Article{Ste72,
  author =       "G. W. Stewart",
  year =         "1972",
  title =        "On the Sensitivity of the Eigenvalue Problem {$Ax =
                 \lambda Bx$}",
  journal =      SIAMNumAnal,
  volume =       "9",
  pages =        "669--686",
}

@Article{Ste73a,
  author =       "G. W. Stewart",
  year =         "1973",
  title =        "Conjugate Direction Methods for Solving Systems of
                 Linear Equations",
  journal =      NumerMath,
  volume =       "21",
  pages =        "284--297",
}

@Article{Ste73b,
  author =       "G. W. Stewart",
  year =         "1973",
  title =        "Error and Perturbation Bounds for Subspaces
                 Associated with Certain Eigenvalue Problems",
  journal =      SIAMReview,
  volume =       "15",
  pages =        "727--764",
}

@Book{Ste73c,
  author =       "G. W. Stewart",
  year =         "1973",
  title =        "Introduction to Matrix Computations",
  publisher =    Academic,
  address =      "New York, NY, USA",
}

@Inproceedings{Ste74,
  author =       "G. W. Stewart",
  year =         "1974",
  title =        "The Numerical Treatment of Large Eigenvalue Problems",
  booktitle =    "Proceedings {IFIP} Congress 74",
  publisher =    NorthHolland,
  pages =        "666--672",
}

@Article{Ste75a,
  author =       "G. W. Stewart",
  year =         "1975",
  title =        "The Convergence of the Method of Conjugate Gradients
                 at Isolated Extreme Points in the Spectrum",
  journal =      NumerMath,
  volume =       "24",
  pages =        "85--93",
}

@Article{Ste75b,
  author =       "G. W. Stewart",
  year =         "1975",
  title =        "{Gershgorin} Theory for the Generalized Eigenvalue
                 Problem {$Ax = \lambda Bx$}",
  journal =      MathComp,
  volume =       "29",
  pages =        "600--606",
}

@Incollection{Ste75c,
  author =       "G. W. Stewart",
  year =         "1975",
  title =        "Methods of Simultaneous Iteration for Calculating
                 Eigenvectors of Matrices",
  booktitle =    "Topics in Numerical Analysis {II}",
  editor =       "J. H. Miller",
  publisher =    Academic,
  address =      "New York, NY, USA",
  pages =        "185--196",
}

@Article{Ste76a,
  author =       "G. W. Stewart",
  year =         "1976",
  title =        "Algorithm~406 {HQR3 and~EXCHNG}: {Fortran}
                 Subroutines for Calculating and Ordering and
                 Eigenvalues of a Real Upper {Hessenberg} Matrix",
  journal =      ACMMathSoft,
  volume =       "2",
  pages =        "275--280",
}

@Incollection{Ste76b,
  author =       "G. W. Stewart",
  year =         "1976",
  title =        "A Bibliographical Tour of the Large Sparse
                 Generalized Eigenvalue Problem",
  booktitle =    "Sparse Matrix Computations",
  editor =       "J. R. Bunch and D. J. Rose",
  publisher =    Academic,
  address =      "New York, NY, USA",
}

@Article{Ste76c,
  author =       "G. W. Stewart",
  year =         "1976",
  title =        "The Economical Storage of Plane Rotations",
  journal =      NumerMath,
  volume =       "25",
  pages =        "137--138",
}

@Article{Ste76d,
  author =       "G. W. Stewart",
  year =         "1976",
  title =        "Simultaneous Iteration for Computing Invariant
                 Subspaces of Non-{Hermitian} Matrices",
  journal =      NumerMath,
  volume =       "25",
  pages =        "12--36",
}

@Article{Ste77a,
  author =       "G. W. Stewart",
  year =         "1977",
  title =        "On the Perturbation of Pseudo-Inverses, Projections,
                 and Linear Least Squares Problems",
  journal =      SIAMReview,
  volume =       "19",
  pages =        "634--662",
}

@Article{Ste77b,
  author =       "G. W. Stewart",
  year =         "1977",
  title =        "Perturbation Bounds for the {QR} Factorization of a
                 Matrix",
  journal =      SIAMNumAnal,
  volume =       "14",
  pages =        "509--518",
}

@Techreport{Ste77c,
  author =       "G. W. Stewart",
  year =         "1977",
  title =        "Sensitivity Coefficients for the Effects of Errors in
                 the Independent Variables in a Linear Regression",
  number =       "TR-571",
  institution =  "Computer Science, University of Maryland",
  address =      "College Park, MD, USA",
}

@Incollection{Ste78,
  author =       "G. W. Stewart",
  year =         "1978",
  title =        "Perturbation Theory for the Generalized Eigenvalue
                 Problem",
  booktitle =    "Recent Advances in Numerical Analysis",
  editor =       "C. de Boor and G. H. Golub",
  publisher =    Academic,
  address =      "New York, NY, USA",
}

