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%%% -*-BibTeX-*-
%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Sven Hammarling",
%%%     version         = "1.61",
%%%     date            = "08 August 2018",
%%%     time            = "06:41:10 MDT",
%%%     filename        = "wilkinson-james-hardy.bib",
%%%     address         = "The Numerical Algorithms Group
%%%                        Wilkinson House
%%%                        Jordan Hill Road
%%%                        Oxford OX2 8DR
%%%                        UK",
%%%     telephone       = "?n/a?",
%%%     FAX             = "?n/a?",
%%%     checksum        = "15862 6128 27288 273271",
%%%     email           = "na.hammarling at na-net.ornl.gov (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "eigenvalue, eigenvector, numerical
%%%                        analysis, rounding error",
%%%     license         = "public domain",
%%%     supported       = "yes",
%%%     docstring       = "This is a bibliography of publications of the
%%%                        late James H. Wilkinson (27 September 1919--5
%%%                        October 1986).  The companion LaTeX file
%%%                        wilkinson-james-hardy.ltx can be used to
%%%                        typeset this bibliography.
%%%
%%%                        See
%%%
%%%                            http://www-history.mcs.st-and.ac.uk/Biographies/Wilkinson.html
%%%
%%%                        and entry Fox:1987:JHW for biographies of
%%%                        James H. Wilkinson.
%%%
%%%                        At version 1.61, the year coverage looked
%%%                        like this:
%%%
%%%                             1948 (   5)    1970 (  10)    1992 (   1)
%%%                             1949 (   0)    1971 (  25)    1993 (   0)
%%%                             1950 (   0)    1972 (   5)    1994 (   1)
%%%                             1951 (   3)    1973 (   0)    1995 (   0)
%%%                             1952 (   1)    1974 (  13)    1996 (   0)
%%%                             1953 (   0)    1975 (   6)    1997 (   0)
%%%                             1954 (   3)    1976 (   6)    1998 (   0)
%%%                             1955 (   4)    1977 (   4)    1999 (   0)
%%%                             1956 (   0)    1978 (   8)    2000 (   0)
%%%                             1957 (   8)    1979 (   3)    2001 (   0)
%%%                             1958 (   4)    1980 (   6)    2002 (   1)
%%%                             1959 (   4)    1981 (   4)    2003 (   1)
%%%                             1960 (   4)    1982 (   3)    2004 (   0)
%%%                             1961 (   7)    1983 (   1)    2005 (   3)
%%%                             1962 (   9)    1984 (   6)    2006 (   0)
%%%                             1963 (   5)    1985 (   2)    2007 (   0)
%%%                             1964 (   1)    1986 (   3)    2008 (   0)
%%%                             1965 (  10)    1987 (   9)    2009 (   0)
%%%                             1966 (   8)    1988 (   1)    2010 (   0)
%%%                             1967 (   8)    1989 (   1)    2011 (   1)
%%%                             1968 (  11)    1990 (   4)    2012 (   1)
%%%                             1969 (   3)    1991 (   0)
%%%
%%%                             Article:        107
%%%                             Book:            13
%%%                             InBook:           1
%%%                             InCollection:    35
%%%                             InProceedings:   24
%%%                             Proceedings:     15
%%%                             TechReport:      27
%%%                             Unpublished:      5
%%%
%%%                             Total entries:  227
%%%
%%%                        This file is available as part of the BibNet
%%%                        Project.  The master copy is available for
%%%                        public access on ftp.math.utah.edu in the
%%%                        directory tree /pub/bibnet/authors.  It is
%%%                        mirrored to netlib.bell-labs.com in the directory
%%%                        tree /netlib/bibnet/authors, from which it is
%%%                        available via anonymous ftp and the Netlib
%%%                        service.
%%%
%%%                        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.",
%%%  }
%%% ====================================================================
@Preamble{
    "\def \cprime {$'$} "
  # "\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi"
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%%% ====================================================================
%%% Institution abbreviations:
@String{inst-ANL-am             = "Applied Mathematics Division, Argonne
                                  National Laboratory"}
@String{inst-ANL-mcs            = "Mathematics and Computer Science
                                  Division, Argonne National Laboratory"}
@String{inst-ANL:adr            = "Argonne, Illinois 60439, USA"}

@String{inst-CPAM-UCB           = "Center for Pure and Applied Mathematics,
                                  University of California, Berkeley"}
@String{inst-CPAM-UCB:adr       = "Berkeley, CA, USA"}

@String{inst-ETH-AM             = "Seminar f{\"{u}}r Angewandte Mathematik,
                                  Eidgen{\"{o}}ssische Technische Hochschule"}
@String{inst-ETH:adr            = "ETH-Zentrum CH-8092 Zurich, Switzerland"}

@String{inst-NPL                = "National Physical Laboratory"}
@String{inst-NPL:adr            = "Teddington, Middlesex TW11 0LW, UK"}

@String{inst-SU-cs              = "Computer Science Department, Stanford
                                  University"}
@String{inst-SU:adr             = "Stanford, California 94305, USA"}

@String{inst-UTK-cs             = "Department of Computer Science, University of
                                  Tennessee"}
@String{inst-UTK:adr            = "107 Ayres Hall, Knoxville, TN 37996-1301,
                                  USA"}

%%% ====================================================================
%%% Journal abbreviations:
@String{j-ACM                   = "J. ACM"}

@String{j-ADV-COMPUT-MATH       = "Advances in Computational Mathematics"}

@String{j-AMER-MATH-MONTHLY     = "American Mathematical Monthly"}

@String{j-AP                    = "Automn Prog."}

@String{j-APL-MAT               = "Aplikace Matematiky"}

@String{j-BIOGRAPH-MEMOIRS-FELLOWS-ROY-SOC = "Biographical Memoirs of Fellows of
                                  the Royal Society"}

@String{j-BULL-INST-MATH-APPL   = "Bulletin of the Institute of Mathematics and
                                  its Applications"}

@String{j-BULL-LOND-MATH-SOC    = "Bulletin of the London Mathematical Society"}

@String{j-BYTE                  = "BYTE Magazine"}

@String{j-CACM                  = "Communications of the ACM"}

@String{j-COMP-J                = "The Computer Journal"}

@String{j-CONG-NUM              = "Congressus Numerantium"}

@String{j-CompB                 = "Comput. Bull."}

@String{j-IMA-J-NUMER-ANAL      = "IMA Journal of Numerical Analysis"}

@String{j-IP                    = "J. Inst. Petrol."}

@String{j-J-ACM                 = "Journal of the ACM"}

@String{j-J-COMPUT-APPL-MATH    = "Journal of Computational and Applied
                                  Mathematics"}

@String{j-J-COMPUT-PHYS         = "Journal of Computational Physics"}

@String{j-J-INST-MATH-APPL      = "Journal of the Institute of Mathematics and
                                  its Applications"}

@String{j-J-SIAM                = "Journal of the Society for Industrial and
                                  Applied Mathematics"}

@String{j-LINEAR-ALGEBRA-APPL   = "Linear Algebra Appl."}

@String{j-LINEAR-ALGEBRA-APPL   = "Linear Algebra and its Applications"}

@String{j-MATH-TABLES-OTHER-AIDS-COMPUT = "Mathematical Tables and Other Aids
                                  to Computation"}

@String{j-NAG                   = "NAG Newsletter"}

@String{j-NUM-MATH              = "Numerische Mathematik"}

@String{j-NatureL               = "Nature, Lond."}

@String{j-PHILOS-TRANS-R-SOC-LOND-SER-A = "Philosophical transactions of the
                                  Royal Society of London Series A"}

@String{j-PROC-CAMBRIDGE-PHIL-SOC = "Proceedings of the Cambridge
                                  Philosophical Society. Mathematical and
                                  physical sciences"}

@String{j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI = "Proceedings of the Royal
                                  Society of London. Series A, Mathematical
                                  and physical sciences"}

@String{j-PRSL                  = "Proc. R. Soc. Lond."}

@String{j-PSaMAMS               = "Proc. Symp. appl. Math. Am. Math. Soc."}

@String{j-QUART-J-MECH-APPLIED-MATH = "Quarterly Journal of Mechanics and
                                  Applied Mathematics"}

@String{j-RADIO-ELECTRON-ENG    = "The Radio and Electronic Engineer"}

@String{j-SIAM-J-MAT-ANA-APPL   = "SIAM Journal on Matrix Analysis and
                                  Applications"}

@String{j-SIAM-J-NUMER-ANAL     = "SIAM Journal on Numerical Analysis"}

@String{j-SIAM-REVIEW           = "SIAM Review"}

@String{j-SINum                 = "SIAM J. Num. Anal."}

@String{j-SIRev                 = "SIAM Review"}

@String{j-UM                    = "Util. Math."}

@String{j-sI                    = "J. scient. Instrum."}

%%% ====================================================================
%%% Publisher abbreviations:
@String{pub-ACADEMIC            = "Academic Press"}
@String{pub-ACADEMIC:adr        = "New York, NY, USA"}

@String{pub-ACM                 = "ACM Press"}
@String{pub-ACM:adr             = "New York, NY 10036, USA"}

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

@String{pub-AW                  = "Ad{\-d}i{\-s}on-Wes{\-l}ey"}
@String{pub-AW:adr              = "Reading, MA, USA"}

@String{pub-But                 = "Butterworth"}
@String{pub-But:adr             = "London, UK"}

@String{pub-DOVER               = "Dover"}
@String{pub-DOVER:adr           = "New York, NY, USA"}

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

@String{pub-IMA                 = "Institute of Mathematics and its Applications"}
@String{pub-IMA:adr             = "Southend-on-Sea, UK"}

@String{pub-MATH-ASSOC-AMER     = "Mathematical Association of America"}
@String{pub-MATH-ASSOC-AMER:adr = "Washington, DC"}

@String{pub-MCGRAW-HILL         = "McGraw-Hill"}
@String{pub-MCGRAW-HILL:adr     = "New York"}

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

@String{pub-NAUKA               = "Nauka"}
@String{pub-NAUKA:adr           = "Moscow, Russia"}

@String{pub-NORTH-HOLLAND       = "North-Hol{\-}land"}
@String{pub-NORTH-HOLLAND:adr   = "Amsterdam, The Netherlands"}

@String{pub-NAG                 = "The Numerical Algorithms Group Ltd"}
@String{pub-NAG:adr             = "Wilkinson House, Jordan Hill Road,
                                  Oxford OX2 8DR, UK"}

@String{pub-OXFORD              = "Oxford University Press"}
@String{pub-OXFORD:adr          = "Walton Street, Oxford OX2 6DP, UK"}

@String{pub-PH                  = "Pren{\-}tice-Hall"}
@String{pub-PH:adr              = "Upper Saddle River, NJ 07458, USA"}

@String{pub-PITMAN              = "Pitman Publishing"}
@String{pub-PITMAN:adr          = "London, UK"}

@String{pub-SPRINGER            = "Springer-Verlag"}
@String{pub-SPRINGER:adr        = "Berlin, Heidelberg, New York, Tokyo"}

@String{pub-SV                  = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SV:adr              = "Berlin, Germany~/ Heidelberg,
                                  Germany~/ London, UK~/ etc."}

@String{pub-UMP                 = "Utilitas Mathematica Publishers"}
@String{pub-UMP:adr             = "Winnipeg, Manitoba, Canada"}

@String{pub-WILEY               = "Wiley"}
@String{pub-WILEY:adr           = "New York, NY, USA"}

@String{pub-WRE                 = "Weapons Research Establishment"}
@String{pub-WRE:adr             = "Salisbury, Australia"}

%%% ====================================================================
%%%         Part 1 (of 2) --- James H. Wilkinson and his works
%%%
%%% Bibliography entries, sorted by ascending year and then by citation
%%% label:
@Article{Fox:1948:NSA,
  author =       "L. Fox and H. D. Huskey and J. H. Wilkinson",
  title =        "Notes on the solution of algebraic linear simultaneous
                 equations",
  journal =      j-QUART-J-MECH-APPLIED-MATH,
  volume =       "1",
  pages =        "149--173",
  year =         "1948",
  CODEN =        "QJMMAV",
  DOI =          "https://doi.org/10.1093/qjmam/1.1.149",
  ISSN =         "0033-5614 (print), 1464-3855 (electronic)",
  ISSN-L =       "0033-5614",
  MRclass =      "65.0X",
  MRnumber =     "MR0026421 (10,152i)",
  MRreviewer =   "E. Bodewig",
  bibdate =      "Fri May 14 17:18:08 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  abstract =     "In this paper four methods of solving simultaneous
                 equations and inverting matrices are described from the
                 viewpoint of the practical computer. The first three
                 methods can be performed on ordinary desk calculating
                 machines; the fourth uses Hollerith punched card
                 equipment. The desk methods considered are the method
                 of elimination or pivotal condensation, the method of
                 orthogonal vectors, and the method of Choleski. The
                 elimination method is, with slight variants, the simple
                 method taught at school, used in such a way that
                 solutions are obtained with the maximum possible speed
                 and accuracy. In the method of orthogonal vectors,
                 applicable only to symmetric matrices, a new set of
                 variables is chosen in such a way that the matrix is
                 transformed to a diagonal form, from which the solution
                 of equations or the inverse of the matrix is
                 immediately obtainable. The Choleski method, applied
                 here again only to symmetric matrices, expresses the
                 square matrix as the product of two triangular
                 matrices, the reciprocation of which is a relatively
                 simple operation. This method is quicker and more
                 accurate than the others and can be used, with slight
                 modifications, in the case of unsymmetric matrices. The
                 procedure used with punched card equipment is
                 essentially a mechanization of the elimination method,
                 with a considerable advantage in speed over the
                 corresponding desk method.",
  acknowledgement = ack-nhfb,
  fjournal =     "The Quarterly Journal of Mechanics and Applied
                 Mathematics",
  journal-URL =  "http://qjmam.oxfordjournals.org/content/by/year",
}

@TechReport{Fox:1948:SAL,
  author =       "L. Fox and H. D. Huskey and J. H. Wilkinson",
  title =        "The Solution of Algebraic Linear Simultaneous
                 Equations by Punched Card Methods",
  type =         "Maths",
  institution =  inst-NPL,
  address =      inst-NPL:adr,
  year =         "1948",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@Article{Hartree:1948:DCM,
  author =       "D. R. Hartree and M. H. A. Newman and M. V. Wilkes and
                 F. C. Williams and J. H. Wilkinson and A. D. Booth",
  title =        "A discussion on computing machines",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
  volume =       "195",
  number =       "1042",
  pages =        "265--287 (2 plates)",
  day =          "22",
  month =        dec,
  year =         "1948",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.1948.0118",
  ISSN =         "0080-4630",
  MRclass =      "65.0X",
  MRnumber =     "MR0028103 (10,405f)",
  bibdate =      "Fri May 14 17:18:08 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  URL =          "http://www.jstor.org/stable/98328",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Royal Society. London. Series A.
                 Mathematical, Physical and Engineering Sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/content/current",
}

@TechReport{Wilkinson:1948:PRA,
  author =       "J. H. Wilkinson",
  title =        "Progress Report on the {Automatic Computing Engine}",
  type =         "Report",
  number =       "MA/17/1024",
  institution =  inst-NPL,
  address =      inst-NPL:adr,
  pages =        "????",
  month =        apr,
  year =         "1948",
  bibdate =      "Mon Nov 1 19:29:36 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  URL =          "http://www.alanturing.net/turing_archive/archive/l/l10/L10-001.html",
}

@Article{Wilkinson:1948:ACE,
  author =       "J. H. Wilkinson",
  title =        "The {Automatic Computing Engine} at the {National
                 Physical Laboratory}",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
  volume =       "195",
  number =       "1042",
  pages =        "285--286",
  day =          "22",
  month =        dec,
  year =         "1948",
  CODEN =        "PRLAAZ",
  ISSN =         "0080-4630",
  bibdate =      "Thu Aug 25 09:25:29 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  URL =          "http://www.jstor.org/stable/98328",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Royal Society. London. Series A.
                 Mathematical, Physical and Engineering Sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/content/current",
}

@TechReport{Wilkinson:1951:PCP,
  author =       "J. H. Wilkinson",
  title =        "Programming and Coding for the Pilot Model of the
                 {ACE}",
  type =         "Ma Report",
  institution =  inst-NPL,
  address =      inst-NPL:adr,
  year =         "1951",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@TechReport{Wilkinson:1951:PGR,
  author =       "J. H. Wilkinson",
  title =        "Programmes for the {GPO Radar Data Analyser}",
  type =         "Maths",
  institution =  inst-NPL,
  address =      inst-NPL:adr,
  year =         "1951",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@TechReport{Wilkinson:1951:RPM,
  author =       "J. H. Wilkinson",
  title =        "Report on the Pilot Model of the {Automatic Computing
                 Engine. II.} The Logical Design of the Pilot Model",
  type =         "Maths Division and Electronics Section",
  institution =  inst-NPL,
  address =      inst-NPL:adr,
  year =         "1951",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@TechReport{Wilkinson:1952:PCP,
  author =       "J. H. Wilkinson",
  title =        "Programming and Coding for the Pilot Model of the
                 {ACE}",
  type =         "Ma Report",
  number =       "No. 22",
  institution =  inst-NPL,
  address =      inst-NPL:adr,
  year =         "1952",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Reissue",
}

@Article{Wilkinson:1954:CLR,
  author =       "J. H. Wilkinson",
  title =        "The Calculation of the Latent Roots and Vectors of
                 Matrices on the {Pilot Model} of the {ACE}",
  journal =      j-PROC-CAMBRIDGE-PHIL-SOC,
  volume =       "50",
  number =       "4",
  pages =        "536--566",
  year =         "1954",
  CODEN =        "PCPSA4",
  DOI =          "https://doi.org/10.1017/S0305004100029674",
  ISSN =         "0008-1981",
  MRclass =      "65.0X",
  MRnumber =     "MR0063775 (16,178b)",
  MRreviewer =   "A. S. Householder",
  bibdate =      "Fri May 14 17:18:08 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  abstract =     "The problem of finding the latent roots and vectors of
                 matrices has been treated in a number of papers ((2)
                 (7)) mainly from the point of view of desk computers.
                 In this paper the problem is treated from the
                 standpoint of users of high-speed automatic computers.
                 In the first section a number of iterative processes
                 are described and, in the second, the techniques
                 developed for using these processes on the Pilot Model
                 of the Automatic Computing Engine. It is shown that the
                 methods give very high accuracy and can be used to deal
                 with matrices of high orders even on a machine of very
                 limited storage capacity. They have been used on
                 numerous matrices of orders up to 60 mainly on problems
                 arising in the aircraft industry and on eigenvalue
                 problems for systems of ordinary differential
                 equations.",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Cambridge Philosophical Society.
                 Mathematical and physical sciences",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=PSP",
  received =     "February 9, 1954",
}

@InProceedings{Wilkinson:1954:LAP,
  author =       "J. H. Wilkinson",
  booktitle =    "Automatic Digital Computation",
  title =        "Linear Algebra on the {Pilot ACE}",
  publisher =    pub-HMSO,
  address =      pub-HMSO:adr,
  pages =        "129--136",
  year =         "1954",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Proceedings of Symposium at the National Physical
                 Laboratory, 1953",
}

@InProceedings{Wilkinson:1954:PA,
  author =       "J. H. Wilkinson",
  booktitle =    "Automatic Digital Computation",
  title =        "The {Pilot ACE}",
  publisher =    pub-HMSO,
  address =      pub-HMSO:adr,
  pages =        "5--14",
  year =         "1954",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Proceedings of Symposium at the National Physical
                 Laboratory, 1953. Reprinted in
                 \cite[pp.~193--199]{Bell:1971:CSR} and in
                 \cite[pp.~219--228]{Williams:1989:EBC}.",
}

@Article{Wilkinson:1955:ASO,
  author =       "J. H. Wilkinson",
  title =        "An Assessment of the System of Optimum Coding Used on
                 the {Pilot ACE} at the {National Physical Laboratory}",
  journal =      j-PHILOS-TRANS-R-SOC-LOND-SER-A,
  volume =       "248",
  pages =        "253--281",
  year =         "1955",
  CODEN =        "PTRMAD, PTMSFB",
  DOI =          "https://doi.org/10.1098/rsta.1955.0016",
  ISSN =         "0080-4614",
  ISSN-L =       "1364-503X",
  MRclass =      "68.0X",
  MRnumber =     "MR0071885 (17,197i)",
  bibdate =      "Fri May 14 17:18:08 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  abstract =     "The paper describes the system of optimum coding which
                 is used on the Pilot ACE, the electronic computer at
                 the National Physical Laboratory. It includes a number
                 of simple examples of programs prepared for the machine
                 and gives an assessment of the gain in speed which
                 results from the use of optimum coding in general. It
                 concludes with a description of the design of the
                 full-scale ACE which takes full advantage of the
                 general principles embodied in the design of the Pilot
                 ACE.",
  acknowledgement = ack-nhfb,
  fjournal =     "Philosophical Transactions of the Royal Society of
                 London. Series A. Mathematical and Physical Sciences",
  journal-URL =  "http://rsta.royalsocietypublishing.org/",
}

@Article{Wilkinson:1955:ECM,
  author =       "J. H. Wilkinson",
  title =        "Electronic computing machines and their uses",
  journal =      j-sI,
  volume =       "32",
  pages =        "409--415",
  year =         "1955",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@TechReport{Wilkinson:1955:RVU,
  author =       "J. H. Wilkinson",
  title =        "Report on Visit to {U.S.A., 17 September--14 December
                 1954}",
  type =         "Maths",
  institution =  inst-NPL,
  address =      inst-NPL:adr,
  year =         "1955",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@Article{Wilkinson:1955:UIM,
  author =       "J. H. Wilkinson",
  title =        "The Use of Iterative Methods for Finding the Latent
                 Roots and Vectors of Matrices",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "9",
  pages =        "184--191",
  year =         "1955",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  MRclass =      "65.3X",
  MRnumber =     "MR0079833 (18,154b)",
  MRreviewer =   "E. Stiefel",
  bibdate =      "Fri May 14 17:18:08 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Wilkinson:1957:BPD,
  author =       "J. H. Wilkinson",
  title =        "{British} Progress in Digital Computer Design",
  journal =      j-AP,
  volume =       "2",
  pages =        "5--9, 36",
  year =         "1957",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  fjournal =     "Automn Prog.",
}

@InProceedings{Wilkinson:1957:CEC,
  author =       "J. H. Wilkinson",
  booktitle =    "Conference Proceedings",
  title =        "The Calculation of the Eigenvectors of Codiagonal
                 Matrices Produced by the {Givens} and {Lanczos}
                 Processes",
  publisher =    pub-WRE,
  address =      pub-WRE:adr,
  pages =        "112:1--112:15",
  year =         "1957",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@Article{Wilkinson:1957:CFG,
  author =       "J. H. Wilkinson",
  title =        "Computing Facilities in {Great Britain}",
  journal =      j-IP,
  volume =       "43",
  pages =        "101--107",
  year =         "1957",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@InCollection{Wilkinson:1957:EUD,
  author =       "J. H. Wilkinson",
  booktitle =    "Modern Computing Methods, 1st Edition",
  title =        "Example of the Use of {DEUCE}",
  publisher =    pub-HMSO,
  address =      pub-HMSO:adr,
  pages =        "116--122",
  year =         "1957",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  series =       "National Physical Laboratory, Notes on Applied
                 Science, Volume 16",
}

@InCollection{Wilkinson:1957:HPD,
  author =       "J. H. Wilkinson",
  booktitle =    "Modern Computing Methods, 1st Edition",
  title =        "Hyperbolic Partial Differential Equations",
  publisher =    pub-HMSO,
  address =      pub-HMSO:adr,
  pages =        "61--71",
  year =         "1957",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  series =       "National Physical Laboratory, Notes on Applied
                 Science, Volume 16",
}

@InCollection{Wilkinson:1957:LEM,
  author =       "J. H. Wilkinson",
  booktitle =    "Modern Computing Methods, 1st Edition",
  title =        "Linear Equations and Matrices",
  publisher =    pub-HMSO,
  address =      pub-HMSO:adr,
  pages =        "12--19",
  year =         "1957",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  series =       "National Physical Laboratory, Notes on Applied
                 Science, Volume 16",
}

@Article{Wilkinson:1957:LOW,
  author =       "J. H. Wilkinson",
  title =        "Loading on an Oscillating Wing of Infinite Aspect
                 Ratio in a Subsonic Stream",
  journal =      "ARC",
  volume =       "19",
  pages =        "344",
  year =         "1957",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Comp. 125.",
}

@InCollection{Wilkinson:1957:LRM,
  author =       "J. H. Wilkinson",
  booktitle =    "Modern Computing Methods, 1st Edition",
  title =        "Latent Roots of Matrices",
  publisher =    pub-HMSO,
  address =      pub-HMSO:adr,
  pages =        "27--35",
  year =         "1957",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  series =       "National Physical Laboratory, Notes on Applied
                 Science, Volume 16",
}

@Article{Wilkinson:1958:CEC,
  author =       "J. H. Wilkinson",
  title =        "The Calculation of the Eigenvectors of Codiagonal
                 Matrices",
  journal =      j-COMP-J,
  volume =       "1",
  number =       "2",
  pages =        "90--96",
  month =        jul,
  year =         "1958",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/1.2.90",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:55:03 MDT 2000",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/010090.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/tiff/90.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/tiff/91.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/tiff/92.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/tiff/93.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/tiff/94.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/tiff/95.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/tiff/96.tif",
  abstract =     "In the Givens method for calculating the eigenvalues
                 and eigenvectors of a matrix, a collineatory
                 transformations is constructed which reduces the matrix
                 to codiagonal form. Givens (1954) has given a complete
                 analysis of the problem of finding the eigenvalues and
                 has described a very satisfactory practical procedure
                 for evaluating them. No such analysis has been given
                 for the eigenvectors, though Givens in an unpublished
                 paper has described a procedure which, in his
                 experience, has given accurate results. In this note an
                 analysis of the problem is given, which explains why
                 the straightforward use of the recursions often gives
                 vectors which are catastrophically in error. A method
                 of solution is described which has been used
                 extensively for calculating the vectors on DEUCE. Much
                 of what is written applies equally well to the
                 codiagonal matrices produced by the method of Lanczos
                 (1950), but because this method is usually programmed
                 using floating-point arithmetic, there are one or two
                 additional complications. These will be the subject of
                 a later note.",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Wilkinson:1958:CEM,
  author =       "J. H. Wilkinson",
  title =        "The Calculation of Eigenvectors by the Method of
                 {Lanczos}",
  journal =      j-COMP-J,
  volume =       "1",
  number =       "3",
  pages =        "148--152",
  month =        oct,
  year =         "1958",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/1.3.148",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  MRclass =      "65.00",
  MRnumber =     "MR0102915 (21 \#1700)",
  MRreviewer =   "H. Rutishauser",
  bibdate =      "Fri Sep 29 08:55:05 MDT 2000",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_03/",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_03/010148.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_03/tiff/148.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_03/tiff/149.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_03/tiff/150.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_03/tiff/151.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_03/tiff/152.tif",
  abstract =     "This paper describes a technique for calculating the
                 eigenvectors of a matrix automatically by means of the
                 Lanczos transformation. Both the symmetric and the
                 unsymmetric forms are treated. It shows that with
                 suitable modifications, the method described by the
                 author for finding the eigenvectors by means of the
                 Givens transformation, can be made to give accurate
                 results for both of the Lanczos transformations.",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Wilkinson:1958:MPN,
  author =       "J. H. Wilkinson",
  title =        "Matrix Programs at the {National Physical
                 Laboratory}",
  journal =      j-ACM,
  volume =       "5",
  pages =        "113--114",
  year =         "1958",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@TechReport{Wilkinson:1958:SRM,
  author =       "J. H. Wilkinson",
  title =        "Stability of the Reduction of a Matrix to Almost
                 Triangular and Triangular Forms by Elementary
                 Similarity Transformations",
  type =         "Mathematics Division",
  number =       "No. 22",
  institution =  inst-NPL,
  address =      inst-NPL:adr,
  year =         "1958",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Reprinted 1962. Published as
                 \cite{Wilkinson:1959:SRM}.",
}

@Article{Davies:1959:ACE,
  author =       "D. W. Davies and J. H. Wilkinson",
  title =        "The {Automatic Computing Engine} at the {National
                 Physical Laboratory}",
  journal =      j-NatureL,
  volume =       "183",
  pages =        "22--23",
  year =         "1959",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@Article{Wilkinson:1959:EZIa,
  author =       "J. H. Wilkinson",
  title =        "The evaluation of the zeros of ill-conditioned
                 polynomials. {I}",
  journal =      j-NUM-MATH,
  volume =       "1",
  pages =        "150--166",
  month =        dec,
  year =         "1959",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01386381",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65.00",
  MRnumber =     "MR0109435 (22 \#321)",
  MRreviewer =   "H. Rutishauser",
  bibdate =      "Mon Oct 18 01:28:20 MDT 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Wilkinson:1959:EZIb,
  author =       "J. H. Wilkinson",
  title =        "The evaluation of the zeros of ill-conditioned
                 polynomials. {II}",
  journal =      j-NUM-MATH,
  volume =       "1",
  pages =        "167--180",
  month =        dec,
  year =         "1959",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01386382",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65.00",
  MRnumber =     "MR0109435 (22 \#321)",
  MRreviewer =   "H. Rutishauser",
  bibdate =      "Mon Oct 18 01:28:20 MDT 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Wilkinson:1959:SRM,
  author =       "J. H. Wilkinson",
  title =        "Stability of the Reduction of a Matrix to Almost
                 Triangular and Triangular Forms by Elementary
                 Similarity Transformations",
  journal =      j-ACM,
  volume =       "6",
  number =       "3",
  pages =        "336--359",
  year =         "1959",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  MRclass =      "65.00",
  MRnumber =     "MR0106542 (21 \#5273)",
  MRreviewer =   "B. A. Chartres",
  bibdate =      "Fri May 14 17:18:08 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Association for Computing Machinery",
}

@Article{Wilkinson:1960:EAF,
  author =       "J. H. Wilkinson",
  title =        "Error Analysis of Floating-Point Computation",
  journal =      j-NUM-MATH,
  volume =       "2",
  pages =        "319--340",
  month =        dec,
  year =         "1960",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65.00",
  MRnumber =     "MR0116477 (22 \#7264)",
  MRreviewer =   "C. B. Haselgrove",
  bibdate =      "Fri May 14 17:18:08 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Wilkinson:1960:HMS,
  author =       "J. H. Wilkinson",
  title =        "{Householder}'s Method for the Solution of the
                 Algebraic Eigenproblem",
  journal =      j-COMP-J,
  volume =       "3",
  number =       "1",
  pages =        "23--27",
  month =        apr,
  year =         "1960",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/3.1.23",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  MRclass =      "65.00",
  MRnumber =     "MR0111131 (22 \#1995)",
  MRreviewer =   "A. S. Householder",
  bibdate =      "Fri Sep 29 08:55:18 MDT 2000",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_03/Issue_01/",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_03/Issue_01/030023.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_03/Issue_01/tiff/23.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_03/Issue_01/tiff/24.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_03/Issue_01/tiff/25.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_03/Issue_01/tiff/26.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_03/Issue_01/tiff/27.tif",
  abstract =     "In this paper a practical procedure is described for
                 the solution of the eigenproblem based on a method due
                 to Householder. It is claimed that the technique
                 described is the most satisfactory of known methods for
                 general symmetric matrices and may have considerable
                 advantages for unsymmetric matrices. The details of the
                 computation for a simple numerical example are given,
                 and also the results obtained for a $ 14 \times 14 $
                 matrix using the ACE computer.",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@InProceedings{Wilkinson:1960:MSL,
  author =       "J. H. Wilkinson",
  booktitle =    "Proceedings of UNESCO Conference on Information
                 Processing, 1959",
  title =        "On Methods for Solving Linear Equations",
  publisher =    pub-But,
  address =      pub-But:adr,
  pages =        "108--109",
  year =         "1960",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@InProceedings{Wilkinson:1960:REA,
  author =       "J. H. Wilkinson",
  booktitle =    "Proceedings of UNESCO Conference on Information
                 Processing, 1959",
  title =        "Rounding Errors in Algebraic Processes",
  publisher =    pub-But,
  address =      pub-But:adr,
  pages =        "44--53",
  year =         "1960",
  MRclass =      "65.00",
  MRnumber =     "MR0121976 (22 \#12703)",
  MRreviewer =   "B. A. Chartres",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@Article{Rollett:1961:ESC,
  author =       "J. S. Rollett and J. H. Wilkinson",
  title =        "An efficient scheme for the co-diagonalization of a
                 symmetric matrix by {Givens}' method in a computer with
                 a two-level store",
  journal =      j-COMP-J,
  volume =       "4",
  number =       "2",
  pages =        "177--180",
  month =        jul,
  year =         "1961",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  MRclass =      "65.35",
  MRnumber =     "MR0129126 (23 \#B2163)",
  MRreviewer =   "B. A. Chartres",
  bibdate =      "Fri Sep 29 08:55:29 MDT 2000",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_02/",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_02/040177.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_02/tiff/177.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_02/tiff/178.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_02/tiff/179.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_02/tiff/180.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@InCollection{Wilkinson:1961:EA,
  author =       "J. H. Wilkinson",
  booktitle =    "Modern Computing Methods, 2nd Edition",
  title =        "Error Analysis",
  publisher =    pub-HMSO,
  address =      pub-HMSO:adr,
  pages =        "41--52",
  year =         "1961",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  series =       "National Physical Laboratory, Notes on Applied
                 Science, Volume 16",
}

@Article{Wilkinson:1961:EAD,
  author =       "J. H. Wilkinson",
  title =        "Error Analysis of Direct Methods of Matrix Inversion",
  journal =      j-J-ACM,
  volume =       "8",
  number =       "3",
  pages =        "281--330",
  year =         "1961",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "65.35",
  MRnumber =     "MR0176602 (31 \#874)",
  MRreviewer =   "V. K. Saud{\cprime}ev",
  bibdate =      "Fri May 14 17:18:08 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Association for Computing Machinery",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}

@InCollection{Wilkinson:1961:HPD,
  author =       "J. H. Wilkinson",
  booktitle =    "Modern Computing Methods, 2nd Edition",
  title =        "Hyperbolic Partial Differential Equations",
  publisher =    pub-HMSO,
  address =      pub-HMSO:adr,
  pages =        "101--111",
  year =         "1961",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  series =       "National Physical Laboratory, Notes on Applied
                 Science, Volume 16",
}

@InCollection{Wilkinson:1961:LEM,
  author =       "J. H. Wilkinson",
  booktitle =    "Modern Computing Methods, 2nd Edition",
  title =        "Linear Equations and Matrices",
  publisher =    pub-HMSO,
  address =      pub-HMSO:adr,
  pages =        "13--33",
  year =         "1961",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  series =       "National Physical Laboratory, Notes on Applied
                 Science, Volume 16",
}

@Article{Wilkinson:1961:RA,
  author =       "J. H. Wilkinson",
  title =        "Remarks on {Algorithms 2} and 3",
  journal =      j-CACM,
  volume =       "4",
  number =       "3",
  pages =        "153--153",
  month =        mar,
  year =         "1961",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:31 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@Article{Wilkinson:1961:REB,
  author =       "J. H. Wilkinson",
  title =        "Rigorous Error Bounds for Computed Eigensystems",
  journal =      j-COMP-J,
  volume =       "4",
  number =       "3",
  pages =        "230--241",
  month =        oct,
  year =         "1961",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/4.3.230",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  MRclass =      "65.40",
  MRnumber =     "MR0129124 (23 \#B2161)",
  MRreviewer =   "A. S. Householder",
  bibdate =      "Fri Sep 29 08:55:31 MDT 2000",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/040230.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/230.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/231.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/232.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/233.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/234.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/235.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/236.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/237.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/238.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/239.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/240.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/241.tif",
  abstract =     "This paper describes techniques for the automatic
                 determination of rigorous error bounds for a computer
                 eigensystem. The methods used, lead directly to an
                 improved eigensystem and the error bounds are for the
                 improved system. They have the same theoretical basis
                 as the method of H. Jahn, but here the main emphasis is
                 on the organization of the computation which is
                 necessary for the determination of the error bounds.",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@InCollection{Jacobson:1962:SEA,
  author =       "A. W. Jacobson and S. Rosen and J. H. Wilkinson",
  editor =       "H. D. Huskey and G. A. Korn",
  booktitle =    "Computer Handbook",
  title =        "Scientific and Engineering Applications of Digital
                 Computers",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "21:2--21:13",
  year =         "1962",
  bibdate =      "Tue Aug 15 18:20:34 MDT 1995",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Section 2.1.",
}

@Article{Rollett:1962:LEG,
  author =       "J. S. Rollett and J. H. Wilkinson",
  title =        "Letter to the Editor: [{Givens} and {Householder}
                 processes]",
  journal =      j-COMP-J,
  volume =       "4",
  number =       "4",
  pages =        "279--279",
  month =        jan,
  year =         "1962",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Thu Dec 06 12:14:55 2012",
  bibsource =    "http://comjnl.oxfordjournals.org/content/4/4.toc;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/compj1960.bib",
  URL =          "http://comjnl.oxfordjournals.org/cgi/reprint/4/4/279;
                 http://comjnl.oxfordjournals.org/content/4/4/279.full.pdf+html",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Wilkinson:1962:BRB,
  author =       "J. H. Wilkinson",
  title =        "Book Review: {{\booktitle{Solutions Num{\'e}riques des
                 {\'E}quations Alg{\'e}braiques}}, by E. Durand (Paris:
                 Masson et Cie., 1960, pp. 328, 65 NF)}",
  journal =      j-COMP-J,
  volume =       "5",
  number =       "1",
  pages =        "32--32",
  month =        apr,
  year =         "1962",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/5.1.32",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:28 MST 2012",
  bibsource =    "http://comjnl.oxfordjournals.org/content/5/1.toc;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/compj1960.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/5/1/28.full.pdf;
                 http://comjnl.oxfordjournals.org/content/5/1/32.full.pdf+html",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Wilkinson:1962:CESa,
  author =       "J. H. Wilkinson",
  title =        "Calculation of the eigenvalues of a symmetric
                 tridiagonal matrix by the method of bisection",
  journal =      j-NUM-MATH,
  volume =       "4",
  pages =        "362--367",
  month =        dec,
  year =         "1962",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65.35",
  MRnumber =     "MR0148208 (26 \#5716)",
  MRreviewer =   "A. S. Householder",
  bibdate =      "Mon Oct 18 20:10:40 MDT 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  series =       "Handbook Series Linear Algebra",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Wilkinson:1962:CESb,
  author =       "J. H. Wilkinson",
  title =        "Calculation of the eigenvectors of a symmetric
                 tridiagonal matrix by inverse iteration",
  journal =      j-NUM-MATH,
  volume =       "4",
  pages =        "368--376",
  month =        dec,
  year =         "1962",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65.35",
  MRnumber =     "MR0148209 (26 \#5717)",
  MRreviewer =   "A. S. Householder",
  bibdate =      "Mon Oct 18 20:10:40 MDT 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  series =       "Handbook Series Linear Algebra",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Wilkinson:1962:EAE,
  author =       "J. H. Wilkinson",
  title =        "Error Analysis of Eigenvalue Techniques Based on
                 Orthogonal Transformations",
  journal =      j-J-SIAM,
  volume =       "10",
  pages =        "162--195",
  year =         "1962",
  CODEN =        "JSIMAV",
  ISSN =         "0368-4245 (print), 1095-712X (electronic)",
  MRclass =      "65.40",
  MRnumber =     "MR0137294 (25 \#749)",
  MRreviewer =   "A. S. Householder",
  bibdate =      "Fri May 14 17:18:08 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Society for Industrial and Applied
                 Mathematics",
  journal-URL =  "http://epubs.siam.org/loi/smjmap.1",
}