@Article{Ste79b,
  author =       "G. W. Stewart",
  year =         "1979",
  title =        "A Note on the Perturbation of Singular Values",
  journal =      LinAlgApp,
  volume =       "28",
  pages =        "213--216",
}

@Article{Ste79c,
  author =       "G. W. Stewart",
  year =         "1979",
  title =        "Perturbation Bounds for the Definite Generalized
                 Eigenvalue Problem",
  journal =      LinAlgApp,
  volume =       "23",
  pages =        "69--86",
}

@Article{Ste79a,
  author =       "G. W. Stewart",
  year =         "1979",
  title =        "The Effects of Rounding Error on an Algorithm for
                 Downdating a {Cholesky} Factorization",
  journal =      InstMathApp,
  volume =       "23",
  pages =        "203--213",
}

@Article{Ste80,
  author =       "G. W. Stewart",
  year =         "1980",
  title =        "The Efficient Generation of Random Orthogonal
                 Matrices with an Application to Condition Estimators",
  journal =      SIAMNumAnal,
  volume =       "17",
  pages =        "403--409",
}

@Article{Ste81b,
  author =       "G. W. Stewart",
  year =         "1981",
  title =        "On the Implicit Deflation of Nearly Singular Systems
                 of Linear Equations",
  journal =      SIAMSciStat,
  volume =       "2",
  pages =        "136--140",
}

@Incollection{Ste83,
  author =       "G. W. Stewart",
  year =         "1983",
  title =        "A Method for Computing the Generalized Singular Value
                 Decomposition",
  booktitle =    "Matrix Pencils",
  editor =       "B. K{\aa}gstr{\"o}m and A. Ruhe",
  publisher =    Springer,
  address =      "New York, NY, USA",
  pages =        "207--220",
}

@Article{Ste84c,
  author =       "G. W. Stewart",
  year =         "1984",
  title =        "Rank Degeneracy",
  journal =      SIAMSciStat,
  volume =       "5",
  pages =        "403--413",
}

@Article{Ste84a,
  author =       "G. W. Stewart",
  year =         "1984",
  title =        "On the Asymptotic Behavior of Scaled Singular Value
                 and {QR} Decompositions",
  journal =      MathComp,
  volume =       "43",
  pages =        "483--490",
}

@Article{Ste84d,
  author =       "G. W. Stewart",
  year =         "1984",
  title =        "A Second Order Perturbation Expansion for Small
                 Singular Values",
  journal =      LinAlgApp,
  volume =       "56",
  pages =        "231--236",
}

@Article{Ste84b,
  author =       "G. W. Stewart",
  year =         "1984",
  title =        "On the Invariance of Perturbed Null Vectors Under
                 Column Scaling",
  journal =      NumerMath,
  volume =       "33,34",
  pages =        "61--66",
}

@Article{Ste85,
  author =       "G. W. Stewart",
  year =         "1985",
  title =        "A {Jacobi}-Like Algorithm for Computing the {Schur}
                 Decomposition of a Nonhermitian Matrix",
  journal =      SIAMSciStat,
  volume =       "6",
  pages =        "853--862",
}

@Article{Ste87,
  author =       "G. W. Stewart",
  year =         "1987",
  title =        "Collinearity and Least Squares Regression",
  journal =      StatScience,
  volume =       "2",
  pages =        "68--100",
}

@Article{Sto73,
  author =       "H. S. Stone",
  year =         "1973",
  title =        "An Efficient Parallel Algorithm for the Solution of a
                 Tridiagonal Linear System of Equations",
  journal =      JACM,
  volume =       "20",
  pages =        "27--38",
}

@Article{Sto75b,
  author =       "H. S. Stone",
  year =         "1975",
  title =        "Parallel Tridiagonal Equation Solvers",
  journal =      ACMMathSoft,
  volume =       "1",
  pages =        "289--307",
}

@Book{Str88,
  author =       "G. Strang",
  year =         "1988",
  title =        "Linear Algebra and Its Applications",
  edition =      "third",
  publisher =    Academic,
  address =      "New York, NY, USA",
}

@Article{Sto75a,
  author =       "H. Stone",
  year =         "1975",
  title =        "Parallel Tridiagonal Equation Solvers",
  journal =      ACMMathSoft,
  volume =       "1",
  pages =        "289--307",
}

@Article{Str69,
  author =       "V. Strassen",
  year =         "1969",
  title =        "{Gaussian} Elimination is Not Optimal",
  journal =      NumerMath,
  volume =       "13",
  pages =        "354--356",
}

@Article{Sun82,
  author =       "J. Guang Sun",
  year =         "1982",
  title =        "A Note on {Stewart}'s Theorem for Definite Matrix
                 Pairs",
  journal =      LinAlgApp,
  volume =       "48",
  pages =        "331--339",
}

@Article{Sun83,
  author =       "J. Guang Sun",
  year =         "1983",
  title =        "Perturbation Analysis for the Generalized Singular
                 Value Problem",
  journal =      SIAMNumAnal,
  volume =       "20",
  pages =        "611--625",
}