@Article{Wilkinson:1962:HMS,
  author =       "J. H. Wilkinson",
  title =        "{Householder}'s method for symmetric matrices",
  journal =      j-NUM-MATH,
  volume =       "4",
  pages =        "354--361",
  month =        dec,
  year =         "1962",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65.35",
  MRnumber =     "MR0148207 (26 \#5715)",
  MRreviewer =   "A. S. Householder",
  bibdate =      "Mon Oct 18 20:10:40 MDT 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  series =       "Handbook Series Linear Algebra",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Wilkinson:1962:IEM,
  author =       "J. H. Wilkinson",
  title =        "Instability of the Elimination Method of Reducing a
                 Matrix to Tri-Diagonal Form",
  journal =      j-COMP-J,
  volume =       "5",
  number =       "1",
  pages =        "61--70",
  month =        apr,
  year =         "1962",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  MRclass =      "65.35",
  MRnumber =     "MR0137292 (25 \#747)",
  MRreviewer =   "A. S. Householder",
  bibdate =      "Fri Sep 29 08:55:36 MDT 2000",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_05/Issue_01/",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_05/Issue_01/050061.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_05/Issue_01/tiff/61.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_05/Issue_01/tiff/62.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_05/Issue_01/tiff/63.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_05/Issue_01/tiff/64.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_05/Issue_01/tiff/65.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_05/Issue_01/tiff/66.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_05/Issue_01/tiff/67.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_05/Issue_01/tiff/68.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_05/Issue_01/tiff/69.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_05/Issue_01/tiff/70.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Wilkinson:1962:NQC,
  author =       "J. H. Wilkinson",
  title =        "Note on the quadratic convergence of the cyclic
                 {Jacobi} process",
  journal =      j-NUM-MATH,
  volume =       "4",
  pages =        "296--300",
  month =        dec,
  year =         "1962",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65.40",
  MRnumber =     "MR0146954 (26 \#4473)",
  MRreviewer =   "S. V. Parter",
  bibdate =      "Mon Oct 18 20:10:40 MDT 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Wilkinson:1963:BRB,
  author =       "J. H. Wilkinson",
  title =        "Book Review: {{\booktitle{Solutions Num{\'e}riques des
                 {\'E}quations Alg{\'e}braiques}}, Volume II, by E.
                 Durand (Paris: Masson et Cie., 1961, pp. 445, 90 NF)}",
  journal =      j-COMP-J,
  volume =       "5",
  number =       "4",
  pages =        "263--263",
  month =        jan,
  year =         "1963",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/5.4.263",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:29 MST 2012",
  bibsource =    "http://comjnl.oxfordjournals.org/content/5/4.toc;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/compj1960.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/5/4/258.full.pdf;
                 http://comjnl.oxfordjournals.org/content/5/4/263.full.pdf+html",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Wilkinson:1963:ELS,
  author =       "J. H. Wilkinson",
  title =        "Errors in Large-Scale Numerical Problems",
  journal =      j-CompB,
  volume =       "6",
  pages =        "124--125",
  year =         "1963",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@InProceedings{Wilkinson:1963:PRF,
  author =       "J. H. Wilkinson",
  title =        "Plane Rotations in Floating-Point Arithmetic",
  crossref =     "Metropolis:1963:PFS",
  pages =        "185--198",
  year =         "1963",
  MRclass =      "65.35",
  MRnumber =     "MR0158521 (28 \#1744)",
  MRreviewer =   "A. S. Householder",
  bibdate =      "Mon Jun 18 11:32:12 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Oettli:1964:ASL,
  author =       "W. Oettli and W. Prager and J. H. Wilkinson",
  title =        "Admissible Solutions of Linear Systems with not
                 Sharply Defined Coefficients",
  type =         "Research Paper",
  number =       "RZ-166",
  institution =  "IBM Research Division",
  address =      "IBM Zurich Research Laboratory, R{\"{u}}schlikon,
                 Zurich, Switzerland",
  year =         "1964",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Published as \cite{Oettli:1965:ASL}.",
}

@Article{Martin:1965:SDPa,
  author =       "R. S. Martin and J. H. Wilkinson",
  title =        "Symmetric Decomposition of Positive Definite Band
                 Matrices",
  journal =      j-NUM-MATH,
  volume =       "7",
  number =       "5",
  pages =        "355--361",
  month =        oct,
  year =         "1965",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01436248",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "Contributed Item",
  MRnumber =     "MR1553944",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 Theory/Matrix.bib",
  note =         "Also in \cite[pp. 50--56]{Wilkinson:1971:LA}.",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "band matrix; lud; nla; software; symmetric matrix",
}

@Article{Martin:1965:SDPb,
  author =       "R. S. Martin and G. Peters and J. H. Wilkinson",
  title =        "Symmetric Decomposition of a Positive Definite
                 Matrix",
  journal =      j-NUM-MATH,
  volume =       "7",
  number =       "5",
  pages =        "362--383",
  month =        oct,
  year =         "1965",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01436249",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "Contributed Item",
  MRnumber =     "MR1553945",
  bibdate =      "Sun Oct 17 16:12:48 MDT 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 Theory/Matrix.bib",
  note =         "Also in \cite[pp. 9--30]{Wilkinson:1971:LA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "Cholesky decomposition; nla; software",
}

@Article{Oettli:1965:ASL,
  author =       "W. Oettli and W. Prager and J. H. Wilkinson",
  title =        "Admissible Solutions of Linear Systems with not
                 Sharply Defined Coefficients",
  journal =      j-SINum,
  volume =       "2",
  pages =        "291--299",
  year =         "1965",
  MRclass =      "65.35",
  MRnumber =     "MR0184416 (32 \#1888)",
  MRreviewer =   "L. W. Ehrlich",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@Book{Wilkinson:1965:AEP,
  author =       "J. H. Wilkinson",
  booktitle =    "The Algebraic Eigenvalue Problem",
  title =        "The Algebraic Eigenvalue Problem",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xviii + 662",
  year =         "1965",
  ISBN =         "0-19-853403-5",
  ISBN-13 =      "978-0-19-853403-7",
  LCCN =         "QA218 .W686 1965",
  MRclass =      "65.40",
  MRnumber =     "MR0184422 (32 \#1894)",
  MRreviewer =   "A. S. Householder",
  bibdate =      "Tue Aug 15 18:20:34 MDT 1995",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/master.bib",
  shorttableofcontents = "1. Theoretical Background \\
                 2. Perturbation Theory \\
                 3. Error Analysis \\
                 4. Solution of Linear Algebraic Equations \\
                 5. Hermitian Matrices \\
                 6. Reduction of a General Matrix to Condensed Form \\
                 7. Eigenvalues of Matrices of Condensed Forms \\
                 8. The $ L R $ and $ Q R $ Algorithms \\
                 9. Iterative Methods \\
                 Bibliography / 649 \\
                 Index / 657",
  tableofcontents = "1. Theoretical Background \\
                 Introduction / 1 \\
                 Definitions / 2 \\
                 Eigenvalues and eigenvectors of the transposed matrix /
                 3 \\
                 Distinct eigenvalues / 4 \\
                 Similarity transformations / 6 \\
                 Multiple eigenvalues and canonical forms for general
                 matrices / 7 \\
                 Defective system of eigenvectors / 9 \\
                 The Jordan (classical) canonical form / 10 \\
                 The elementary divisors / 12 \\
                 Companion matrix of the characteristic polynomial of
                 $A$ / 12 \\
                 Non-derogatory matrices / 13 \\
                 The Frobenius (rational) canonical form / 15 \\
                 Relationship between the Jordan and Frobenius canonical
                 forms / 16 \\
                 Equivalence transformations / 17 \\
                 Lambda matrices / 18 \\
                 Elementary operations / 19 \\
                 Smith's canonical form / 19 \\
                 The highest common factor of $k$-rowed minors of a
                 $A$-matrix / 22 \\
                 Invariant factors of $ (A - \lambda M) $ / 22 \\
                 The triangular canonical form / 24 \\
                 Hermitian and symmetric matrices / 24 \\
                 Elementary properties of Hermitian matrices / 25 \\
                 Complex symmetric matrices / 26 \\
                 Reduction to triangular form by unitary transformations
                 / 27 \\
                 Quadratic forms / 27 \\
                 Necessary and sufficient conditions for positive
                 definiteness / 28 \\
                 Differential equations with constant coefficients / 30
                 \\
                 Solutions corresponding to non-linear elementary
                 divisors / 31 \\
                 Differential equations of higher order / 32 \\
                 Second-order equations of special form / 34 \\
                 Explicit solution of $ B \ddot{y} = -A y$ / 35 \\
                 Equations of the form $(AB - \lambda I) x = 0$ / 35 \\
                 The minimum polynomial of a vector / 36 \\
                 The minimum polynomial of a matrix / 37 \\
                 Cayley--Hamilton theorem / 38 \\
                 Relation between minimum polynomial and canonical forms
                 / 39 \\
                 Principal vectors / 42 \\
                 Elementary similarity transformations / 43 \\
                 Properties of elementary matrices / 45 \\
                 Reduction to triangular canonical form by elementary
                 similarity transformations / 46 \\
                 Elementary unitary transformations / 47 \\
                 Elementary unitary Hermitian matrices / 48 \\
                 Reduction to triangular form by elementary unitary
                 transformations / 50 \\
                 Normal matrices / 51 \\
                 Commuting matrices / 52 \\
                 Eigenvalues of $A B$ / 54 \\
                 Vector and matrix norms / 55 \\
                 Subordinate matrix norms / 56 \\
                 The Euclidean and spectral norms / 57 \\
                 Norms and limits / 58 \\
                 Avoiding use of infinite matrix series / 60 \\
                 2. Perturbation Theory \\
                 Introduction / 62 \\
                 Ostrowski's theorem on continuity of the eigenvalues /
                 63 \\
                 Algebraic functions / 64 \\
                 Numerical examples / 65 \\
                 Perturbation theory for simple eigenvalues / 66 \\
                 Perturbation of corresponding eigenvectors / 67 \\
                 Matrix with linear elementary divisors / 68 \\
                 First-order perturbations of eigenvalues / 68 \\
                 First-order perturbations of eigenvectors / 69 \\
                 Higher-order perturbations / 70 \\
                 Multiple eigenvalues / 70 \\
                 Gerschgorin's theorems / 71 \\
                 Perturbation theory based on Gerschgorin's theorems /
                 72 \\
                 Case 1. Perturbation of a simple eigenvalue $\lambda_1$
                 of a matrix having linear elementary divisors / 72 \\
                 Case 2. Perturbation of a multiple eigenvalue
                 $\lambda_1$ of a matrix having linear elementary
                 divisors / 75 \\
                 Case 3. Perturbation of a simple eigenvalue of a matrix
                 having one or more non-linear elementary divisors / 77
                 \\
                 Case 4. Perturbations of the eigenvalues corresponding
                 to a non-linear elementary divisor of a non-derogatory
                 matrix / 79 \\
                 Case 5. Perturbations of eigenvalues $\lambda_i$ when
                 there is more than one divisor involving $(\lambda_i -
                 \lambda_)$ and at least one of them is non-linear / 80
                 \\
                 Perturbations corresponding to the general distribution
                 of non-linear divisors / 81 \\
                 Perturbation theory for the eigenvectors from Jordan
                 canonical form / 81 \\
                 Perturbations of eigenvectors corresponding to a
                 multiple eigenvalue (linear elementary divisors) / 83
                 \\
                 Limitations of perturbation theory / 84 \\
                 Relationships between the $s_i$ / 85 \\
                 The condition of a computing problem / 86 \\
                 Condition numbers / 86 \\
                 Spectral condition number of A with respect to its
                 eigenproblem / 87 \\
                 Properties of spectral condition number / 88 \\
                 Invariant properties of condition numbers / 89 \\
                 Very ill-conditioned matrices / 90 \\
                 Perturbation theory for real symmetric matrices / 93
                 \\
                 Unsymmetric perturbations / 93 \\
                 Symmetric perturbations / 94 \\
                 Classical techniques / 94 \\
                 Symmetric matrix of rank unity / 97 \\
                 Extremal properties of eigenvalues / 98 \\
                 Minimax characterization of eigenvalues / 99 \\
                 Eigenvalues of the sum of two symmetric matrices / 101
                 \\
                 Practical applications / 102 \\
                 Further applications of minimax principle / 103 \\
                 Separation theorem / 103 \\
                 The Wielandt--Hoffman theorem / 104 \\
                 3. Error Analysis \\
                 Introduction / 110 \\
                 Fixed-point operations / 110 \\
                 Accumulation of inner-products / 111 \\
                 Floating-point operations / 112 \\
                 Simplified expressions for error bounds / 113 \\
                 Error bounds for some basic floating-point computations
                 / 114 \\
                 Bounds for norms of the error matrices / 115 \\
                 Accumulation of inner-products in floating-point
                 arithmetic / 116 \\
                 Error bounds for some basic $\fl_2( )$ computations /
                 117 \\
                 Computation of square roots / 118 \\
                 Block-floating vectors and matrices / 119 \\
                 Fundamental limitations oft-digit computation / 120 \\
                 Eigenvalue techniques based on reduction by similarity
                 transformations / 123 \\
                 Error analysis of methods based on elementary
                 non-unitary transformations / 124 \\
                 Error analysis of methods based on elementary unitary
                 transformations / 126 \\
                 Superiority of the unitary transformation / 128 \\
                 Real symmetric matrices / 129 \\
                 Limitations of unitary transformations / 129 \\
                 Error analysis of floating-point computation of plane
                 rotations / 131 \\
                 Multiplication by a plane rotation / 133 \\
                 Multiplication by a sequence of plane rotations / 134
                 \\
                 Error in product of approximate plane rotations / 139
                 \\
                 Errors in similarity transforms / 140 \\
                 Symmetric matrices / 141 \\
                 Plane rotations in fixed-point arithmetic / 143 \\
                 Alternative computation of $\sin \theta$ and $\cos
                 \theta$ / 145 \\
                 Pre-multiplication by an approximate fixed-point
                 rotation / 145 \\
                 Multiplication by a sequence of plane rotations
                 (fixed-point) / 147 \\
                 The computed product of an approximate set of plane
                 rotations / 148 \\
                 Errors in similarity transformations / 148 \\
                 General comments on the error bounds / 151 \\
                 Elementary Hermitian matrices in floating-point / 152
                 \\
                 Error analysis of the computation of an elementary
                 Hermitian matrix / 153 \\
                 Numerical example / 156 \\
                 Pre-multiplication by an approximate elementary
                 Hermitian matrix / 157 \\
                 Multiplication by a sequence of approximate elementary
                 Hermitians / 160 \\
                 Non-unitary elementary matrices analogous to plane
                 rotations / 162 \\
                 Non-unitary elementary matrices analogous to elementary
                 Hermitian matrices / 163 \\
                 Pre-multiplication by a sequence of non-unitary
                 matrices / 165 \\
                 A priori error bounds / 166 \\
                 Departure from normality / 167 \\
                 Simple examples / 169 \\
                 A posteriori bounds / 170 \\
                 A posteriori bounds for normal matrices / 170 \\
                 Rayleigh quotient / 172 \\
                 Error in Rayleigh quotient / 173 \\
                 Hermitian matrices / 174 \\
                 Pathologically close eigenvalues / 176 \\
                 Non-normal matrices / 178 \\
                 Error analysis for a complete eigensystem / 180 \\
                 Numerical example / 181 \\
                 Conditions limiting attainable accuracy / 181 \\
                 Non-linear elementary, divisors / 182 \\
                 Approximate invariant subspaces / 184 \\
                 Almost normal matrices / 187 \\
                 4. Solution of Linear Algebraic Equations \\
                 Introduction / 189 \\
                 Perturbation theory / 189 \\
                 Condition numbers / 191 \\
                 Equilibrated matrices / 192 \\
                 Simple practical examples / 193 \\
                 Condition of matrix of eigenvectors / 193 \\
                 Explicit solution / 194 \\
                 General comments on condition of matrices / 195 \\
                 Relation of ill-conditioning to near-singularity / 196
                 \\
                 Limitations imposed by t-digit arithmetic / 197 \\
                 Algorithms for solving linear equations / 198 \\
                 Gaussian elimination / 200 \\
                 Triangular decomposition / 201 \\
                 Structure of triangular decomposition matrices / 201
                 \\
                 Explicit expressions for elements of the triangles /
                 202 \\
                 Breakdown of Gaussian elimination / 204 \\
                 Numerical stability / 205 \\
                 Significance of the interchanges / 206 \\
                 Numerical example / 207 \\
                 Error analysis of Gaussian elimination / 209 \\
                 Upper bounds for the perturbation matrices using
                 fixed-point arithmetic / 211 \\
                 Upper bound for elements of reduced matrices / 212 \\
                 Complete pivoting / 212 \\
                 Practical procedure with partial pivoting / 214 \\
                 Floating-point error analysis / 214 \\
                 Floating-point decomposition without pivoting / 215 \\
                 Loss of significant figures / 217 \\
                 A popular fallacy / 217 \\
                 Matrices of special form / 218 \\
                 Gaussian elimination on a high-speed computer / 220 \\
                 Solutions corresponding to different right-hand sides /
                 221 \\
                 Direct triangular decomposition / 221 \\
                 Relations between Gaussian elimination and direct
                 triangular decomposition / 223 \\
                 Examples of failure and non-uniqueness of decomposition
                 / 224 \\
                 Triangular decomposition with row interchanges / 225
                 \\
                 Error analysis of triangular decomposition / 227 \\
                 Evaluation of determinants / 228 \\
                 Cholesky decomposition / 229 \\
                 Symmetric matrices which are not positive definite /
                 230 \\
                 Error analysis of Cholesky decomposition in fixed-point
                 arithmetic / 231 \\
                 An ill-conditioned matrix / 233 \\
                 Triangularization using elementary Hermitian matrices /
                 233 \\
                 Error analysis of Householder triangularization / 236
                 \\
                 Triangularization by elementary stabilized matrices of
                 the type M1, / 236 \\
                 Evaluation of determinants of leading principal minors
                 / 237 \\
                 Triangularization by plane rotations / 239 \\
                 Error analysis of Givens reduction / 240 \\
                 Uniqueness of orthogonal triangularization / 241 \\
                 Schmidt orthogonalization / 242 \\
                 Comparison of the methods of triangularization / 244
                 \\
                 Back-substitution / 247 \\
                 High accuracy of computed solutions of triangular sets
                 of equations / 249 \\
                 Solution of a general set of equations / 251 \\
                 Computation of the inverse of a general matrix / 252
                 \\
                 Accuracy of computed solutions / 253 \\
                 Ill-conditioned matrices which give no small pivots /
                 254 \\
                 Iterative improvements of approximate solution / 255
                 \\
                 Effect of rounding errors on the iterative process /
                 256 \\
                 The iterative procedure in fixed-point computation /
                 257 \\
                 Simple example of iterative procedure / 258 \\
                 General comments on the iterative procedure / 260 \\
                 Related iterative procedures / 261 \\
                 Limitations of the iterative procedure / 261 \\
                 Rigorous justification of the iterative method / 262
                 \\
                 5. Hermitian Matrices \\
                 Introduction / 265 \\
                 The classical Jacobi method for real symmetric matrices
                 / 266 \\
                 Rate of convergence / 267 \\
                 Convergence to fixed diagonal matrix / 268 \\
                 Serial Jacobi method / 269 \\
                 The Gerschgorin discs / 269 \\
                 Ultimate quadratic convergence of Jacobi methods / 270
                 \\
                 Close and multiple eigenvalues / 271 \\
                 Numerical examples / 273 \\
                 Calculation of cos 8 and sin B / 274 \\
                 Simpler determination of the angles of rotation / 276
                 \\
                 The threshold Jacobi method / 277 \\
                 Calculation of the eigenvectors / 278 \\
                 Numerical example / 279 \\
                 Error analysis of the Jacobi method / 279 \\
                 Accuracy of the computed eigenvectors / 280 \\
                 Error bounds for fixed-point computation / 281 \\
                 Organizational problems / 282 \\
                 Givens' method / 282 \\
                 Givens' process on a computer with a two-level store /
                 284 \\
                 Floating-point error analysis of Givens' process / 286
                 \\
                 Fixed-point error analysis / 287 \\
                 Numerical example / 288 \\
                 Householder's method / 290 \\
                 Taking advantage of symmetry / 292 \\
                 Storage considerations / 293 \\
                 Householder's process on a computer with a two-level
                 store / 294 \\
                 Householder's method in fixed-point arithmetic / 294
                 \\
                 Numerical example / 296 \\
                 Error analyses of Householder's method / 297 \\
                 Eigenvalues of a symmetric tri-diagonal matrix / 299
                 \\
                 Sturm sequence property / 300 \\
                 Method of bisection / 302 \\
                 Numerical stability of the bisection method / 302 \\
                 Numerical example / 305 \\
                 General comments on the bisection method / 306 \\
                 Small eigenvalues / 307 \\
                 Close eigenvalues and small $\beta_i$ / 308 \\
                 Fixed-point computation of the eigenvalues / 312 \\
                 Computation of the eigenvectors of a tri-diagonal form
                 / 315 \\
                 Instability of the explicit expression for the
                 eigenvector / 316 \\
                 Numerical examples / 319 \\
                 Inverse iteration / 321 \\
                 Choice of initial vector $b$ / 322 \\
                 Error analysis / 323 \\
                 Numerical example / 325 \\
                 Close eigenvalues and small $\beta_i$ / 327 \\
                 Independent vectors corresponding to coincident
                 eigenvalues / 328 \\
                 Alternative method for computing the eigenvectors / 330
                 \\
                 Numerical example / 331 \\
                 Comments on the eigenproblem for tri-diagonal matrices
                 / 332 \\
                 Completion of the Givens and Householder methods / 333
                 \\
                 Comparison of methods / 334 \\
                 Quasi-symmetric tri-diagonal matrices / 335 \\
                 Calculation of the eigenvectors / 336 \\
                 Equations of the form $A x = \lambda B x$ and $A B x =
                 \lambda X $ / 337 \\
                 Numerical example / 339 \\
                 Simultaneous reduction of $A$ and $B$ to diagonal form
                 / 340 \\
                 Tri-diagonal $A$ and $B$ / 340 \\
                 Complex Hermitian matrices / 342 \\
                 6. Reduction of a General Matrix to Condensed Form \\
                 Introduction / 345 \\
                 Givens' method / 345 \\
                 Householder's method / 347 \\
                 Storage considerations / 350 \\
                 Error analysis / 350 \\
                 Relationship between the Givens and Householder methods
                 / 351 \\
                 Elementary stabilized transformations / 353 \\
                 Significance of the permutations / 355 \\
                 Direct reduction to Hessenberg form / 357 \\
                 Incorporation of interchanges / 359 \\
                 Numerical example / 360 \\
                 Error analysis / 363 \\
                 Related error analyses / 365 \\
                 Poor determination of the Hessenberg matrix / 368 \\
                 Reduction to Hessenberg form using stabilized matrices
                 of the type $ M^'_{ji} $ / 368 \\
                 The method of Krylov / 369 \\
                 Gaussian elimination by columns / 370 \\
                 Practical difficulties / 371 \\
                 Condition of O for some standard distributions of
                 eigenvalues / 372 \\
                 Initial vectors of grade less than n / 374 \\
                 Practical experience / 376 \\
                 Generalized Hessenberg processes / 377 \\
                 Failure of the generalized Hessenberg process / 378 \\
                 The Hessenberg method / 379 \\
                 Practical procedure / 380 \\
                 Relation between the Hessenberg method and earlier
                 methods / 381 \\
                 The method of Arnoldi / 382 \\
                 Practical considerations / 383 \\
                 Significance of re-orthogonalization / 385 \\
                 The method of Lanczos / 388 \\
                 Failure of procedure / 389 \\
                 Numerical example / 390 \\
                 The practical Lanczos process / 391 \\
                 Numerical example / 392 \\
                 General comments on the unsymmetric Lanczos process /
                 394 \\
                 The symmetric Lanczos process / 394 \\
                 Reduction of a Hessenberg matrix to a more compact form
                 / 395 \\
                 Reduction of a lower Hessenberg matrix to tri-diagonal
                 form / 396 \\
                 The use of interchanges / 397 \\
                 Effect of a small pivotal element / 398 \\
                 Error analysis / 399 \\
                 The Hessenberg process applied to a lower Hessenberg
                 matrix / 402 \\
                 Relationship between the Hessenberg process and the
                 Lanczos process / 402 \\
                 Reduction of a general matrix to tri-diagonal form /
                 403 \\
                 Comparison with Lanczos method / 404 \\
                 Re-examination of reduction to tri-diagonal form / 404
                 \\
                 Reduction from upper Hessenberg form to Frobenius form
                 / 405 \\
                 Effect of small pivot / 407 \\
                 Numerical example / 408 \\
                 General comments on the stability / 408 \\
                 Specialized upper Hessenberg form / 409 \\
                 Direct determination of the characteristic polynomial /
                 410 \\
                 7. Eigenvalues of Matrices of Condensed Forms \\
                 Introduction / 413 \\
                 Explicit polynomial form / 413 \\
                 Condition numbers of explicit polynomials / 416 \\
                 Some typical distributions of zeros / 417 \\
                 Final assessment of Krylov's method / 421 \\
                 General comments on explicit polynomials / 421 \\
                 Tri-diagonal matrices / 423 \\
                 Determinants of Hessenberg matrices / 426 \\
                 Effect of rounding errors / 427 \\
                 Floating-point accumulation / 428 \\
                 Evaluation by orthogonal transformations / 429 \\
                 Evaluation of determinants of general matrices / 431
                 \\
                 The generalized eigenvalue problem / 432 \\
                 Indirect determinations of the characteristic
                 polynomial / 432 \\
                 Le Verrier's method / 434 \\
                 Iterative methods based on interpolation / 435 \\
                 Asymptotic rate of convergence / 436 \\
                 Multiple zeros / 437 \\
                 Inversion of the functional relationship / 439 \\
                 The method of bisection / 440 \\
                 Newton's method / 441 \\
                 Comparison of Newton's method with interpolation / 442
                 \\
                 Methods giving cubic convergence / 443 \\
                 Laguerre's method / 443 \\
                 Complex zeros / 446 \\
                 Complex conjugate zeros / 447 \\
                 Bairstow's method / 449 \\
                 The generalized Bairstow method / 450 \\
                 Practical considerations / 452 \\
                 Effect of rounding errors on asymptotic convergence /
                 453 \\
                 The method of bisection / 453 \\
                 Successive linear interpolation / 455 \\
                 Multiple and pathologically close eigenvalues / 457 \\
                 Other interpolation methods / 458 \\
                 Methods involving the use of a derivative / 459 \\
                 Criterion for acceptance of a zero / 461 \\
                 Effect of rounding errors / 462 \\
                 Suppression of computed zeros / 464 \\
                 Deflation for Hessenberg matrices / 465 \\
                 Deflation of tri-diagonal matrices / 468 \\
                 Deflation by rotations or stabilized elementary
                 transformations / 469 \\
                 Stability of the deflation / 472 \\
                 General comments on deflation / 474 \\
                 Suppression of computed zeros / 474 \\
                 Suppression of computed quadratic factors / 475 \\
                 General comments on the methods of suppression / 476
                 \\
                 Asymptotic rates of convergence / 478 \\
                 Convergence in the large / 478 \\
                 Complex zeros / 481 \\
                 Recommendations / 482 \\
                 Complex matrices / 483 \\
                 Matrices containing an independent parameter / 483 \\
                 8. The $ L R $ and $ Q R $ Algorithms \\
                 Introduction / 485 \\
                 Real matrices with complex eigenvalues / 486 \\
                 The $ L R $ algorithm / 487 \\
                 Proof of the convergence of the $A_s$ / 489 \\
                 Positive definite Hermitian matrices / 493 \\
                 Complex conjugate eigenvalues / 494 \\
                 Introduction of interchanges / 498 \\
                 Numerical example / 499 \\
                 Convergence of the modified process / 501 \\
                 Preliminary reduction of original matrix / 501 \\
                 Invariance of upper Hessenberg form / 502 \\
                 Simultaneous row and column operations / 504 \\
                 Acceleration of convergence / 505 \\
                 Incorporation of shifts of origin / 506 \\
                 Choice of shift of origin / 507 \\
                 Deflation of the matrix / 509 \\
                 Practical experience of convergence / 510 \\
                 Improved shift strategy / 511 \\
                 Complex conjugate eigenvalues / 512 \\
                 Criticisms of the modified $ L R $ algorithm. / 515 \\
                 The $ Q R $ algorithm / 515 \\
                 Convergence of the $ Q R $ algorithm / 516 \\
                 Formal proof of convergence / 517 \\
                 Disorder of the eigenvalues / 519 \\
                 Eigenvalues of equal modulus / 520 \\
                 Alternative proof for the $ L R $ technique / 521 \\
                 Practical application of the $ Q R $ algorithm / 523
                 \\
                 Shifts of origin / 524 \\
                 Decomposition of A8 / 525 \\
                 Numerical example / 527 \\
                 Practical procedure / 527 \\
                 Avoiding complex conjugate shifts / 528 \\
                 Double $ Q R $ step using elementary Hermitians / 532
                 \\
                 Computational details / 534 \\
                 Decomposition of A8 / 535 \\
                 Double-shift technique for $ L R $ / 537 \\
                 Assessment of $ L R $ and $ Q R $ algorithms / 538 \\
                 Multiple eigenvalues / 540 \\
                 Special use of the deflation process / 543 \\
                 Symmetric matrices / 544 \\
                 Relationship between $ L R $ and $ Q R $ algorithms /
                 545 \\
                 Convergence of the Cholesky $ L R $ algorithm / 546 \\
                 Cubic convergence of the $ Q R $ algorithm / 548 \\
                 Shift of origin in Cholesky $ L R $ / 549 \\
                 Failure of the Cholesky decomposition / 550 \\
                 Cubically convergent $ L R $ process / 551 \\
                 Band matrices / 553 \\
                 $ Q R $ decomposition of a band matrix / 557 \\
                 Error analysis / 561 \\
                 Unsymmetric band matrices / 562 \\
                 Simultaneous decomposition and recombination in $ Q R $
                 algorithm / 565 \\
                 Reduction of band width / 567 \\
                 9. ITERATIVE METHODS \\
                 Introduction / 570 \\
                 The power method / 570 \\
                 Direct iteration with a single vector / 571 \\
                 Shift of origin / 572 \\
                 Effect of rounding errors / 573 \\
                 Variation of $p$ / 576 \\
                 {\em Ad hoc\/} choice of $p$ / 577 \\
                 Aitken's acceleration technique / 578 \\
                 Complex conjugate eigenvalues / 579 \\
                 Calculation of the complex eigenvector / 581 \\
                 Shift of origin / 582 \\
                 Non-linear divisors / 582 \\
                 Simultaneous determination of several eigenvalues / 583
                 \\
                 Complex matrices / 584 \\
                 Deflation / 584 \\
                 Deflation based on similarity transformations / 585 \\
                 Deflation using invariant subspaces / 587 \\
                 Deflation using stabilized elementary transformations /
                 587 \\
                 Deflation using unitary transformations / 589 \\
                 Numerical stability / 590 \\
                 Numerical example / 592 \\
                 Stability of unitary transformations / 594 \\
                 Deflation by non-similarity transformations / 596 \\
                 General reduction using invariant subspaces / 599 \\
                 Practical application / 601 \\
                 Treppen-iteration / 602 \\
                 Accurate determination of complex conjugate eigenvalues
                 / 604 \\
                 Very close eigenvalues / 606 \\
                 Orthogonalization techniques / 606 \\
                 Analogue of treppen-iteration using orthogonalization /
                 607 \\
                 Bi-iteration / 609 \\
                 Numerical example / 610 \\
                 Richardson's purification process / 614 \\
                 Matrix squaring / 615 \\
                 Numerical stability / 616 \\
                 Use of Chebyshev polynomials / 617 \\
                 General assessment of methods based on direct iteration
                 / 618 \\
                 Inverse iteration / 619 \\
                 Error analysis of inverse iteration / 620 \\
                 General comments on the analysis / 621 \\
                 Further refinement of eigenvectors / 622 \\
                 Non-linear elementary divisors / 626 \\
                 Inverse iteration with Hessenberg matrices / 626 \\
                 Degenerate cases / 627 \\
                 Inverse iteration with band matrices / 628 \\
                 Complex conjugate eigenvectors / 629 \\
                 Error analysis / 631 \\
                 Numerical example / 633 \\
                 The generalized eigenvalue problem / 633 \\
                 Variation of approximate eigenvalues / 635 \\
                 Refinement of eigensystems / 637 \\
                 Numerical example / 639 \\
                 Refinement of the eigenvectors / 641 \\
                 Complex conjugate eigenvalues / 643 \\
                 Coincident and pathologically close eigenvalues / 644
                 \\
                 Comments on the ACE programmes / 646 \\
                 Bibliography / 649 \\
                 Index / 657",
}

@Article{Wilkinson:1965:ARS,
  author =       "J. H. Wilkinson",
  title =        "The {$ Q R $} Algorithm for Real Symmetric Matrices
                 with Multiple Eigenvalues",
  journal =      j-COMP-J,
  volume =       "8",
  number =       "1",
  pages =        "85--87",
  month =        apr,
  year =         "1965",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  MRclass =      "65.40",
  MRnumber =     "MR0181100 (31 \#5329)",
  MRreviewer =   "E. R. Hansen",
  bibdate =      "Fri Sep 29 08:56:03 MDT 2000",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/080085.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/tiff/85.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/tiff/86.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/tiff/87.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/tiff/88.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Wilkinson:1965:CLP,
  author =       "J. H. Wilkinson",
  title =        "The Calculation of {Lam{\'e}} Polynomials",
  journal =      j-COMP-J,
  volume =       "8",
  number =       "3",
  pages =        "273--277",
  month =        oct,
  year =         "1965",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  MRclass =      "65.25",
  MRnumber =     "MR0184412 (32 \#1884)",
  bibdate =      "Fri Sep 29 08:56:08 MDT 2000",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_03/",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_03/080273.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_03/tiff/273.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_03/tiff/274.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_03/tiff/275.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_03/tiff/276.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_03/tiff/277.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Wilkinson:1965:CRA,
  author =       "J. H. Wilkinson",
  title =        "Convergence of the {$ L R $}, {$ Q R $} and related
                 algorithms",
  journal =      j-COMP-J,
  volume =       "8",
  number =       "1",
  pages =        "77--84",
  month =        apr,
  year =         "1965",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  MRclass =      "65.40",
  MRnumber =     "MR0183108 (32 \#590)",
  MRreviewer =   "E. R. Hansen",
  bibdate =      "Fri Sep 29 08:56:03 MDT 2000",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/;
                 Theory/Matrix.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/080077.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/tiff/77.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/tiff/78.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/tiff/79.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/tiff/80.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/tiff/81.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/tiff/82.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/tiff/83.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/tiff/84.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "nla, eig, QR algorithm, LR algorithm",
}

@InProceedings{Wilkinson:1965:EAT,
  author =       "J. H. Wilkinson",
  title =        "Error Analysis for Transformations Based on the Use of
                 Matrices of the form {$ I - 2 w w^H $}",
  crossref =     "Rall:1965:EDCb",
  pages =        "77--101",
  year =         "1965",
  MRclass =      "65.80",
  MRnumber =     "MR0189284 (32 \#6711)",
  MRreviewer =   "J. M. Ortega",
  bibdate =      "Mon Jun 18 11:38:02 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  xxtitle =      "Error Analysis of Transformations Based on the Use of
                 Matrices of the form {$ I - 2 w w^H $}",
}

@Article{Bowdler:1966:SRC,
  author =       "H. J. Bowdler and R. S. Martin and G. Peters and J. H.
                 Wilkinson",
  title =        "Solution of Real and Complex Systems of Linear
                 Equations",
  journal =      j-NUM-MATH,
  volume =       "8",
  number =       "3",
  pages =        "217--234",
  year =         "1966",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF02162559",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "Contributed Item",
  MRnumber =     "MR1553947",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "See also \cite[pp.~93--110]{Wilkinson:1971:LA}.",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@InProceedings{Golub:1966:IRL,
  author =       "G. H. Golub and J. H. Wilkinson",
  booktitle =    "Proceedings of the IFIP Congress 65, Volume 2",
  title =        "Iterative Refinement of Least Square Solution",
  publisher =    "International Federation for Information Processing
                 (IFIP)",
  pages =        "606--607",
  year =         "1966",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@Article{Golub:1966:NIR,
  author =       "G. H. Golub and J. H. Wilkinson",
  title =        "Note on the Iterative Refinement of Least Squares
                 Solution",
  journal =      j-NUM-MATH,
  volume =       "9",
  number =       "2",
  pages =        "139--148",
  month =        dec,
  year =         "1966",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65.20",
  MRnumber =     "35 \#3849",
  MRreviewer =   "W. J. Kotz{\'e}",
  bibdate =      "Sun Oct 17 19:01:15 MDT 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/gvl.bib;
                 Theory/Matrix.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "condition; iterative refinement; la; lsq; nla; pert",
}

@Article{Martin:1966:IRS,
  author =       "R. S. Martin and G. Peters and J. H. Wilkinson",
  title =        "Iterative Refinement of the Solution of a Positive
                 Definite System of Equations",
  journal =      j-NUM-MATH,
  volume =       "8",
  number =       "3",
  pages =        "203--216",
  month =        may,
  year =         "1966",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF02162558",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "Contributed Item",
  MRnumber =     "MR1553946",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 Theory/Matrix.bib",
  note =         "Also in \cite[pp. 31--44]{Wilkinson:1971:LA}.",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "iterative refinement; linear system; nla; positive
                 definite matrix; software",
}

@InProceedings{Wilkinson:1966:CEM,
  author =       "J. H. Wilkinson",
  editor =       "J. Walsh",
  booktitle =    "Numerical Analysis: An Introduction",
  title =        "Calculation of Eigensystems of Matrices",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "27--61",
  year =         "1966",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@Article{Wilkinson:1967:BRB,
  author =       "J. H. Wilkinson",
  title =        "Book Review: {{\booktitle{The Matrix Analysis of
                 Vibration}}, by R. E. D. Bishop, G. M. L. Gladwell, and
                 S. Michaelson, 1965; 404 pages (London: Cambridge
                 University Press, 100s)}",
  journal =      j-COMP-J,
  volume =       "10",
  number =       "1",
  pages =        "77--77",
  month =        may,
  year =         "1967",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/10.1.77",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:37 MST 2012",
  bibsource =    "http://comjnl.oxfordjournals.org/content/10/1.toc;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/compj1960.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/10/1/74.full.pdf;
                 http://comjnl.oxfordjournals.org/content/10/1/77.full.pdf+html",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Book{Wilkinson:1967:BZW,
  author =       "J. H. Wilkinson",
  title =        "Bledy Zaokragle{\'n} w Procesach Algebraicznych.
                 ({Polish}) [{Rounding} errors in algebraic Processes]",
  publisher =    "PWW",
  address =      "Warszawa, Poland",
  pages =        "????",
  year =         "1967",
  bibdate =      "Thu Aug 25 09:28:02 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Polish translation of \cite{Wilkinson:1963:REA}",
  acknowledgement = ack-nhfb,
  language =     "Polish",
}