@Article{Swa79,
  author =       "P. N. Swarztrauber",
  year =         "1979",
  title =        "A Parallel Algorithm for Solving General Tridiagonal
                 Equations",
  journal =      MathComp,
  volume =       "33",
  pages =        "185--199",
}

@Article{SwaS73,
  author =       "P. N. Swarztrauber and R. A. Sweet",
  year =         "1973",
  title =        "The Direct Solution of the Discrete {Poisson}
                 Equation on a Disk",
  journal =      SIAMNumAnal,
  volume =       "10",
  pages =        "900--907",
}

@Article{Swe74,
  author =       "R. A. Sweet",
  year =         "1974",
  title =        "A Generalized Cyclic Reduction Algorithm",
  journal =      SIAMNumAnal,
  volume =       "11",
  pages =        "506--520",
}

@Article{Swe77,
  author =       "R. A. Sweet",
  year =         "1977",
  title =        "A Cyclic Reduction Algorithm for Solving Block
                 Tridiagonal Systems of Arbitrary Dimension",
  journal =      SIAMNumAnal,
  volume =       "14",
  pages =        "706--720",
}

@Article{SymW80,
  author =       "H. J. Symm and J. H. Wilkinson",
  year =         "1980",
  title =        "Realistic Error Bounds for a Simple Eigenvalue and
                 Its Associated Eigenvector",
  journal =      NumerMath,
  volume =       "35",
  pages =        "113--126",
}

@Article{TanG81,
  author =       "W. P. Tang and G. H. Golub",
  year =         "1981",
  title =        "The Block Decomposition of a {Vandermonde} Matrix and
                 Its Applications",
  journal =      BIT,
  volume =       "21",
  pages =        "505--517",
}

@Article{ThoW70,
  author =       "G. L. Thompson and R. L. Weil",
  year =         "1970",
  title =        "Reducing the Rank of {$A - \lambda B$}",
  journal =      ProcAMS,
  volume =       "26",
  pages =        "548--554",
}

@Article{ThoW72,
  author =       "G. L. Thompson and R. L. Weil",
  year =         "1972",
  title =        "Roots of Matrix Pencils {$Ay = \lambda By$}:
                 Existence, Calculations, and Relations to Game Theory",
  journal =      LinAlgApp,
  volume =       "5",
  pages =        "207--226",
}

@Techreport{TreS87,
  author =       "L. N. Trefethen and R. S. Schreiber",
  year =         "1987",
  title =        "Average Case Stability of {Gaussian} Elimination",
  number =       "88-3",
  institution =  "Numerical Analysis, Department of Mathematics, MIT",
  address =      "MA",
}

@Article{Tre64,
  author =       "W. F. Trench",
  year =         "1964",
  title =        "An Algorithm for the Inversion of Finite {Toeplitz}
                 Matrices",
  journal =      "J. SIAM",
  volume =       "12",
  pages =        "515--522",
}

@Article{Tre74,
  author =       "W. F. Trench",
  year =         "1974",
  title =        "Inversion of {Toeplitz} Band Matrices",
  journal =      MathComp,
  volume =       "28",
  pages =        "1089--1095",
}

@Article{Tsa75,
  author =       "N. K. Tsao",
  year =         "1975",
  title =        "A Note on Implementing the {Householder}
                 Transformation",
  journal =      SIAMNumAnal,
  volume =       "12",
  pages =        "53--58",
}

@Book{TurA61,
  author =       "H. W. Turnbull and A. C. Aitken",
  year =         "1961",
  title =        "An Introduction to the Theory of Canonical Matrices",
  publisher =    DoverPub,
  address =      "New York, NY, USA",
}

@Article{Uhl73,
  author =       "F. Uhlig",
  year =         "1973",
  title =        "Simultaneous Block Diagonalization of Two Real
                 Symmetric Matrices",
  journal =      LinAlgApp,
  volume =       "7",
  pages =        "281--289",
}

@Article{Uhl76,
  author =       "F. Uhlig",
  year =         "1976",
  title =        "A Canonical Form for a Pair of Real Symmetric
                 Matrices that Generate a Nonsingular Pencil",
  journal =      LinAlgApp,
  volume =       "14",
  pages =        "189--210",
}

@Techreport{Und75,
  author =       "R. Underwood",
  year =         "1975",
  title =        "An Iterative Block {Lanczos} Method for the Solution
                 of Large Sparse Symmetric Eigenproblems",
  number =       "STAN-CS-75-496",
  institution =  "Computer Science, Stanford University",
  address =      "Stanford, CA, USA",
}

@Article{Van71,
  author =       "J. Vandergraft",
  year =         "1971",
  title =        "Generalized {Rayleigh} Methods with Applications to
                 Finding Eigenvalues of Large Matrices",
  journal =      LinAlgApp,
  volume =       "4",
  pages =        "353--368",
}