@Article{Barth:1967:CES,
  author =       "R. S. Martin W. Barth and J. H. Wilkinson",
  title =        "Calculation of the Eigenvalues of a Symmetric
                 Tridiagonal matrix by the Method of Bisection",
  journal =      j-NUM-MATH,
  volume =       "9",
  number =       "5",
  pages =        "386--393",
  month =        apr,
  year =         "1967",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF02162154",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "Contributed Item",
  MRnumber =     "MR1553954",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 Theory/Matrix.bib",
  note =         "Also in \cite[pp. 249--256]{Wilkinson:1971:LA}.",
  series =       "Handbook Series Linear Algebra",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "eig; nla; software; Sturm sequence; symmetric matrix;
                 tridiagonal matrix",
}

@Article{Martin:1967:SSU,
  author =       "R. S. Martin and J. H. Wilkinson",
  title =        "Solution of Symmetric and Unsymmetric Band Equations
                 and the Calculation of Eigenvectors of Band Matrices",
  journal =      j-NUM-MATH,
  volume =       "9",
  number =       "4",
  pages =        "279--301",
  month =        feb,
  year =         "1967",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF02162421",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "Contributed Item",
  MRnumber =     "MR1553951",
  bibdate =      "Sun Oct 17 12:54:13 MDT 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 Theory/Matrix.bib",
  note =         "Also in \cite[pp. 70--92]{Wilkinson:1971:LA}.",
  series =       "Handbook Series Linear Algebra",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "band matrix; eig; linear system; nla; software",
}

@TechReport{Wilkinson:1967:ADM,
  author =       "J. H. Wilkinson",
  title =        "Almost Diagonal Matrices with Multiple or Close
                 Eigenvalues",
  type =         "Technical Report",
  number =       "CS 59",
  institution =  inst-SU-cs,
  address =      inst-SU:adr,
  year =         "1967",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Published as \cite{Wilkinson:1968:ADM}.",
}

@InCollection{Wilkinson:1967:SIC,
  author =       "J. H. Wilkinson",
  editor =       "A. Ralston and H. Wilf",
  booktitle =    "Mathematical Methods for Digital Computers, Volume 2",
  title =        "The Solution of Ill-Conditioned Linear Equations",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "65--93",
  year =         "1967",
  bibdate =      "Tue Aug 15 18:20:34 MDT 1995",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@InCollection{Wilkinson:1967:SLA,
  author =       "J. H. Wilkinson",
  editor =       "M. Klarer and G. A. Korn",
  booktitle =    "Digital Computer Users' Handbook",
  title =        "Solution of Linear Algebraic Equations and Matrix
                 Problems by Direct Methods",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "2:18--2:55",
  year =         "1967",
  bibdate =      "Tue Aug 15 18:20:34 MDT 1995",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@TechReport{Wilkinson:1967:TAB,
  author =       "J. H. Wilkinson",
  title =        "Two Algorithms Based on Successive Linear
                 Interpolation",
  type =         "Technical Report",
  number =       "CS 60",
  institution =  inst-SU-cs,
  address =      inst-SU:adr,
  year =         "1967",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@Article{Bowdler:1968:ASM,
  author =       "H. J. Bowdler and R. S. Martin and C. Reinsch and J.
                 H. Wilkinson",
  title =        "The {$ Q R $} and {$ Q L $} Algorithms for Symmetric
                 Matrices",
  journal =      j-NUM-MATH,
  volume =       "11",
  number =       "4",
  pages =        "293--306",
  year =         "1968",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF02166681",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "Contributed Item",
  MRnumber =     "MR1553961",
  bibdate =      "Fri May 14 17:18:08 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "See also \cite[pp.~227--240]{Wilkinson:1971:LA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Martin:1968:HTS,
  author =       "R. S. Martin and C. Reinsch and J. H. Wilkinson",
  title =        "{Householder}'s tridiagonalization of a symmetric
                 matrix",
  journal =      j-NUM-MATH,
  volume =       "11",
  number =       "3",
  pages =        "181--195",
  month =        mar,
  year =         "1968",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF02161841",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "Contributed Item",
  MRnumber =     "MR1553959",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 Theory/Matrix.bib",
  note =         "Also in \cite[pp. 212--226]{Wilkinson:1971:LA}.",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "eig; Householder transformation; nla; software;
                 symmetric matrix; tridiagonal matrix",
}

@Article{Martin:1968:IA,
  author =       "Roger S. Martin and J. H. Wilkinson",
  title =        "The Implicit {$ Q L $} Algorithm",
  journal =      j-NUM-MATH,
  volume =       "12",
  number =       "5",
  pages =        "377--383",
  month =        dec,
  year =         "1968",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF02161360",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "Contributed Item",
  MRnumber =     "MR1553967",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 Theory/Matrix.bib",
  note =         "Also in \cite[pp.~241--248]{Wilkinson:1971:LA}, where
                 A. A. Dubrulle and is listed as the lead author.",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "eig; nla; QL algorithm; QR algorithm; software;
                 tridiagonal matrix",
}

@Article{Martin:1968:MAC,
  author =       "Roger S. Martin and J. H. Wilkinson",
  title =        "The Modified {$ L R $} Algorithm for Complex
                 {Hessenberg} Matrices",
  journal =      j-NUM-MATH,
  volume =       "12",
  number =       "5",
  pages =        "369--376",
  month =        dec,
  year =         "1968",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF02161359",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "Contributed Item",
  MRnumber =     "MR1553966",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 Theory/Matrix.bib",
  note =         "Also in \cite[pp. 396--403]{Wilkinson:1971:LA}.",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "complex matrix; eig; Hessenberg matrix; LR algorithm;
                 nla; software",
}

@Article{Martin:1968:RSE,
  author =       "R. S. Martin and J. H. Wilkinson",
  title =        "Reduction of the Symmetric Eigenproblem {$ A x =
                 \lambda B x $} and Related Problems to Standard Form",
  journal =      j-NUM-MATH,
  volume =       "11",
  number =       "2",
  pages =        "99--110",
  month =        feb,
  year =         "1968",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF02165306",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "Contributed Item",
  MRnumber =     "MR1553957",
  bibdate =      "Sun Oct 17 16:12:48 MDT 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 Theory/Matrix.bib",
  note =         "Also in \cite[pp. 303--314]{Wilkinson:1971:LA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "geig; nla; software; symmetric matrix",
}

@Article{Martin:1968:SRG,
  author =       "R. S. Martin and J. H. Wilkinson",
  title =        "Similarity Reduction of a General Matrix to
                 {Hessenberg} Form",
  journal =      j-NUM-MATH,
  volume =       "12",
  number =       "5",
  pages =        "349--368",
  month =        dec,
  year =         "1968",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF02161358",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "Contributed Item",
  MRnumber =     "MR1553965",
  bibdate =      "Sun Oct 17 16:12:48 MDT 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 Theory/Matrix.bib",
  note =         "Also in \cite[pp. 339--358]{Wilkinson:1971:LA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "eig; Hessenberg matrix; nla; nonsymmetric matrix;
                 software",
}

@Article{Wilkinson:1968:ADM,
  author =       "J. H. Wilkinson",
  title =        "Almost Diagonal Matrices with Multiple or Close
                 Eigenvalues",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "1",
  pages =        "1--12",
  year =         "1968",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15.25 (65.00)",
  MRnumber =     "MR0225794 (37 \#1386)",
  MRreviewer =   "John Todd",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@InProceedings{Wilkinson:1968:BFE,
  author =       "J. H. Wilkinson",
  booktitle =    "Programmation en Math{\'e}matiques Num{\'e}riques",
  title =        "The Basic Forms of Error Analysis of Matrix
                 Processes",
  publisher =    "{\'E}ditions Centre Nat. Recherche Sci.",
  address =      "Paris, France",
  pages =        "127--133",
  year =         "1968",
  MRclass =      "65.35",
  MRnumber =     "MR0231522 (37 \#7075)",
  MRreviewer =   "L. W. Ehrlich",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Colloq. Int. Cent. Nat. Rech. Sci. 165,
                 Besan{\c{c}}on, Paris",
}

@Article{Wilkinson:1968:GCT,
  author =       "J. H. Wilkinson",
  title =        "Global Convergence of Tridiagonal {$ Q R $} Algorithm
                 with Origin Shifts",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "1",
  number =       "3",
  pages =        "409--420",
  month =        jul,
  year =         "1968",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/0024-3795(68)90017-7",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "65.40",
  MRnumber =     "MR0234622 (38 \#2938)",
  MRreviewer =   "E. R. Hansen",
  bibdate =      "Tue Feb 16 18:47:41 MST 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/linala1960.bib;
                 http://www.math.utah.edu/pub/tex/bib/linala1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0024379568900177",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795/",
}

@InProceedings{Wilkinson:1968:PEA,
  author =       "J. H. Wilkinson",
  editor =       "I. G. Petrovsky",
  booktitle =    "Proc. Int. Congr. Mthns",
  title =        "A Priori Error Analysis of Algebraic Processes",
  publisher =    "Izdatel'stvo Mir",
  address =      "Moscow, USSR",
  pages =        "629--640",
  year =         "1968",
  MRclass =      "65.80",
  MRnumber =     "MR0233532 (38 \#1853)",
  MRreviewer =   "A. S. Householder",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@Article{Wilkinson:1968:SEA,
  author =       "James Hardy Wilkinson",
  title =        "A Survey of Error Analysis of Matrix Algorithms",
  journal =      j-APL-MAT,
  volume =       "13",
  pages =        "93--102",
  year =         "1968",
  CODEN =        "APMTAK",
  ISSN =         "0373-6725",
  MRclass =      "65.80",
  MRnumber =     "MR0228213 (37 \#3797)",
  MRreviewer =   "B. N. Parlett",
  bibdate =      "Fri May 14 17:09:52 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  fjournal =     "\v Ceskoslovensk\'a Akademie V\v ed. Aplikace
                 Matematiky",
}

@Article{Peters:1969:EBS,
  author =       "G. Peters and J. H. Wilkinson",
  title =        "Eigenvalues of {$ A x = \lambda B x $} with Band
                 Symmetric {$A$} and {$B$}",
  journal =      j-COMP-J,
  volume =       "12",
  number =       "4",
  pages =        "398--404",
  month =        nov,
  year =         "1969",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  MRclass =      "65.35",
  MRnumber =     "MR0253543 (40 \#6757)",
  bibdate =      "Fri Sep 29 08:51:40 MDT 2000",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/120397.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/tiff/398.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/tiff/399.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/tiff/400.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/tiff/401.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/tiff/402.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/tiff/403.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/tiff/404.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C4140 (Linear algebra)",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "algebra; eigenvalues and eigenfunctions;
                 interpolation; matrix; nla, geig, band matrix,
                 symmetric matrix; poles and zeros; subroutines",
}

@InProceedings{Wilkinson:1969:GCA,
  author =       "James H. Wilkinson",
  booktitle =    "Proceedings of the IFIP Congress 1968, Edinburgh,
                 Volume 1",
  title =        "Global Convergence of {$ Q R $} Algorithm (with
                 discussion)",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "130--133",
  year =         "1969",
  MRclass =      "65.40",
  MRnumber =     "MR0255039 (40 \#8246)",
  bibdate =      "Fri May 14 17:13:35 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@Book{Wilkinson:1969:R,
  author =       "J. H. Wilkinson",
  title =        "{Rundungsfehler}",
  volume =       "44",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 208",
  year =         "1969",
  MRclass =      "68.00 (12.00)",
  MRnumber =     "MR0242399 (39 \#3730)",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "German translation by G. Goos.",
  series =       "Heidelberger Taschenb{\"u}cher",
}

@Article{Householder:1970:NGI,
  author =       "Alston S. Householder and Richard S. Varga and James
                 H. Wilkinson",
  title =        "A Note on {Gerschgorin}'s Inclusion Theorem for
                 Eigenvalues of Matrices",
  journal =      j-NUM-MATH,
  volume =       "16",
  pages =        "141--144",
  year =         "1970",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65.40 (15.00)",
  MRnumber =     "MR0275648 (43 \#1401)",
  MRreviewer =   "J. Stoer",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Martin:1970:ABS,
  author =       "R. S. Martin and C. Reinsch and J. H. Wilkinson",
  title =        "The {$ Q R $} algorithm for band symmetric matrices",
  journal =      j-NUM-MATH,
  volume =       "16",
  number =       "2",
  pages =        "85--92",
  month =        nov,
  year =         "1970",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF02308862",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "Contributed Item",
  MRnumber =     "MR1553977",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "See also \cite[pp.~266--272]{Wilkinson:1971:LA}.",
  acknowledgement = ack-nhfb,
  classification = "C4140 (Linear algebra)",
  corpsource =   "Nat. Phys. Lab., Teddington, UK",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "eigenvalues and eigenfunctions and matrix algebra",
}

@Article{Martin:1970:ARH,
  author =       "R. S. Martin and G. Peters and J. H. Wilkinson",
  title =        "The {$ Q R $} Algorithm for real {Hessenberg}
                 matrices",
  journal =      j-NUM-MATH,
  volume =       "14",
  number =       "3",
  pages =        "219--231",
  month =        feb,
  year =         "1970",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF02163331",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "Contributed Item",
  MRnumber =     "MR1553971",
  bibdate =      "Tue Jan 28 17:21:29 1997",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 Theory/Matrix.bib",
  note =         "Also in \cite[pp. 359--371]{Wilkinson:1971:LA}.",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "eig; Hessenberg matrix; nla; QR algorithm; software",
}

@Article{Peters:1970:ERC,
  author =       "G. Peters and J. H. Wilkinson",
  title =        "Eigenvectors of Real and Complex Matrices by {$ L R $}
                 and {$ Q R $} Triangularization",
  journal =      j-NUM-MATH,
  volume =       "16",
  number =       "3",
  pages =        "181--204",
  month =        dec,
  year =         "1970",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF02219772",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "Contributed Item",
  MRnumber =     "MR1553978",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 Theory/Matrix.bib",
  note =         "Also in \cite[pp. 372--395]{Wilkinson:1971:LA}.",
  acknowledgement = ack-nhfb,
  classification = "C4140 (Linear algebra)",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "complex matrix; eig; eigenvalues and eigenfunctions;
                 matrix algebra; nla; nonsymmetric matrix; software",
}

@Article{Peters:1970:GE,
  author =       "G. Peters and J. H. Wilkinson",
  title =        "{$ A x = \lambda B x $} and the Generalized
                 Eigenproblem",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "7",
  pages =        "479--492",
  year =         "1970",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65.40",
  MRnumber =     "MR0277106 (43 \#2843)",
  MRreviewer =   "E. Deutsch",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
}

@Article{Peters:1970:LSP,
  author =       "G. Peters and J. H. Wilkinson",
  title =        "The Least Squares Problem and Pseudo-Inverses",
  journal =      j-COMP-J,
  volume =       "13",
  number =       "3",
  pages =        "309--316",
  month =        aug,
  year =         "1970",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:51:46 MDT 2000",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_13/Issue_03/",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_13/Issue_03/130309.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_13/Issue_03/tiff/309.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_13/Issue_03/tiff/310.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_13/Issue_03/tiff/311.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_13/Issue_03/tiff/312.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_13/Issue_03/tiff/313.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_13/Issue_03/tiff/314.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_13/Issue_03/tiff/315.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_13/Issue_03/tiff/316.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C4140 (Linear algebra)",
  corpsource =   "Nat. Phys. Lab., Teddington, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "least squares approximations; matrix algebra",
}

@Book{Wilkinson:1970:APS,
  author =       "J. H. Wilkinson",
  title =        "Algebraicheskaya problema sobstvennyh znachenii'.
                 ({Russian}) [The Algebraic Eigenvalue Problem]",
  publisher =    pub-NAUKA,
  address =      pub-NAUKA:adr,
  pages =        "564",
  year =         "1970",
  bibdate =      "Thu Aug 25 09:30:04 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Russian translation of \cite{Wilkinson:1965:AEP}",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@Article{Wilkinson:1970:BRB,
  author =       "J. H. Wilkinson",
  title =        "Book Review: {{\booktitle{A Collection of Matrices for
                 Testing Computational Algorithms}}, by Robert T.
                 Gregory, D. L. Karney, 1969; 154 pages. (John Wiley and
                 Sons Ltd., \pounds 4.75)}",
  journal =      j-COMP-J,
  volume =       "13",
  number =       "4",
  pages =        "391--391",
  month =        nov,
  year =         "1970",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/13.4.391",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:46 MST 2012",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://comjnl.oxfordjournals.org/content/13/4.toc;
                 http://www.math.utah.edu/pub/tex/bib/compj1970.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/13/4/387.full.pdf;
                 http://comjnl.oxfordjournals.org/content/13/4/391.full.pdf+html",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Wilkinson:1970:BRH,
  author =       "J. H. Wilkinson",
  title =        "Book Review: {{\em A Handbook of Numerical Matrix
                 Inversion and Solution of Linear Equations}, by Joan
                 Westlake: pp. 171; 90s. (John Wiley and Sons, New York,
                 1968)}",
  journal =      j-BULL-LOND-MATH-SOC,
  volume =       "2",
  number =       "3",
  pages =        "378--379",
  month =        nov,
  year =         "1970",
  CODEN =        "LMSBBT",
  DOI =          "https://doi.org/10.1112/blms/2.3.378",
  ISSN =         "0024-6093 (print), 1469-2120 (electronic)",
  ISSN-L =       "0024-6093",
  bibdate =      "Thu Aug 25 10:29:07 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  URL =          "http://blms.oxfordjournals.org/content/2/3/378.full.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Bulletin of the London Mathematical Society",
  journal-URL =  "http://blms.oxfordjournals.org/content/by/year",
}

@TechReport{Wilkinson:1970:EPW,
  author =       "J. H. Wilkinson",
  title =        "Elementary Proof of the {Wielandt--Hoffman} Theorem
                 and of its Generalization",
  type =         "Technical Report",
  number =       "CS 150",
  institution =  inst-SU-cs,
  address =      inst-SU:adr,
  year =         "1970",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@InCollection{Barth:1971:CES,
  author =       "W. Barth and R. S. Martin and J. H. Wilkinson",
  title =        "Calculation of the eigenvalues of a symmetric
                 tridiagonal matrix by the method of bisection",
  crossref =     "Wilkinson:1971:LA",
  pages =        "249--256",
  year =         "1971",
  bibdate =      "Tue May 08 14:20:56 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
}

@Book{Bell:1971:CSR,
  editor =       "C. G. Bell and A. Newell",
  title =        "Computer Structures: Readings and Examples",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  year =         "1971",
  ISBN =         "0-07-004357-4",
  ISBN-13 =      "978-0-07-004357-2",
  LCCN =         "TK7888.3 .B4",
  bibdate =      "Tue Aug 15 18:20:34 MDT 1995",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@InCollection{Bowdler:1971:ASM,
  author =       "H. Bowdler and R. S. Martin and C. H. Reinsch and J.
                 H. Wilkinson",
  title =        "The {$ Q R $} and {$ Q L $} algorithms for symmetric
                 matrices",
  crossref =     "Wilkinson:1971:LA",
  pages =        "227--240",
  year =         "1971",
  bibdate =      "Tue May 08 14:20:56 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Bowdler:1971:SRC,
  author =       "H. J. Bowdler and R. S. Martin and G. Peters and J. H.
                 Wilkinson",
  title =        "Solution of real and complex systems of linear
                 equations",
  crossref =     "Wilkinson:1971:LA",
  pages =        "93--110",
  year =         "1971",
  bibdate =      "Tue May 08 14:20:56 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Dubrulle:1971:IA,
  author =       "A. Dubrulle and R. S. Martin and J. H. Wilkinson",
  title =        "The implicit {$ Q L $} algorithm",
  crossref =     "Wilkinson:1971:LA",
  pages =        "241--248",
  year =         "1971",
  bibdate =      "Tue May 08 14:20:56 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Martin:1971:ABS,
  author =       "R. S. Martin and C. H. Reinsch and J. H. Wilkinson",
  title =        "The {$ Q R $} algorithm for band symmetric matrices",
  crossref =     "Wilkinson:1971:LA",
  pages =        "266--272",
  year =         "1971",
  bibdate =      "Tue May 08 14:20:56 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Martin:1971:ARH,
  author =       "R. S. Martin and G. Peters and J. H. Wilkinson",
  title =        "The {$ Q R $} algorithm for real Hessenberg matrices",
  crossref =     "Wilkinson:1971:LA",
  pages =        "359--371",
  year =         "1971",
  bibdate =      "Tue May 08 14:20:56 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Martin:1971:HTS,
  author =       "R. S. Martin and C. H. Reinsch and J. H. Wilkinson",
  title =        "Householder's tridiagonalization of a symmetric
                 matrix",
  crossref =     "Wilkinson:1971:LA",
  pages =        "212--226",
  year =         "1971",
  bibdate =      "Tue May 08 14:20:56 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Martin:1971:IRS,
  author =       "R. S. Martin and G. Peters and J. H. Wilkinson",
  title =        "Iterative refinement of the solution of a positive
                 definite system of equations",
  crossref =     "Wilkinson:1971:LA",
  pages =        "31--44",
  year =         "1971",
  bibdate =      "Tue May 08 14:20:56 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Martin:1971:MAC,
  author =       "R. S. Martin and J. H. Wilkinson",
  title =        "The modified {$ L R $} algorithm for complex
                 Hessenberg matrices",
  crossref =     "Wilkinson:1971:LA",
  pages =        "396--403",
  year =         "1971",
  bibdate =      "Tue May 08 14:20:56 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Martin:1971:RSE,
  author =       "R. S. Martin and J. H. Wilkinson",
  title =        "Reduction of the symmetric eigenproblem {$ A x =
                 \lambda B x $} and related problems to standard form",
  crossref =     "Wilkinson:1971:LA",
  pages =        "303--314",
  year =         "1971",
  bibdate =      "Tue May 08 14:20:56 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Martin:1971:SDPa,
  author =       "R. S. Martin and G. Peters and J. H. Wilkinson",
  title =        "Symmetric decomposition of a positive definite
                 matrix",
  crossref =     "Wilkinson:1971:LA",
  pages =        "9--30",
  year =         "1971",
  bibdate =      "Tue May 08 14:20:56 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Martin:1971:SDPb,
  author =       "R. S. Martin and J. H. Wilkinson",
  title =        "Symmetric decomposition of positive definite band
                 matrices",
  crossref =     "Wilkinson:1971:LA",
  pages =        "50--56",
  year =         "1971",
  bibdate =      "Tue May 08 14:20:56 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Martin:1971:SRG,
  author =       "R. S. Martin and J. H. Wilkinson",
  title =        "Similarity reduction of a general matrix to Hessenberg
                 form",
  crossref =     "Wilkinson:1971:LA",
  pages =        "339--358",
  year =         "1971",
  bibdate =      "Tue May 08 14:20:56 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Martin:1971:SSU,
  author =       "R. S. Martin and J. H. Wilkinson",
  title =        "Solution of symmetric and unsymmetric band equations
                 and the calculation of eigenvectors of band matrices",
  crossref =     "Wilkinson:1971:LA",
  pages =        "70--92",
  year =         "1971",
  bibdate =      "Tue May 08 14:20:56 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Peters:1971:CSE,
  author =       "G. Peters and J. H. Wilkinson",
  title =        "The calculation of specified eigenvectors by inverse
                 iteration",
  crossref =     "Wilkinson:1971:LA",
  pages =        "418--439",
  year =         "1971",
  bibdate =      "Tue May 08 14:20:56 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Peters:1971:ERC,
  author =       "G. Peters and J. H. Wilkinson",
  title =        "Eigenvectors of real and complex matrices by {$ L R $}
                 and {$ Q R $} triangularizations",
  crossref =     "Wilkinson:1971:LA",
  pages =        "372--395",
  year =         "1971",
  bibdate =      "Tue May 08 14:20:56 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
}

@Article{Peters:1971:PPA,
  author =       "G. Peters and J. H. Wilkinson",
  title =        "Practical Problems Arising in the Solution of
                 Polynomial Equations",
  journal =      j-J-INST-MATH-APPL,
  volume =       "8",
  pages =        "16--35",
  year =         "1971",
  CODEN =        "JMTAA8",
  ISSN =         "0020-2932",
  MRclass =      "65H05",
  MRnumber =     "MR0298931 (45 \#7980)",
  MRreviewer =   "R. F. Albrecht",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  fjournal =     "Journal of the Institute of Mathematics and its
                 Applications",
  journal-URL =  "http://imamat.oxfordjournals.org/content/by/year",
}

@Article{Wilkinson:1971:DNA,
  author =       "J. H. Wilkinson",
  title =        "A Discussion on Numerical Analysis of Partial
                 Differential Equations. {Introductory} Remarks",
  journal =      j-PRSL,
  volume =       "A 323",
  pages =        "153",
  year =         "1971",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@InCollection{Wilkinson:1971:IPI,
  author =       "J. H. Wilkinson",
  title =        "Introduction to {Part II}: The Algebraic Eigenvalue
                 Problem",
  crossref =     "Wilkinson:1971:LA",
  pages =        "191--201",
  year =         "1971",
  bibdate =      "Tue May 08 14:20:56 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Wilkinson:1971:IPL,
  author =       "J. H. Wilkinson",
  title =        "Introduction to {Part I}: Linear Systems, Least
                 Squares and Linear Programming",
  crossref =     "Wilkinson:1971:LA",
  pages =        "1--8",
  year =         "1971",
  bibdate =      "Tue May 08 14:20:56 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
}

@Article{Wilkinson:1971:IR,
  author =       "J. H. Wilkinson",
  title =        "Introductory Remarks",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
  volume =       "323",
  number =       "??",
  pages =        "153--153",
  day =          "8",
  month =        jun,
  year =         "1971",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.1971.0092",
  ISSN =         "0080-4630",
  bibdate =      "Tue Sep 27 18:55:27 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Royal Society of London. Series A,
                 Mathematical and physical sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/content/current",
}

@Article{Wilkinson:1971:MEA,
  author =       "J. H. Wilkinson",
  title =        "Modern Error Analysis",
  journal =      j-SIAM-REVIEW,
  volume =       "13",
  number =       "4",
  pages =        "548--568",
  month =        "????",
  year =         "1971",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1013095",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "65G05",
  MRnumber =     "MR0305578 (46 \#4708)",
  MRreviewer =   "R. P. Brent",
  bibdate =      "Thu Mar 27 09:06:33 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/13/4;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  note =         "The 1970 von Neumann lecture.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "October 1971",
}

@Article{Wilkinson:1971:SCN,
  author =       "J. H. Wilkinson",
  title =        "Some Comments from a Numerical Analyst",
  journal =      j-J-ACM,
  volume =       "18",
  number =       "2",
  pages =        "137--147",
  month =        apr,
  year =         "1971",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/321637.321638",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "65.00",
  MRnumber =     "MR0282494 (43 \#8205)",
  bibdate =      "Sat Dec 10 15:00:46 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Association for Computing Machinery",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  remark =       "This is the 1970 ACM Turing Award Lecture. Subsequent
                 lectures are published in {\em Communications of the
                 ACM}. Wilkinson comments ``It is perhaps salutary to be
                 reminded that as early as 1946 Turing had considered
                 the possibility of working with both interval and
                 significant digit arithmetic and the report recalled
                 forgotten conversations, not to mention heated
                 arguments, which we had on this topic.'' He also says
                 ``I think it is of vital importance that all the work
                 that has been expended on the development of
                 satisfactory algorithms should be made fully available
                 to the people who need to use it. I would go further
                 than this and claim that it is a social duty to see
                 that this is achieved.''",
}

@TechReport{Golub:1972:LAS,
  author =       "G. H. Golub and R. Underwood and J. H. Wilkinson",
  title =        "The {Lanczos} Algorithm for the Symmetric {$ A x =
                 \lambda B x $} Problem",
  type =         "Technical Report",
  number =       "CS-72-270",
  institution =  inst-SU-cs,
  address =      inst-SU:adr,
  year =         "1972",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@InProceedings{Wilkinson:1972:IIT,
  author =       "J. H. Wilkinson",
  booktitle =    "Symposia Matematico {X}",
  title =        "Inverse Iteration in Theory and in Practice",
  publisher =    "Istituto Nazionale di Alta Matematica",
  address =      "Bologna, Italy",
  pages =        "361--379",
  year =         "1972",
  MRclass =      "65F15",
  MRnumber =     "MR0366017 (51 \#2268)",
  MRreviewer =   "G. Maess",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Monograph, Volume 10.",
}

@Article{Wilkinson:1972:NAN,
  author =       "J. H. Wilkinson",
  title =        "Numerical Analysis at the {National Physical
                 Laboratory}",
  journal =      j-BULL-INST-MATH-APPL,
  volume =       "8",
  number =       "9--10",
  pages =        "297--298",
  year =         "1972",
  CODEN =        "IMTABW",
  ISSN =         "0950-5628",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  fjournal =     "Bulletin of the Institute of Mathematics and its
                 Applications",
}

@Article{Wilkinson:1972:NMV,
  author =       "J. H. Wilkinson",
  title =        "Note on matrices with a very ill-conditioned
                 eigenproblem",
  journal =      j-NUM-MATH,
  volume =       "19",
  number =       "2",
  pages =        "176--178",
  month =        apr,
  year =         "1972",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65F15",
  MRnumber =     "MR0311092 (46 \#10188)",
  MRreviewer =   "G. W. Stewart",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
  classification = "C4140 (Linear algebra)",
  corpsource =   "Nat. Phys. Lab., Teddington, UK",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "eigenvalues and eigenfunctions; eigenvectors; ill
                 conditioned eigenproblem; matrices; matrix algebra;
                 multiple eigenvalue; numerical methods",
  treatment =    "T Theoretical or Mathematical",
}

@InCollection{Peters:1974:ACE,
  author =       "G. Peters and J. H. Wilkinson",
  crossref =     "Scaife:1974:SNA",
  title =        "Accuracy of Computed Eigensystems and Invariant
                 Subspaces",
  pages =        "115--135",
  year =         "1974",
  MRclass =      "65F15",
  MRnumber =     "MR0356471 (50 \#8941)",
  MRreviewer =   "L. W. Ehrlich",
  bibdate =      "Tue Aug 15 18:20:34 MDT 1995",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Festschrift in honour of C. Lanczos commissioned by
                 the Royal Irish Academy.",
}

@TechReport{Peters:1974:APD,
  author =       "G. Peters and J. H. Wilkinson",
  title =        "On an Algorithm for Polynomial Deflation by {Broyden
                 and Ford}",
  type =         "Technical Report",
  number =       "NAC 55",
  institution =  inst-NPL,
  address =      inst-NPL:adr,
  year =         "1974",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@Unpublished{Peters:1974:SAS,
  author =       "G. Peters and J. H. Wilkinson",
  title =        "Some Algorithms for the Solution of the Generalized
                 Symmetric Eigenvalue Problem {$ A u = \lambda B u $}",
  year =         "1974",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Unpublished, Circa 1974. National Physical Laboratory,
                 Teddington, Middlesex TW11 0LW, UK.",
}

@Article{Wilkinson:1974:CEA,
  author =       "J. H. Wilkinson",
  title =        "The Classical Error Analysis for the Solution of
                 Linear Systems",
  journal =      j-BULL-INST-MATH-APPL,
  volume =       "10",
  number =       "5--6",
  pages =        "175--180",
  year =         "1974",
  CODEN =        "IMTABW",
  ISSN =         "0950-5628",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  fjournal =     "Bulletin of the Institute of Mathematics and its
                 Applications",
}

@Unpublished{Wilkinson:1974:HPE,
  author =       "J. H. Wilkinson",
  title =        "Handbook p139 Expanded or Expounded",
  year =         "1974",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Unpublished, Circa 1974. National Physical Laboratory,
                 Teddington, Middlesex TW11 0LW, UK.",
}

@InProceedings{Wilkinson:1974:LAA,
  author =       "J. H. Wilkinson",
  title =        "Linear Algebra Algorithms",
  crossref =     "Evans:1974:SNM",
  pages =        "17--25 (discussion 27--28)",
  year =         "1974",
  MRclass =      "65F99",
  MRnumber =     "MR0362880 (50 \#15318)",
  MRreviewer =   "L. W. Ehrlich",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "With discussion by J. D. Beasley, E. L. Albasiny, O.
                 Tingleff, Linda Hayes, M. G. Cox, M. J. D. Powell and
                 J. H. Wilkinson",
}

@Article{Wilkinson:1974:NII,
  author =       "J. H. Wilkinson",
  title =        "Note on Inverse Iteration and Ill-Conditioned
                 Eigensystems",
  journal =      "Acta Univ. Carol. Math. Phys.",
  volume =       "15",
  number =       "1--2",
  pages =        "173--177",
  year =         "1974",
  MRclass =      "65F15",
  MRnumber =     "MR0386244 (52 \#7102)",
  MRreviewer =   "W. C. Rheinboldt",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@Article{Wilkinson:1974:NLA,
  author =       "J. H. Wilkinson",
  title =        "Numerical Linear Algebra on Digital Computers",
  journal =      j-BULL-INST-MATH-APPL,
  volume =       "10",
  number =       "9--10",
  pages =        "354--356",
  year =         "1974",
  CODEN =        "IMTABW",
  ISSN =         "0950-5628",
  MRclass =      "65-03 (01A65)",
  MRnumber =     "MR0655456 (58 \#31698)",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  fjournal =     "Bulletin of the Institute of Mathematics and its
                 Applications",
}

@Unpublished{Wilkinson:1974:SVD,
  author =       "J. H. Wilkinson",
  title =        "The Singular Value Decomposition and minfit",
  year =         "1974",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Unpublished, Circa 1974. National Physical Laboratory,
                 Teddington, Middlesex TW11 0LW, UK.",
}

@Unpublished{Wilkinson:1974:TMA,
  author =       "J. H. Wilkinson",
  title =        "Test Matrices for Algorithms for Solving Linear
                 Systems and Inverting Matrices",
  year =         "1974",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Unpublished, Circa 1974. National Physical Laboratory,
                 Teddington, Middlesex TW11 0LW, UK.",
}

@InCollection{Fox:1975:F,
  author =       "L. Fox and J. H. Wilkinson",
  booktitle =    "The NAG Library Manual",
  title =        "Foreward",
  publisher =    pub-NAG,
  address =      pub-NAG:adr,
  pages =        "1--3",
  year =         "1975",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@TechReport{Golub:1975:ICE,
  author =       "G. H. Golub and J. H. Wilkinson",
  title =        "Ill-Conditioned Eigensystems and the Computation of
                 the {Jordan} Canonical Form",
  type =         "Technical Report",
  number =       "STAN-CS-75-478",
  institution =  inst-SU-cs,
  address =      inst-SU:adr,
  year =         "1975",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Published as \cite{Golub:1976:ICE}.",
}

@Article{Peters:1975:SGJ,
  author =       "G. Peters and J. H. Wilkinson",
  title =        "On the Stability of {Gauss--Jordan} Elimination with
                 Pivoting",
  journal =      j-CACM,
  volume =       "18",
  number =       "1",
  pages =        "20--24",
  month =        jan,
  year =         "1975",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/360569.360653",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65F05 (65G05)",
  MRnumber =     "MR0371038 (51 \#7261)",
  MRreviewer =   "L. B. Rall",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Collection of articles honoring Alston S.
                 Householder",
  fjournal =     "Communications of the Association for Computing
                 Machinery",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@Article{Wilkinson:1975:AHA,
  author =       "J. H. Wilkinson",
  title =        "{Alston S. Householder} award",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "11",
  number =       "1",
  pages =        "1",
  month =        "????",
  year =         "1975",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Tue Feb 16 18:49:00 MST 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/linala1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0024379575901111",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795/",
}

@InProceedings{Wilkinson:1975:IS,
  author =       "J. H. Wilkinson",
  title =        "Invariant Subspaces",
  crossref =     "ICM:1974:PIC",
  pages =        "443--448",
  year =         "1975",
  MRclass =      "65F15",
  MRnumber =     "MR0426394 (54 \#14337)",
  MRreviewer =   "F. Pecka",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@Article{Wilkinson:1975:PAN,
  author =       "J. H. Wilkinson",
  title =        "The {Pilot ACE at the NPL}",
  journal =      j-RADIO-ELECTRON-ENG,
  volume =       "45",
  number =       "7",
  pages =        "336--340",
  month =        jul,
  year =         "1975",
  CODEN =        "RDEEA4",
  ISSN =         "0033-7722",
  bibdate =      "Mon Nov 1 18:34:26 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  fjournal =     "The Radio and Electronic Engineer",
}

@Article{Golub:1976:ICE,
  author =       "G. H. Golub and J. H. Wilkinson",
  title =        "Ill-Conditioned Eigensystems and the Computation of
                 the {Jordan} Canonical Form",
  journal =      j-SIAM-REVIEW,
  volume =       "18",
  number =       "4",
  pages =        "578--619",
  year =         "1976",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1018113",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "65F15 (15A21)",
  MRnumber =     "MR0413456 (54 \#1570)",
  MRreviewer =   "Robert Todd Gregory",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
}

@TechReport{Hammarling:1976:PBL,
  author =       "S. Hammarling and J. H. Wilkinson",
  title =        "The Practical Behaviour of Linear Iterative Methods
                 with Particular Reference to {S.O.R.}",
  type =         "Technical Report",
  number =       "NAC 69",
  institution =  inst-NPL,
  address =      inst-NPL:adr,
  year =         "1976",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@InProceedings{Wilkinson:1976:LDE,
  author =       "J. H. Wilkinson",
  title =        "Linear Differential Equations and {$ A x = \lambda B x
                 $}",
  crossref =     "Hartnell:1976:PFM",
  pages =        "137--158",
  year =         "1976",
  MRclass =      "65F30",
  MRnumber =     "MR0408226 (53 \#11991)",
  MRreviewer =   "J. D. P. Donnelly",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@TechReport{Wilkinson:1977:DSG,
  author =       "J. H. Wilkinson",
  title =        "The Differential System {$ B \dot {x} = A x $} and the
                 Generalized Eigenvalue Problem {$ A u = \lambda B u
                 $}",
  type =         "Technical Report",
  number =       "NAC 73",
  institution =  inst-NPL,
  address =      inst-NPL:adr,
  year =         "1977",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@InProceedings{Wilkinson:1977:SRA,
  author =       "J. H. Wilkinson",
  title =        "Some Recent Advances in Numerical Linear Algebra",
  crossref =     "Jacobs:1976:SAN",
  pages =        "3--23",
  year =         "1977",
  MRclass =      "65F15 (65-02)",
  MRnumber =     "MR0455326 (56 \#13565)",
  MRreviewer =   "Alan L. Andrew",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  xxpages =      "3--53",
}

@Unpublished{Wilkinson:1977:USP,
  author =       "J. H. Wilkinson",
  title =        "The Use of the Single-Precision Residual in the
                 Solution of Linear Systems",
  year =         "1977",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Unpublished, Circa 1977. National Physical Laboratory,
                 Teddington, Middlesex TW11 0LW, UK.",
}

@Article{Wilkinson:1978:AHA,
  author =       "J. H. Wilkinson",
  title =        "The {Alston S. Householder Award}",
  journal =      j-NUM-MATH,
  volume =       "29",
  number =       "4",
  pages =        "463--463",
  month =        apr,
  year =         "1978",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01432882",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "Contributed Item",
  MRnumber =     "MR1553992",
  bibdate =      "Sun Mar 18 11:40:16 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@TechReport{Wilkinson:1978:KCF,
  author =       "J. H. Wilkinson",
  title =        "{Kronecker}'s Canonical Form and the {$ Q Z $}
                 Algorithm",
  type =         "Technical Report",
  number =       "DNACS 10/78",
  institution =  inst-NPL,
  address =      inst-NPL:adr,
  year =         "1978",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Published as \cite{Wilkinson:1979:KCF}.",
}