@Article{vdS69,
  author =       "A. van der Sluis",
  year =         "1969",
  title =        "Condition Numbers and Equilibration Matrices",
  journal =      NumerMath,
  volume =       "14",
  pages =        "14--23",
}

@Article{vdS70,
  author =       "A. van der Sluis",
  year =         "1970",
  title =        "Condition, Equilibration, and Pivoting in Linear
                 Algebraic Systems",
  journal =      NumerMath,
  volume =       "15",
  pages =        "74--86",
}

@Article{vdS75a,
  author =       "A. van der Sluis",
  year =         "1975",
  title =        "Perturbations of Eigenvalues of Nonnormal Matrices",
  journal =      CACM,
  volume =       "18",
  pages =        "30--36",
}

@Article{vdS75b,
  author =       "A. van der Sluis",
  year =         "1975",
  title =        "Stability of the Solutions of Linear Least Squares
                 Problem",
  journal =      NumerMath,
  volume =       "23",
  pages =        "241--254",
}

@Article{vdSV79,
  author =       "A. van der Sluis and G. W. Veltkamp",
  year =         "1979",
  title =        "Restoring Rank and Consistency by Orthogonal
                 Projection",
  journal =      LinAlgApp,
  volume =       "28",
  pages =        "257--278",
}

@Article{vdSV86,
  author =       "A. van der Sluis and H. A. Van der Vorst",
  year =         "1986",
  title =        "The Rate of Convergence of Conjugate Gradients",
  journal =      NumerMath,
  volume =       "48",
  pages =        "543--560",
}

@Article{dV77,
  author =       "H. Van de Vel",
  year =         "1977",
  title =        "Numerical Treatment of a Generalized {Vandermonde}
                 System of Equations",
  journal =      LinAlgApp,
  volume =       "17",
  pages =        "149--174",
}

@Article{dV82b,
  author =       "H. A. Van der Vorst",
  year =         "1982",
  title =        "A Vectorizable Variant of Some {ICCG} Methods",
  journal =      SIAMSciStat,
  volume =       "3",
  pages =        "350--356",
}

@Article{dV82a,
  author =       "H. A. Van der Vorst",
  year =         "1982",
  title =        "A Generalized {Lanczos} Scheme",
  journal =      MathComp,
  volume =       "39",
  pages =        "559--562",
}

@Article{Doo79,
  author =       "P. Van Dooren",
  year =         "1979",
  title =        "The Computation of {Kronecker}'s Canonical Form of a
                 Singular Pencil",
  journal =      LinAlgApp,
  volume =       "27",
  pages =        "103--140",
}

@Article{Doo81b,
  author =       "P. Van Dooren",
  year =         "1981",
  title =        "A Generalized Eigenvalue Approach for Solving
                 {Riccati} Equations",
  journal =      SIAMSciStat,
  volume =       "2",
  pages =        "121--135",
}

@Article{Doo81a,
  author =       "P. Van Dooren",
  year =         "1981",
  title =        "The Generalized Eigenstructure Problem in Linear
                 System Theory",
  journal =      IEEETransAC,
  volume =       "AC-26",
  pages =        "111--128",
}

@Incollection{Doo83,
  author =       "P. Van Dooren",
  year =         "1983",
  title =        "Reducing Subspaces: definitions, properties and
                 Algorithms",
  booktitle =    "Matrix Pencils",
  editor =       "B. K{\aa}gstr{\"o}m and A. Ruhe",
  publisher =    Springer,
  address =      "New York, NY, USA",
  pages =        "58--73",
}

@Phdthesis{Huf87,
  author =       "S. Van Huffel",
  year =         "1987",
  title =        "Analysis of the Total Least Squares Problem and Its
                 Use in Parameter Estimation",
  school =       "Electrical Engineering, Katholieke Universiteit
                 Leuven",
  address =      "Leuven, Belgium",
}

@Techreport{Huf88,
  author =       "S. Van Huffel",
  year =         "1988",
  title =        "Comments on the Solution of the Nongeneric Total
                 Least Squares Problem",
  number =       "ESAT-KUL-88/3",
  institution =  "Department of Electrical Engineering, Katholieke
                 Universiteit Leuven",
  address =      "Leuven, Belgium",
}

@Article{HufV88a,
  author =       "S. Van Huffel and J. Vandewalle",
  year =         "1988",
  title =        "The Partial Total Least Squares Algorithm",
  journal =      CompApplMath,
  volume =       "21",
  pages =        "333--342",
}

@Article{HufV87,
  author =       "S. Van Huffel and J. Vandewalle",
  year =         "1987",
  title =        "Subset Selection Using the Total Least Squares
                 Approach in Collinearity Problems with Errors in the
                 Variables",
  journal =      LinAlgApp,
  volume =       "88/89",
  pages =        "695--714",
}

@Article{HufVH87,
  author =       "S. Van Huffel and J. Vandewalle and A. Haegemans",
  year =         "1987",
  title =        "An Efficient and Reliable Algorithm for Computing the
                 Singular Subspace of a Matrix Associated with its
                 Smallest Singular Values",
  journal =      CompApplMath,
  volume =       "19",
  pages =        "313--330",
}

@Article{HufV88b,
  author =       "S. Van Huffel and J. Vandewalle",
  year =         "1988",
  title =        "The Partial Total Least Squares Algorithm",
  journal =      CompApplMath,
  volume =       "21",
  pages =        "333--342",
}

@Techreport{KatdV77,
  author =       "J. M. Van Kats and H. A. Van der Vorst",
  year =         "1977",
  title =        "Automatic Monitoring of {Lanczos} Schemes for
                 Symmetric or Skew-Symmetric Generalized Eigenvalue
                 Problems",
  number =       "TR 7",
  institution =  "Academische Computer Centre",
  address =      "Utrecht, The Netherlands",
}

@Article{vK66,
  author =       "H. P. M. van Kempen",
  year =         "1966",
  title =        "On Quadratic Convergence of the Special Cyclic
                 {Jacobi} Method",
  journal =      NumerMath,
  volume =       "9",
  pages =        "19--22",
}

@Phdthesis{Loa73,
  author =       "C. F. Van Loan",
  year =         "1973",
  title =        "Generalized Singular Values with Algorithms and
                 Applications",
  school =       "University of Michigan",
  address =      "Ann Arbor, MI, USA",
}

@Article{Loa75a,
  author =       "C. F. Van Loan",
  year =         "1975",
  title =        "A General Matrix Eigenvalue Algorithm",
  journal =      SIAMNumAnal,
  volume =       "12",
  pages =        "819--834",
}

@Techreport{Loa75b,
  author =       "C. F. Van Loan",
  year =         "1975",
  title =        "A Study of the Matrix Exponential",
  number =       "10",
  institution =  "Numerical Analysis, University of Manchester",
  address =      "UK",
}

@Article{Loa76,
  author =       "C. F. Van Loan",
  year =         "1976",
  title =        "Generalizing the Singular Value Decomposition",
  journal =      SIAMNumAnal,
  volume =       "13",
  pages =        "76--83",
}

@Incollection{Loa77a,
  author =       "C. F. Van Loan",
  year =         "1977",
  title =        "On the Limitation and Application of the {Pad}{\'e}
                 Approximation to the Matrix Exponential",
  booktitle =    "{Pad}{\'e} and Rational Approximation",
  editor =       "E. B. Saff and R. S. Varga",
  publisher =    Academic,
  address =      "New York, NY, USA",
}

@Article{Loa77b,
  author =       "C. F. Van Loan",
  year =         "1977",
  title =        "The Sensitivity of the Matrix Exponential",
  journal =      SIAMNumAnal,
  volume =       "14",
  pages =        "971--981",
}

@Article{Loa78a,
  author =       "C. F. Van Loan",
  year =         "1978",
  title =        "Computing Integrals Involving the Matrix Exponential",
  journal =      IEEETransAC,
  volume =       "AC-23",
  pages =        "395--404",
}

@Article{Loa78b,
  author =       "C. F. Van Loan",
  year =         "1978",
  title =        "A Note on the Evaluation of Matrix Polynomials",
  journal =      IEEETransAC,
  volume =       "AC-24",
  pages =        "320--321",
}

@Incollection{Loa82,
  author =       "C. F. Van Loan",
  year =         "1982",
  title =        "Using the {Hessenberg} Decomposition in Control
                 Theory",
  booktitle =    "Algorithms and Theory in Filtering and Control",
  editor =       "D. C. Sorensen and R. J. Wets",
  series =       "Mathematical Programming Study",
  number =       "18",
  publisher =    NorthHolland,
  address =      "Amsterdam, The Netherlands",
  pages =        "102--111",
}

@Inproceedings{Loa83,
  author =       "C. F. Van Loan",
  year =         "1983",
  title =        "A Generalized {SVD} Analysis of Some Weighting
                 Methods for Equality-Constrained Least Squares",
  booktitle =    "Proceedings of the Conference on Matrix Pencils",
  editor =       "B. K{\aa}gstr{\"o}m and A. Ruhe",
  publisher =    Springer,
  address =      "New York, NY, USA",
}

@Article{Loa84,
  author =       "C. F. Van Loan",
  year =         "1984",
  title =        "A Symplectic Method for Approximating All the
                 Eigenvalues of a {Hamiltonian} Matrix",
  journal =      LinAlgApp,
  volume =       "61",
  pages =        "233--252",
}

@Article{Loa85a,
  author =       "C. F. Van Loan",
  year =         "1985",
  title =        "Computing the {CS} and Generalized Singular Value
                 Decomposition",
  journal =      NumerMath,
  volume =       "46",
  pages =        "479--492",
}