@InProceedings{Wilkinson:1978:LDE,
  author =       "J. H. Wilkinson",
  title =        "Linear Differential Equations and {Kronecker}'s
                 Canonical Form",
  crossref =     "deBoor:1978:RAN",
  pages =        "231--265",
  year =         "1978",
  MRclass =      "65L05",
  MRnumber =     "MR519065 (80e:65077)",
  MRreviewer =   "Ekkehard Wagenf{\"u}hrer",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@TechReport{Wilkinson:1978:NPS,
  author =       "J. H. Wilkinson",
  title =        "Note on the Practical Significance of the {Drazin}
                 Inverse",
  type =         "Technical Report",
  number =       "DNACS 13/79",
  institution =  inst-NPL,
  address =      inst-NPL:adr,
  year =         "1978",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Also produced as Stanford University, Computer Science
                 Department Report STAN-CS-79-736. Published as
                 \cite{Wilkinson:1982:NPS}.",
}

@InProceedings{Wilkinson:1978:PNL,
  author =       "J. H. Wilkinson",
  title =        "A Problem in Numerical Linear Algebra",
  crossref =     "Powell:1977:CDJ",
  pages =        "76--91",
  year =         "1978",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@InProceedings{Wilkinson:1978:SVD,
  author =       "J. H. Wilkinson",
  title =        "Singular-Value Decomposition -- Basic Aspects",
  crossref =     "Jacobs:1978:NSN",
  pages =        "109--135",
  year =         "1978",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@Article{Cline:1979:ECN,
  author =       "A. K. Cline and C. B. Moler and G. W. Stewart and J.
                 H. Wilkinson",
  title =        "An Estimate for the Condition Number of a Matrix",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "16",
  number =       "2",
  pages =        "368--375",
  month =        apr,
  year =         "1979",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/0716029",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65F35 (65F05)",
  MRnumber =     "80g:65048",
  MRreviewer =   "R. P. Tewarson",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
                 JSTOR database",
  ZMnumber =     "Zbl 0403.65012",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  keywords =     "cond, err, math, nla, condition estimation",
}

@Article{Peters:1979:III,
  author =       "G. Peters and J. H. Wilkinson",
  title =        "Inverse Iteration, Ill-Conditioned Equations and
                 {Newton}'s Method",
  journal =      j-SIAM-REVIEW,
  volume =       "21",
  number =       "3",
  pages =        "339--360",
  year =         "1979",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1021052",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "65F10 (65F15)",
  MRnumber =     "MR535118 (80f:65040)",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  fjournal =     "SIAM Review. A Publication of the Society for
                 Industrial and Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/sirev",
}

@Article{Wilkinson:1979:KCF,
  author =       "J. H. Wilkinson",
  title =        "{Kronecker}'s Canonical Form and the {$ Q Z $}
                 Algorithm",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "28",
  pages =        "285--303",
  year =         "1979",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/0024-3795(79)90140-X",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A21 (65F15)",
  MRnumber =     "MR549441 (81a:15015)",
  MRreviewer =   "I. Enescu",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Dedicated to the 75th birthday of A. S. Householder.",
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@TechReport{Hammarling:1980:LSA,
  author =       "S. Hammarling and J. H. Wilkinson",
  title =        "On Linear Systems Arising from Finite Difference
                 Approximations to Elliptic Differential Equations",
  type =         "Technical Report",
  number =       "DNACS 34/80",
  institution =  inst-NPL,
  address =      inst-NPL:adr,
  year =         "1980",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@TechReport{Symm:1980:REBa,
  author =       "H. J. Symm and J. H. Wilkinson",
  title =        "Realistic Error Bounds for a Simple Eigenvalue and its
                 Associated Eigenvector",
  type =         "Technical Report",
  number =       "STAN-CS-80-787",
  institution =  inst-SU-cs,
  address =      inst-SU:adr,
  year =         "1980",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Published as \cite{Symm:1980:REBb}.",
}

@Article{Symm:1980:REBb,
  author =       "H. J. Symm and J. H. Wilkinson",
  title =        "Realistic error bounds for a simple eigenvalue and its
                 associated eigenvector",
  journal =      j-NUM-MATH,
  volume =       "35",
  number =       "2",
  pages =        "113--126",
  month =        jun,
  year =         "1980",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01396310",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65F15",
  MRnumber =     "83b:65037",
  MRreviewer =   "Alan L. Andrew",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 Theory/Matrix.bib",
  acknowledgement = ack-nhfb,
  annote =       "Cited in \cite{govl:89}.",
  classification = "C1100 (Mathematical techniques); C4110 (Error
                 analysis in numerical methods)",
  corpsource =   "Div. of Numerical Analysis and Computer Sci., Nat.
                 Phys. Lab., Teddington, UK",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "eig; eigenvalue; eigenvalues and eigenfunctions;
                 eigenvector; error analysis; error bounds; error
                 estimates; la; pert",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Wilkinson:1980:SRA,
  author =       "J. H. Wilkinson",
  title =        "Some recent advances in numerical linear algebra",
  journal =      "Yingyong Shuxue yu Jisuan Shuxue",
  volume =       "6",
  pages =        "1--19",
  year =         "1980",
  MRclass =      "65-02 (65F15)",
  MRnumber =     "MR653134 (83d:65006)",
  bibdate =      "Fri May 14 18:02:56 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Translated from the English by Ji Guang Sun.",
  acknowledgement = ack-nhfb,
  fjournal =     "Yingyong Shuxue yu Jisuan Shuxue. Applied Mathematics
                 and Computational Mathematics",
}

@InProceedings{Wilkinson:1980:TWN,
  author =       "J. H. Wilkinson",
  title =        "{Turing}'s Work at the {National Physical Laboratory}
                 and the Construction of {Pilot ACE}, {DEUCE}, and
                 {ACE}",
  crossref =     "Metropolis:1980:HCT",
  pages =        "101--114",
  year =         "1980",
  bibdate =      "Sat Mar 31 18:08:36 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Dongarra:1981:IAC,
  author =       "J. J. Dongarra and C. B. Moler and J. H. Wilkinson",
  title =        "Improving the Accuracy of Computed Eigenvalues and
                 Eigenvectors",
  type =         "Technical Report",
  number =       "ANL-81-43",
  institution =  inst-ANL-am,
  address =      inst-ANL:adr,
  year =         "1981",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Published as \cite{Dongarra:1983:IAC}.",
}

@InProceedings{Symm:1981:ADM,
  author =       "Hilary J. Symm and J. H. Wilkinson",
  title =        "Almost Defective Matrices",
  crossref =     "Meek:1981:PTM",
  pages =        "89--131",
  year =         "1981",
  MRclass =      "15A12 (65F15)",
  MRnumber =     "MR635937 (82m:15009)",
  MRreviewer =   "Alan L. Andrew",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@TechReport{Symm:1981:EBC,
  author =       "H. J. Symm and J. H. Wilkinson",
  title =        "Error Bounds for Computed Invariant Subspaces",
  type =         "Research Report",
  number =       "81-02",
  institution =  inst-ETH-AM,
  address =      inst-ETH:adr,
  year =         "1981",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Lecture presented at a Symposium in honour of H.
                 Rutishauser, October 15--17, 1980.",
}

@TechReport{Dongarra:1982:EPH,
  author =       "J. J. Dongarra and J. R. Gabriel and J. H. Wilkinson",
  title =        "The Eigenvalue Problem for {Hermitian} Matrices with
                 Time Reversal Symmetry",
  type =         "Technical Memorandum",
  number =       "3",
  institution =  inst-ANL-mcs,
  address =      inst-ANL:adr,
  year =         "1982",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Published as \cite{Dongarra:1984:EPH} where D. D.
                 Koelling is also an author.",
}

@Article{Olver:1982:PEB,
  author =       "F. W. J. Olver and J. H. Wilkinson",
  title =        "A Posteriori Error Bounds for {Gaussian} Elimination",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "2",
  number =       "4",
  pages =        "377--406",
  year =         "1982",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/2.4.377",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65F05 (65G05)",
  MRnumber =     "MR692286 (84m:65044)",
  MRreviewer =   "E. R. Hansen",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  fjournal =     "IMA (Institute of Mathematics and its Applications).
                 Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
}

@InCollection{Wilkinson:1982:NPS,
  author =       "J. H. Wilkinson",
  editor =       "S. L. Campbell",
  booktitle =    "Recent Applications of Generalized Inverses",
  title =        "Note on the Practical Significance of the {Drazin}
                 Inverse",
  chapter =      "3",
  volume =       "66",
  publisher =    pub-PITMAN,
  address =      pub-PITMAN:adr,
  pages =        "82--99",
  year =         "1982",
  MRclass =      "65F30 (15-04 15A09 47A50 65L05)",
  MRnumber =     "MR666724 (84c:65071)",
  MRreviewer =   "M. Z. Nashed",
  bibdate =      "Tue Aug 15 18:20:34 MDT 1995",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  series =       "Res. Notes in Math.",
}

@Article{Dongarra:1983:IAC,
  author =       "J. J. Dongarra and C. B. Moler and J. H. Wilkinson",
  title =        "Improving the Accuracy of Computed Eigenvalues and
                 Eigenvectors",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "20",
  number =       "1",
  pages =        "23--45",
  month =        feb,
  year =         "1983",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/0720002",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65F15",
  MRnumber =     "MR687365 (84c:65063)",
  MRreviewer =   "M. Lotkin",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  classcodes =   "B0290B (Error analysis in numerical methods); B0290H
                 (Linear algebra); C4110 (Error analysis in numerical
                 methods); C4140 (Linear algebra)",
  corpsource =   "Argonne Nat. Lab., Argonne, IL, USA",
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  keywords =     "accuracy; computed eigenvalues; computed eigenvectors;
                 convergence of numerical methods; eigenfunctions;
                 eigenvalues and; EISPACK; error analysis; extended;
                 matrix algebra; matrix eigenvalues; matrix
                 eigenvectors; Newton's method; nla, eig, iterative
                 refinement; numerical; numerical accuracy; numerically
                 stable implementation; precision arithmetic; residuals;
                 standard; subroutines",
  reviewer =     "M. Lotkin",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Dongarra:1984:EPH,
  author =       "J. J. Dongarra and J. R. Gabriel and D. D. Koelling
                 and J. H. Wilkinson",
  title =        "The Eigenvalue Problem for {Hermitian} Matrices with
                 Time-Reversal Symmetry",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "60",
  pages =        "27--42",
  year =         "1984",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/0024-3795(84)90068-5",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "65F15 (81G55)",
  MRnumber =     "MR749173 (85j:65013)",
  MRreviewer =   "Cs. J. Heged{\H{u}}s",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Dongarra:1984:SSE,
  author =       "J. J. Dongarra and J. R. Gabriel and D. D. Koelling
                 and J. H. Wilkinson",
  title =        "Solving the Secular Equation Including Spin Orbit
                 Coupling for Systems with Inversion and Time-Reversal
                 Symmetry",
  journal =      j-J-COMPUT-PHYS,
  volume =       "54",
  number =       "2",
  pages =        "278--288",
  month =        may,
  year =         "1984",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(84)90119-0",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:19 MST 2012",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.netlib.org/utk/people/JackDongarra/PAPERS/Inversion-and-Time-Reversal-Symmetry.pdf;
                 http://www.sciencedirect.com/science/article/pii/0021999184901190",
  acknowledgement = ack-nhfb,
  classcodes =   "A0230 (Function theory, analysis); A0250 (Probability
                 theory, stochastic processes, and statistics); A0365C
                 (Formalism in quantum theory)",
  corpsource =   "Math. and Computer Sci. Div., Argonne Nat. Lab.,
                 Argonne, IL, USA",
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991",
  keywords =     "computational method; eigenvalues; eigenvalues and
                 eigenfunctions; eigenvectors; inversion symmetry;
                 numerical methods; quantum; quantum mechanics; secular
                 equation; spin orbit coupling; spin-orbit interactions;
                 symmetry; T invariance; theory; time reversal",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Wilkinson:1984:NMQ,
  author =       "J. H. Wilkinson",
  title =        "On neighbouring matrices with quadratic elementary
                 divisors",
  journal =      j-NUM-MATH,
  volume =       "44",
  number =       "1",
  pages =        "1--21",
  month =        jun,
  year =         "1984",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01389751",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65F99",
  MRnumber =     "85h:65096",
  MRreviewer =   "Colette Lebaud",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "In honour of the 60th birthday of F. L. Bauer.",
  acknowledgement = ack-nhfb,
  classification = "B0210 (Algebra); C1110 (Algebra)",
  corpsource =   "Computer Sci. Dept., Stanford Univ., Stanford, CA,
                 USA",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "matrix algebra; neighbouring matrices; quadratic
                 elementary divisors",
  treatment =    "T Theoretical or Mathematical",
}

@InCollection{Wilkinson:1984:PP,
  author =       "James H. Wilkinson",
  editor =       "G. H. Golub",
  booktitle =    "Studies in Numerical Analysis",
  title =        "The Perfidious Polynomial",
  chapter =      "1",
  volume =       "24",
  publisher =    pub-MATH-ASSOC-AMER,
  address =      pub-MATH-ASSOC-AMER:adr,
  pages =        "1--28",
  year =         "1984",
  MRclass =      "65H05 (65D15)",
  MRnumber =     "MR925210",
  bibdate =      "Fri May 14 17:12:31 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Awarded the Chauvenet Prize of the Mathematical
                 Association of America.",
  series =       "MAA Stud. Math.",
}

@TechReport{Wilkinson:1984:SAE,
  author =       "J. H. Wilkinson",
  title =        "The State of the Art in Error Analysis",
  type =         "Technical Memorandum",
  number =       "42",
  institution =  inst-ANL-mcs,
  address =      inst-ANL:adr,
  year =         "1984",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Informal Proceedings of the Symposium on Computational
                 Mathematics -- State of the Art held at Argonne
                 National Laboratory, September 20--21, 1984 in honour
                 of the 65th birthday of James H. Wilkinson.",
}

@Article{Wilkinson:1984:SE,
  author =       "J. H. Wilkinson",
  title =        "Sensitivity of Eigenvalues",
  journal =      j-UM,
  volume =       "25",
  pages =        "5--76",
  year =         "1984",
  CODEN =        "UTMADA",
  ISSN =         "0315-3681",
  MRclass =      "65F15 (15A18)",
  MRnumber =     "MR752846 (85i:65051)",
  MRreviewer =   "Ludwig Elsner",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  fjournal =     "Utilitas Mathematica. An International Journal of
                 Discrete and Combinatorial Mathematics, and Statistical
                 Design",
}

@Article{Nash:1985:BC,
  author =       "J. C. Nash and J. H. Wilkinson",
  title =        "The Birth of a Computer",
  journal =      j-BYTE,
  volume =       "10",
  number =       "2",
  pages =        "177--??",
  month =        "????",
  year =         "1985",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Tue Jun 4 11:27:38 MDT 2013",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "BYTE Magazine",
}

@Article{Wilkinson:1985:SAE,
  author =       "J. H. Wilkinson",
  title =        "The State of the Art in Error Analysis",
  journal =      j-NAG,
  volume =       "2/85",
  pages =        "5--28",
  year =         "1985",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Invited lecture for the NAG 1984 Annual General
                 Meeting.",
}

@Article{Wilkinson:1986:EAR,
  author =       "J. H. Wilkinson",
  title =        "Error Analysis Revisited",
  journal =      j-BULL-INST-MATH-APPL,
  volume =       "22",
  number =       "11--12",
  pages =        "192--200",
  year =         "1986",
  CODEN =        "IMTABW",
  ISSN =         "0950-5628",
  MRclass =      "65G05",
  MRnumber =     "MR900724",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Invited lecture at Lancaster University in honour of
                 C. W. Clenshaw, 1985.",
  fjournal =     "Bulletin of the Institute of Mathematics and its
                 Applications",
}

@Article{Wilkinson:1986:ICN,
  author =       "J. H. Wilkinson",
  title =        "Ill-Condition in Numerical Linear Algebra",
  journal =      j-CONG-NUM,
  volume =       "51",
  pages =        "59--81",
  year =         "1986",
  ISSN =         "0384-9864",
  MRclass =      "65F35 (65F15)",
  MRnumber =     "MR883981 (88e:65048)",
  MRreviewer =   "David R. Kincaid",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Proceedings of the fifteenth Manitoba conference on
                 numerical mathematics and computing (Winnipeg,
                 Manitoba, 1985).",
  fjournal =     "Congressus Numerantium. A Conference Journal on
                 Numerical Themes",
}

@Article{Wilkinson:1986:SEI,
  author =       "J. H. Wilkinson",
  title =        "Sensitivity of Eigenvalues {II}",
  journal =      j-UM,
  volume =       "30",
  pages =        "243--286",
  year =         "1986",
  CODEN =        "UTMADA",
  ISSN =         "0315-3681",
  MRclass =      "65F15 (15A18 47A55)",
  MRnumber =     "MR864826 (88f:65066)",
  MRreviewer =   "William W. Hager",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  fjournal =     "Utilitas Mathematica. An International Journal of
                 Discrete and Combinatorial Mathematics, and Statistical
                 Design",
}

@InProceedings{Wilkinson:1987:EP,
  author =       "J. H. Wilkinson",
  title =        "Eigenvalue Problems",
  crossref =     "Iserles:1987:SAN",
  pages =        "1--39",
  year =         "1987",
  MRclass =      "65F15 (15A21 15A22 65-02)",
  MRnumber =     "MR921660 (89d:65042)",
  MRreviewer =   "Alan L. Andrew",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Proceedings of the IMA/SIAM Conference, University of
                 Birmingham, 1986.",
}

@InCollection{Wilkinson:1987:SCN,
  author =       "J. H. Wilkinson",
  title =        "Some comments from a numerical analyst",
  crossref =     "Ashenhurst:1987:ATA",
  pages =        "??--??",
  year =         "1987",
  DOI =          "https://doi.org/10.1145/1283920.1283925",
  bibdate =      "Tue Jun 21 11:01:04 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/acm-turing-awards.bib",
  acknowledgement = ack-nhfb,
}

@Article{Wilkinson:1987:TF,
  author =       "J. H. Wilkinson",
  title =        "On a Theorem of {Feingold}",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "88/89",
  pages =        "13--30",
  year =         "1987",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/0024-3795(87)90100-5",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A42 (15A60)",
  MRnumber =     "MR882438 (88d:15022)",
  MRreviewer =   "Lajos L{\'a}szl{\'o}",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Issue in honour of the 65th birthday of J. H.
                 Wilkinson.",
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Book{Wilkinson:1988:AEP,
  author =       "J. H. Wilkinson",
  title =        "The Algebraic Eigenvalue Problem",
  publisher =    "The Clarendon Press, Oxford University Press",
  address =      "New York",
  pages =        "xviii + 662",
  year =         "1988",
  ISBN =         "0-19-853418-3",
  ISBN-13 =      "978-0-19-853418-1",
  MRclass =      "65Fxx (15-02 65-02)",
  MRnumber =     "MR950175 (89j:65031)",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Oxford Science Publications",
  series =       "Monographs on Numerical Analysis",
}

@Book{Williams:1989:EBC,
  editor =       "M. R. Williams and Martin Campbell-Kelly",
  title =        "The Early {British} Computer Conferences",
  volume =       "14",
  publisher =    pub-MIT,
  address =      pub-MIT:adr,
  pages =        "xvi + 508",
  year =         "1989",
  ISBN =         "0-262-23136-0",
  ISBN-13 =      "978-0-262-23136-7",
  LCCN =         "QA76.17 .E171 1989",
  bibdate =      "Wed Sep 06 11:19:04 1995",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  series =       "{Charles Babbage Institute} Reprint Series for the
                 History of Computing",
}

@TechReport{Dongarra:1990:NCC,
  author =       "J. J. Dongarra and S. Hammarling and J. H. Wilkinson",
  title =        "Numerical Considerations in Computing Invariant
                 Subspaces. {LAPACK Working Note No.~25}",
  type =         "Technical Report",
  number =       "CS-90-117",
  institution =  inst-UTK-cs,
  address =      inst-UTK:adr,
  year =         "1990",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Also produced as Oak Ridge National Laboratory Report,
                 ORNL/TM-11704. Published as \cite{Dongarra:1992:NCC}.",
}