@Article{Loa85c,
  author =       "C. F. Van Loan",
  year =         "1985",
  title =        "On the Method of Weighting for Equality Constrained
                 Least Squares Problems",
  journal =      SIAMNumAnal,
  volume =       "22",
  pages =        "851--864",
}

@Article{Loa85b,
  author =       "C. F. Van Loan",
  year =         "1985",
  title =        "How Near is a Stable Matrix to an Unstable Matrix?",
  journal =      ContempMath,
  volume =       "47",
  pages =        "465--477",
}

@Article{Loa87,
  author =       "C. F. Van Loan",
  year =         "1987",
  title =        "On Estimating the Condition of Eigenvalues and
                 Eigenvectors",
  journal =      LinAlgApp,
  volume =       "88/89",
  pages =        "715--732",
}

@Article{Var68a,
  author =       "J. M. Varah",
  year =         "1968",
  title =        "The Calculation of the Eigenvectors of a General
                 Complex Matrix by Inverse Iteration",
  journal =      MathComp,
  volume =       "22",
  pages =        "785--791",
}

@Article{Var68b,
  author =       "J. M. Varah",
  year =         "1968",
  title =        "Rigorous Machine Bounds for the Eigensystem of a
                 General Complex Matrix",
  journal =      MathComp,
  volume =       "22",
  pages =        "793--801",
}

@Article{Var70a,
  author =       "J. M. Varah",
  year =         "1970",
  title =        "Computing Invariant Subspaces of a General Matrix
                 when the Eigensystem is Poorly Determined",
  journal =      MathComp,
  volume =       "24",
  pages =        "137--149",
}

@Article{Var79,
  author =       "J. M. Varah",
  year =         "1979",
  title =        "On the Separation of Two Matrices",
  journal =      SIAMNumAnal,
  volume =       "16",
  pages =        "216--222",
}

@Article{Var72,
  author =       "J. M. Varah",
  year =         "1972",
  title =        "On the Solution of Block-Tridiagonal Systems Arising
                 from Certain Finite-Difference Equations",
  journal =      MathComp,
  volume =       "26",
  pages =        "859--868",
}

@Article{Var73,
  author =       "J. M. Varah",
  year =         "1973",
  title =        "On the Numerical Solution of Ill-Conditioned Linear
                 Systems with Applications to Ill-Posed Problems",
  journal =      SIAMNumAnal,
  volume =       "10",
  pages =        "257--267",
}

@Article{Var75,
  author =       "J. M. Varah",
  year =         "1975",
  title =        "A Lower Bound for the Smallest Singular Value of a
                 Matrix",
  journal =      LinAlgApp,
  volume =       "11",
  pages =        "1--2",
}

@Article{Var61,
  author =       "R. S. Varga",
  year =         "1961",
  title =        "On Higher-Order Stable Implicit Methods for Solving
                 Parabolic Partial Differential Equations",
  journal =      MathPhys,
  volume =       "40",
  pages =        "220--231",
}

@Book{Var62,
  author =       "R. S. Varga",
  year =         "1962",
  title =        "Matrix Iterative Analysis",
  publisher =    PrenticeHall,
  address =      "Englewood Cliffs, NJ, USA",
}

@Article{Var70b,
  author =       "R. S. Varga",
  year =         "1970",
  title =        "Minimal {Gershgorin} Sets for Partitioned Matrices",
  journal =      SIAMNumAnal,
  volume =       "7",
  pages =        "493--507",
}

@Article{Var76,
  author =       "R. S. Varga",
  year =         "1976",
  title =        "On Diagonal Dominance Arguments for Bounding
                 {$\|A^{-1}\|$}",
  journal =      LinAlgApp,
  volume =       "14",
  pages =        "211--217",
}

@Article{Vet75,
  author =       "W. J. Vetter",
  year =         "1975",
  title =        "Vector Structures and Solutions of Linear Matrix
                 Equations",
  journal =      LinAlgApp,
  volume =       "10",
  pages =        "181--188",
}

@Book{Wac66,
  author =       "E. L. Wachpress",
  year =         "1966",
  title =        "Iterative Solution of Elliptic Systems",
  publisher =    PrenticeHall,
  address =      "Englewood Cliffs, NJ, USA",
}

@Inproceedings{WalAC+88,
  author =       "D. W. Walker and T. Aldcroft and A. Cisneros and G.
                 Fox and W. Furmanski",
  year =         "1988",
  title =        "{LU} Decomposition of Banded Matrices and the
                 Solution of Linear Systems on Hypercubes",
  booktitle =    "The Third Conference on Hypercube Concurrent
                 Computers and Applications, Vol. {II}, Applications",
  editor =       "G. Fox",
  publisher =    ACMPress,
  address =      "New York, NY, USA",
  pages =        "1635--1655",
}

@Article{Wal88,
  author =       "H. F. Walker",
  year =         "1988",
  title =        "Implementation of the {GMRES} Method Using
                 {Householder} Transformations",
  journal =      SIAMSciStat,
  volume =       "9",
  pages =        "152--163",
}

@Article{War75,
  author =       "R. C. Ward",
  year =         "1975",
  title =        "The Combination Shift {QZ} Algorithm",
  journal =      SIAMNumAnal,
  volume =       "12",
  pages =        "835--853",
}

@Article{War77,
  author =       "R. C. Ward",
  year =         "1977",
  title =        "Numerical Computation of the Matrix Exponential with
                 Accuracy Estimate",
  journal =      SIAMNumAnal,
  volume =       "14",
  pages =        "600--614",
}

@Article{War81,
  author =       "R. C. Ward",
  year =         "1981",
  title =        "Balancing the Generalized Eigenvalue Problem",
  journal =      SIAMSciStat,
  volume =       "2",
  pages =        "141--152",
}

@Article{WarG78,
  author =       "R. C. Ward and L. J. Gray",
  year =         "1978",
  title =        "Eigensystem Computation for Skew-Symmetric and a
                 Class of Symmetric Matrices",
  journal =      ACMMathSoft,
  volume =       "4",
  pages =        "278--285",
}

@Article{Wat82,
  author =       "D. S. Watkins",
  year =         "1982",
  title =        "Understanding the {QR} Algorithm",
  journal =      SIAMReview,
  volume =       "24",
  pages =        "427--440",
}

@Article{Wat73,
  author =       "G. A. Watson",
  year =         "1973",
  title =        "An Algorithm for the Inversion of Block Matrices of
                 {Toeplitz} Form",
  journal =      JACM,
  volume =       "20",
  pages =        "409--415",
}

@Article{Wat88,
  author =       "G. A. Watson",
  year =         "1988",
  title =        "The Smallest Perturbation of a Submatrix which Lowers
                 the Rank of the Matrix",
  journal =      IMANumerAna,
  volume =       "8",
  pages =        "295--304",
}

@Article{Wed72,
  author =       "P.{\AA}. Wedin",
  year =         "1972",
  title =        "Perturbation Bounds in Connection with the Singular
                 Value Decomposition",
  journal =      BIT,
  volume =       "12",
  pages =        "99--111",
}

@Article{Wed73a,
  author =       "P.{\AA}. Wedin",
  year =         "1973",
  title =        "On the Almost Rank-Deficient Case of the Least
                 Squares Problem",
  journal =      BIT,
  volume =       "13",
  pages =        "344--354",
}

@Article{Wed73b,
  author =       "P.{\AA}. Wedin",
  year =         "1973",
  title =        "Perturbation Theory for Pseudo-Inverses",
  journal =      BIT,
  volume =       "13",
  pages =        "217--232",
}

@Article{Wid78,
  author =       "O. Widlund",
  year =         "1978",
  title =        "A {Lanczos} Method for a Class of Nonsymmetric
                 Systems of Linear Equations",
  journal =      SIAMNumAnal,
  volume =       "15",
  pages =        "801--812",
}

@Article{Wil61,
  author =       "J. H. Wilkinson",
  year =         "1961",
  title =        "Error Analysis of Direct Methods of Matrix Inversion",
  journal =      JACM,
  volume =       "10",
  pages =        "281--330",
}

@Book{Wil63,
  author =       "J. H. Wilkinson",
  year =         "1963",
  title =        "Rounding Errors in Algebraic Processes",
  publisher =    PrenticeHall,
  address =      "Englewood Cliffs, NJ, USA",
}

@Book{Wil65a,
  author =       "J. H. Wilkinson",
  year =         "1965",
  title =        "The Algebraic Eigenvalue Problem",
  publisher =    ClaredonPress,
  address =      "Oxford, UK",
}

@Article{Wil65b,
  author =       "J. H. Wilkinson",
  year =         "1965",
  title =        "Convergence of the {LR}, {QR}, and Related
                 Algorithms",
  journal =      CompJour,
  volume =       "8",
  pages =        "77--84",
}

@Article{Wil68a,
  author =       "J. H. Wilkinson",
  year =         "1968",
  title =        "Almost Diagonal Matrices with Multiple or Close
                 Eigenvalues",
  journal =      LinAlgApp,
  volume =       "1",
  pages =        "1--12",
}

@Article{Wil68c,
  author =       "J. H. Wilkinson",
  year =         "1968",
  title =        "Global Convergence of Tridiagonal {QR} Algorithm with
                 Origin Shifts",
  journal =      LinAlgApp,
  volume =       "1",
  pages =        "409--420",
}

@Inproceedings{Wil68b,
  author =       "J. H. Wilkinson",
  year =         "1968",
  title =        "A Priori Error Analysis of Algebraic Processes",
  booktitle =    "Proceedings International Congress Math. ({Moscow}:
                 {Izdat}. {Mir})",
  pages =        "629--639",
}

@Article{Wil71,
  author =       "J. H. Wilkinson",
  year =         "1971",
  title =        "Modern Error Analysis",
  journal =      SIAMReview,
  volume =       "14",
  pages =        "548--568",
}

@Article{Wil72,
  author =       "J. H. Wilkinson",
  year =         "1972",
  title =        "Note on Matrices with a Very Ill-Conditioned
                 Eigenproblem",
  journal =      NumerMath,
  volume =       "19",
  pages =        "176--178",
}

@Incollection{Wil77,
  author =       "J. H. Wilkinson",
  year =         "1977",
  title =        "Some Recent Advances in Numerical Linear Algebra",
  booktitle =    "The State of the Art in Numerical Analysis",
  editor =       "D. A. H. Jacobs",
  publisher =    Academic,
  address =      "New York, NY, USA",
  pages =        "1--53",
}

@Incollection{Wil78,
  author =       "J. H. Wilkinson",
  year =         "1978",
  title =        "Linear Differential Equations and {Kronecker}'s
                 Canonical Form",
  booktitle =    "Recent Advances in Numerical Analysis",
  editor =       "C. de Boor and G. H. Golub",
  publisher =    Academic,
  address =      "New York, NY, USA",
  pages =        "231--265",
}

@Article{Wil79,
  author =       "J. H. Wilkinson",
  year =         "1979",
  title =        "{Kronecker}'s Canonical Form and the {QZ} Algorithm",
  journal =      LinAlgApp,
  volume =       "28",
  pages =        "285--303",
}

@Book{WilR71,
  editor =       "J. H. Wilkinson and C. Reinsch",
  year =         "1971",
  title =        "Linear Algebra",
  volume =       "2",
  series =       "Handbook for Automatic Computation",
  publisher =    Springer,
  address =      "New York, NY, USA",
}

@Article{Wil84,
  author =       "J. H. Wilkinson",
  year =         "1984",
  title =        "On Neighboring Matrices with Quadratic Elementary
                 Divisors",
  journal =      NumerMath,
  volume =       "44",
  pages =        "1--21",
}

@Article{WimZ72,
  author =       "H. Wimmer and A. D. Ziebur",
  year =         "1972",
  title =        "Solving the Matrix Equation {$\sum
                 f_{p}(A)Xg_{p}(A)$}",
  journal =      SIAMReview,
  volume =       "14",
  pages =        "318--323",
}

@Article{Win68,
  author =       "S. Winograd",
  year =         "1968",
  title =        "A New Algorithm for Inner Product",
  journal =      IEEETransComp,
  volume =       "C-17",
  pages =        "693--694",
}

@Article{Woz80,
  author =       "H. Wozniakowski",
  year =         "1980",
  title =        "Roundoff Error Analysis of a New Class of Conjugate
                 Gradient Algorithms",
  journal =      LinAlgApp,
  volume =       "29",
  pages =        "507--529",
}

@Article{Wra73,
  author =       "A. Wragg",
  year =         "1973",
  title =        "Computation of the Exponential of a Matrix {I}:
                 Theoretical Considerations",
  journal =      InstMathApp,
  volume =       "11",
  pages =        "369--375",
}

@Article{Wra75,
  author =       "A. Wragg",
  year =         "1975",
  title =        "Computation of the Exponential of a Matrix {II}:
                 Practical Considerations",
  journal =      InstMathApp,
  volume =       "15",
  pages =        "273--278",
}

@Article{Yoh79,
  author =       "J. M. Yohe",
  year =         "1979",
  title =        "Software for Interval Arithmetic: A Reasonable
                 Portable Package",
  journal =      ACMMathSoft,
  volume =       "5",
  pages =        "50--63",
}

@Article{You70,
  author =       "D. M. Young",
  year =         "1970",
  title =        "Convergence Properties of the Symmetric and
                 Unsymmetric Over-Relaxation Methods",
  journal =      MathComp,
  volume =       "24",
  pages =        "793--807",
}

@Book{You71,
  author =       "D. M. Young",
  year =         "1971",
  title =        "Iterative Solution of Large Linear Systems",
  publisher =    Academic,
  address =      "New York, NY, USA",
}

@Article{You72,
  author =       "D. M. Young",
  year =         "1972",
  title =        "Generalization of Property~{$A$} and Consistent
                 Ordering",
  journal =      SIAMNumAnal,
  volume =       "9",
  pages =        "454--463",
}

@Article{YouJ80,
  author =       "D. M. Young and K. C. Jea",
  year =         "1980",
  title =        "Generalized Conjugate Gradient Acceleration of
                 Nonsymmetrizable Iterative Methods",
  journal =      LinAlgApp,
  volume =       "34",
  pages =        "159--194",
}

@Article{Zoh69,
  author =       "S. Zohar",
  year =         "1969",
  title =        "{Toeplitz} Matrix Inversion: The Algorithm of
                 {W}.{F}. {Trench}",
  journal =      "JACM",
  volume =       "16",
  pages =        "592--601",
}