@Article{Dongarra:1992:NCC,
  author =       "Jack J. Dongarra and Sven Hammarling and James H.
                 Wilkinson",
  title =        "Numerical considerations in computing invariant
                 subspaces",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "13",
  number =       "1",
  pages =        "145--161",
  year =         "1992",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/0613013",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F15",
  MRnumber =     "MR1146658 (93a:65049)",
  MRreviewer =   "Colette Lebaud",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@InCollection{Turing:2005:TWL,
  author =       "Alan M. Turing and James H. Wilkinson",
  title =        "The {Turing--Wilkinson} lecture series (1946--1947)",
  crossref =     "Copeland:2005:ATA",
  pages =        "??--??",
  year =         "2005",
  DOI =          "https://doi.org/10.1093/acprof:oso/9780198565932.003.0023",
  bibdate =      "Mon Nov 01 18:18:06 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Edited with an introduction by B. Jack Copeland.",
  abstract =     "This chapter presents the nine lectures given by
                 Turing and his assistant Jim Wilkinson from December
                 1946 to February 1947. The lectures add substantially
                 to the understanding of the evolution of the design of
                 the ACE. Turing and Wilkinson describe Versions V, VI,
                 and VII of the design.",
  acknowledgement = ack-nhfb,
}

@InCollection{Wilkinson:2005:PAN,
  author =       "James H. Wilkinson",
  title =        "The {Pilot ACE} at the {National Physical
                 Laboratory}",
  crossref =     "Copeland:2005:ATA",
  pages =        "93--105",
  year =         "2005",
  DOI =          "https://doi.org/10.1093/acprof:oso/9780198565932.003.0005",
  bibdate =      "Mon Nov 01 18:18:06 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  URL =          "http://www.ingentaconnect.com/content/oso/2353639/2005/00000001/00000001/art00006",
  abstract =     "This chapter discusses the pilot Automatic Computing
                 Engine (ACE) project at the National Physical
                 Laboratory. The Pilot ACE had been designed purely as
                 an experimental machine to demonstrate the competence
                 of the team as computer engineers. It was originally
                 intended that when it was successfully completed a
                 full-scale computer would be built. However, when it
                 was successful, it was the only electronic computer in
                 a government department and the engineers came under
                 very heavy pressure to use the Pilot ACE for serious
                 computing. They implemented a small set of
                 modifications which included the addition of an
                 automatic multiplier and improvements to the control
                 unit which made programming a little less arduous. The
                 computer was then put into general use and did yeoman
                 service for a number of years.",
  acknowledgement = ack-nhfb,
  remark =       "Reprint of article in {\em The Radio and Electronic
                 Engineer, Vol. 45, No. 7, pp. 336--340, July 1975}.
                 From the article:\par

                 ``A great deal of quite detailed coding was done by the
                 ACE team in the period from 1946--1948. It included
                 basic subroutines for such things as multi-length
                 arithmetic (including multiplication, division and
                 square roots), floating-point arithmetic (both
                 single-precision and double-precision) and interval
                 arithmetic. The subroutines for floating-point
                 arithmetic were particularly detailed; they were coded
                 by G. G. Alway and myself in 1947 and were for both
                 Version V and Version VII. They were almost certainly
                 the earliest floating-point subroutines and it is
                 interesting that those for the Version V were
                 essentially the same as the subroutines which were
                 subsequently used on the Pilot ACE itself. At a time
                 when the arithmetic provided on modern computers is
                 often so disappointing it is interesting to recall that
                 the subroutines included provision for accumulating
                 inner-products in double-precision floating-point
                 arithmetic and all rounding was
                 immaculate.''\par

                 ``Even double precision and triple precision
                 floating-point routines were reasonably fast and we
                 gained extensive experience with such computation long
                 before it was much used elsewhere. I think it is not
                 unreasonable to claim that the development of
                 floating-point error analysis at NPL, which was well in
                 advance of that elsewhere, was an indirect consequence
                 of our use of optimum coding.''",
}

%%% ====================================================================
%%% Part 2 (of 2) --- publications about James H. Wilkinson and his
%%% works
%%%
%%% Bibliography entries, sorted by year, and then by citation label,
%%% with `bibsort -byyear':
@Article{Grau:1966:BRB,
  author =       "A. A. Grau",
  title =        "Book Review: {{\booktitle{Rounding Errors in Algebraic
                 Processes}} (J. H. Wilkinson)}",
  journal =      j-SIAM-REVIEW,
  volume =       "8",
  number =       "3",
  pages =        "397--398",
  month =        "????",
  year =         "1966",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1008087",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:05:37 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/8/3;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "July 1966",
}

@Article{Parlett:1966:BRB,
  author =       "B. N. Parlett",
  title =        "Book Review: {{\booktitle{The Algebraic Eigenvalue
                 Problem}} (J. H. Wilkinson)}",
  journal =      j-SIAM-REVIEW,
  volume =       "8",
  number =       "4",
  pages =        "543--545",
  month =        "????",
  year =         "1966",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1008125",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:05:39 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/8/4;
                 http://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "October 1966",
}

@Article{Wilkes:1966:BRB,
  author =       "M. V. Wilkes",
  title =        "Book Review: {{\booktitle{The Algebraic Eigenvalue
                 Problem}}}",
  journal =      j-COMP-J,
  volume =       "8",
  number =       "4",
  pages =        "382--382",
  month =        jan,
  year =         "1966",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/8.4.382",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:34 MST 2012",
  bibsource =    "http://comjnl.oxfordjournals.org/content/8/4.toc;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/compj1960.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/8/4/382.full.pdf+html",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Partlett:1972:BRB,
  author =       "B. Partlett",
  title =        "Book Review: {{\booktitle{Handbook for Automatic
                 Computation, Vol. II, Linear Algebra}} (J. H. Wilkinson
                 and C. Reinsch)}",
  journal =      j-SIAM-REVIEW,
  volume =       "14",
  number =       "4",
  pages =        "658--661",
  month =        "????",
  year =         "1972",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1014116",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:06:44 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/14/4;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "October 1972",
}

@Article{Fox:1987:JHW,
  author =       "L. Fox",
  title =        "{James Hardy Wilkinson: 27 September 1919--5 October
                 1986}",
  journal =      j-BIOGRAPH-MEMOIRS-FELLOWS-ROY-SOC,
  volume =       "33",
  pages =        "671--708",
  month =        dec,
  year =         "1987",
  CODEN =        "BMFRA3",
  ISSN =         "0080-4606 (print), 1748-8494 (electronic)",
  ISSN-L =       "0080-4606",
  bibdate =      "Thu Jun 9 12:00:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  URL =          "http://www.jstor.org/stable/769967",
  acknowledgement = ack-nhfb,
  fjournal =     "Biographical Memoirs of Fellows of the Royal Society",
  journal-URL =  "http://www.jstor.org/journals/00804606.html",
}

@Article{Fox:1987:ODJ,
  author =       "Leslie Fox",
  title =        "Obituary: {Dr. J. H. Wilkinson, F.R.S.}",
  journal =      j-COMP-J,
  volume =       "30",
  number =       "1",
  pages =        "1--1",
  year =         "1987",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/30.1.1",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  MRclass =      "01A70",
  MRnumber =     "88e:01054",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_30/Issue_01/",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_30/Issue_01/tiff/1.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@TechReport{Parlett:1987:CJH,
  author =       "Beresford N. Parlett",
  title =        "A contribution of {J. H. Wilkinson} to numerical
                 analysis",
  type =         "Technical Report",
  number =       "PAM-372",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        apr,
  year =         "1987",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
  xxnote =       "Check author list??",
}

@Article{Barrio:2002:REB,
  author =       "Roberto Barrio",
  title =        "Rounding error bounds for the {Clenshaw} and
                 {Forsythe} algorithms for the evaluation of orthogonal
                 polynomial series",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "138",
  number =       "2",
  pages =        "185--204",
  day =          "15",
  month =        jan,
  year =         "2002",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:45:23 MST 2017",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037704270100382X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Barrio:2003:URE,
  author =       "R. Barrio",
  title =        "A unified rounding error bound for polynomial
                 evaluation",
  journal =      j-ADV-COMPUT-MATH,
  volume =       "19",
  number =       "4",
  pages =        "385--399",
  month =        nov,
  year =         "2003",
  CODEN =        "ACMHEX",
  DOI =          "https://doi.org/10.1023/A:1024203520270",
  ISSN =         "1019-7168 (print), 1572-9044 (electronic)",
  ISSN-L =       "1019-7168",
  MRclass =      "65G50",
  MRnumber =     "1989623",
  bibdate =      "Sat Feb 3 18:22:17 MST 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/advcomputmath.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer.com/article/10.1023/A:1024203520270",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances in Computational Mathematics",
  journal-URL =  "http://link.springer.com/journal/10444",
  keywords =     "Bernstein polynomial; Clenshaw--Forsythe algorithm;
                 de-Casteljau algorithm; Horner's algorithm; polynomial
                 evaluation; recurrence relations; rounding errors;
                 Szeg{\H{o}} polynomial",
}

@Article{Watkins:2011:FA,
  author =       "David S. Watkins",
  title =        "{Francis}'s Algorithm",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "118",
  number =       "5",
  pages =        "387--403",
  month =        may,
  year =         "2011",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.4169/amer.math.monthly.118.05.387",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Thu May 26 16:28:05 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  URL =          "http://www.jstor.org/stable/info/10.4169/amer.math.monthly.118.05.387",
  abstract =     "John Francis's implicitly shifted QR algorithm turned
                 the problem of matrix eigenvalue computation from
                 difficult to routine almost overnight about fifty years
                 ago. It was named one of the top ten algorithms of the
                 twentieth century by Dongarra and Sullivan, and it
                 deserves to be more widely known and understood by the
                 general mathematical community. This article provides
                 an efficient introduction to Francis's algorithm that
                 follows a novel path. Efficiency is gained by omitting
                 the traditional but wholly unnecessary detour through
                 the basic QR algorithm. A brief history of the
                 algorithm is also included. It was not a one-man show;
                 some other important names are Rutishauser, Wilkinson,
                 and Kublanovskaya. Francis was never a specialist in
                 matrix computations. He was employed in the early
                 computer industry, spent some time on the problem of
                 eigenvalue computation and did amazing work, and then
                 moved on to other things. He never looked back, and he
                 remained unaware of the huge impact of his work until
                 many years later.",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/page/journal/amermathmont/about.html",
}

@Article{Campbell-Kelly:2012:ATO,
  author =       "Martin Campbell-Kelly",
  title =        "{Alan Turing}'s other universal machine",
  journal =      j-CACM,
  volume =       "55",
  number =       "7",
  pages =        "31--33",
  month =        jul,
  year =         "2012",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/2209249.2209277",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Tue Jul 3 13:54:33 MDT 2012",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 http://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/cacm2010.bib",
  abstract =     "Reflections on the Turing ACE computer and its
                 influence.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  keywords =     "ACE; Alan Turing; Bendix G-15; DEUCE; Donald Davis;
                 EDSAC; EDVAC; English Electric Company; Harry Huskey;
                 James Hardy Wilkinson; Manchester Mark I; Maurice
                 Wilkes; Pilot ACE",
}

%%% ====================================================================
%%% Cross-referenced entries must come last:
@Proceedings{Metropolis:1963:PFS,
  editor =       "N. Metropolis and A. H. Taub and John Todd and C. B.
                 Tompkins",
  booktitle =    "{Experimental arithmetic, high speed computing and
                 mathematics: Proceedings of the fifteenth Symposium in
                 Applied Mathematics of the American Mathematical
                 Society held in Chicago, Illinois, April 12--14, 1962
                 and Atlantic City, New Jersey, April 16-19, 1962}",
  title =        "{Experimental arithmetic, high speed computing and
                 mathematics: Proceedings of the fifteenth Symposium in
                 Applied Mathematics of the American Mathematical
                 Society held in Chicago, Illinois, April 12--14, 1962
                 and Atlantic City, New Jersey, April 16-19, 1962}",
  volume =       "15",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "ix + 396",
  year =         "1963",
  LCCN =         "QA297 .S987 1962",
  bibdate =      "Tue Mar 20 10:37:16 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "1. Purposeful and unpurposeful computing / Cohn \\
                 2. Eliminating the irrelevant from mechanical proofs /
                 Davis \\
                 3. The mechanization of mathematical arguments / Wang
                 \\
                 4. Towards more versatile mechanical translators /
                 Irons \\
                 5. Information theory and decoding computations / Elias
                 \\
                 6. Adaptive neural networks as brain models / Block \\
                 7. Computer investigation of orthogonal Latin squares
                 of order ten / Parker \\
                 8. Determination of division algebra with 32 elements /
                 Walker \\
                 9. How programming difficulties lead to theoretical
                 advances / Dade and Zassenhaus \\
                 10. Methods of successive restrictions in computational
                 problems involving discrete variables / Tompkins \\
                 11. An experimental study of the simplex method / Kuhn
                 and Quandt \\
                 12. Large and nonconvex problems in linear programming
                 / GoMory \\
                 13. Some high speed logic / Lehmer \\
                 14. Stability questions for some numerical methods for
                 ordinary differential equations / Dahlquist \\
                 15. Some applications of the quotient--difference
                 algorithm / Henrici \\
                 16. Plane-rotations in floating-point arithmetic /
                 Wilkinson \\
                 17. New aspects in numerical quadrature / Bauer,
                 kutishauser, and Stiefel \\
                 18. On Jacobi rotation patterns / Rutishauser \\
                 19. Automatic numerical integration of ordinary
                 differential equations / Nordsieck \\
                 20. Survey of stability of different schemes for
                 solving initial value problems for hyperbolic equations
                 / Lax \\
                 21. Unexpected dividends in the theory of prime numbers
                 / Rosser \\
                 22. The particle-in-cell method for numerical solution
                 of problems in fluid dynamics / Harlow \\
                 23. Numerical experiments in atmospheric hydrodynamics
                 / Charney \\
                 24. The oscillations of the earth and of the atmosphere
                 / MacDonald \\
                 25. Few particle experiments in statistical mechanics /
                 Alder \\
                 26. An approach to the Ising problem using a large
                 scale fast digital computer / Yang \\
                 27. Applied mathematics as used in theoretical
                 chemistry / Hirschfelder \\
                 28. The mechanization of science / Hamming",
}

@Book{Wilkinson:1963:REA,
  author =       "J. H. Wilkinson",
  booktitle =    "Rounding Errors in Algebraic Processes",
  title =        "Rounding Errors in Algebraic Processes",
  volume =       "32",
  publisher =    pub-HMSO,
  address =      pub-HMSO:adr,
  pages =        "vi + 161",
  year =         "1963",
  ISBN =         "0-486-67999-3 (Dover)",
  ISBN-13 =      "978-0-486-67999-0 (Dover)",
  LCCN =         "QA76.5 .W53 1964",
  MRclass =      "65.80",
  MRnumber =     "MR0161456 (28 \#4661)",
  MRreviewer =   "A. S. Householder",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Also published by Prentice-Hall, Englewood Cliffs, NJ,
                 USA, 1964, translated into Polish as {\em Bledy
                 Zaokragle{\'n} w Procesach Algebraicznych\/} by PWW,
                 Warsaw, Poland, 1967 and translated into German as {\em
                 Rundungsfehler\/} by Springer-Verlag, Berlin, Germany,
                 1969. Reprinted by Dover Publications, New York,
                 1994.",
  series =       "Notes on Applied Science",
  tableofcontents = "1. The Fundamental Arithmetic Operations \\
                 Digital computation / 1 \\
                 Fixed-point and floating-point computation / 1 \\
                 Notational conventions / 2 \\
                 Rounding errors in fixed-point computation / 4 \\
                 Fixed-point accumulation of inner-products / 6 \\
                 Rounding errors in floating-point computation / 7 \\
                 Round-off with single-precision accumulator / 11 \\
                 Comparison of fixed-point and floating-point
                 computation / 14 \\
                 Common floating-point operations / 16 \\
                 More precise bounds / 19 \\
                 Floating-point accumulation of sums and inner-products
                 / 23 \\
                 Statistical error bounds / 25 \\
                 Block-floating vectors and matrices / 26 \\
                 Fundamental limitations oft-digit computation / 27 \\
                 Ill-conditioned problems / 28 \\
                 Condition numbers / 29 \\
                 Rounding errors in the computation / 30 \\
                 Additional comments / 33 \\
                 2. Computations Involving Polynomials \\
                 Evaluation of power series / 34 \\
                 Fixed-point representation / 34 \\
                 Floating-point representation / 36 \\
                 Calculation of zeros of functions defined by power
                 series / 37 \\
                 Polynomials with arbitrary coefficients / 38 \\
                 Condition of a polynomial with respect to the
                 computation of its zeros / 38 \\
                 Some typical distributions of zeros / 41 \\
                 Linear distributions of zeros / 41 \\
                 Geometric distribution / 44 \\
                 Chebyshev polynomial / 46 \\
                 Significance of the condition of the zeros of
                 polynomials 4 / 7 \\
                 Determination of the zeros / 49 \\
                 Iterative methods / 52 \\
                 Effect of rounding errors on Newton's process / 53 \\
                 Simple examples / 54 \\
                 Polynomial deflation / 55 \\
                 Analysis of errors inherent in deflation / 56 \\
                 Examples of deflation / 59 \\
                 Deflation of ill-conditioned polynomials / 62 \\
                 General comments on iteration and deflation / 64 \\
                 Purification in the original polynomial / 65 \\
                 Other iterative methods / 66 \\
                 The root-squaring process / 67 \\
                 Forward error analysis of root-squaring / 69 \\
                 Relative error in computed coefficients / 71 \\
                 Numerical example / 72 \\
                 Deterioration of condition / 74 \\
                 General comments on the computation of zeros of
                 polynomials / 76 \\
                 Additional comments / 78 \\
                 3. Matrix Computations \\
                 Introduction / 79 \\
                 Vector and matrix norms / 80 \\
                 Error analysis of simple matrix operations / 82 \\
                 Matrix multiplication / 83 \\
                 Matrix operations in block-floating arithmetic / 85 \\
                 Matrices which are not infinity row standardized / 85
                 \\
                 Orthogonalization of vectors / 86 \\
                 Numerical example / 87 \\
                 General case / 89 \\
                 Solution of equations and matrix inversion / 91 \\
                 Rounding of matrix of coefficients / 93 \\
                 Error analysis of Gaussian elimination / 94 \\
                 Computational equations / 95 \\
                 Floating-point bounds / 96 \\
                 Gaussian elimination in fixed-point / 99 \\
                 Determinant evaluation / 99 \\
                 Solution of a triangular set of equations using
                 standard floating-point arithmetic / 99 \\
                 Accuracy of computed solution / 102 \\
                 Solution of triangular set of equations with
                 floating-point accumulation of inner-products / 103 \\
                 Inversion of a triangular matrix / 104 \\
                 High accuracy of solutions of triangular equations /
                 105 \\
                 Solution of a general set of equations / 107 \\
                 Inversion of a general matrix / 109 \\
                 Left-handed and right-handed inverses / 110 \\
                 Numerical example / 111 \\
                 Comments on example / 113 \\
                 Compact methods of triangular decomposition / 114 \\
                 Triangular decomposition with partial pivoting / 115
                 \\
                 Positive definite matrix / 117 \\
                 Numerical example / 118 \\
                 Comments on the solution / 119 \\
                 Residual corresponding to block-floating solution / 120
                 \\
                 Iterative refinement of the solution / 121 \\
                 Practical procedure / 122 \\
                 Analysis of the practical procedure / 124 \\
                 Assessment of accuracy of the computed solution / 126
                 \\
                 The use of an estimate for $||A^{-1}||$ / 126 \\
                 Assessment of a computed inverse / 127 \\
                 Use of the approximate inverse to solve equations / 128
                 \\
                 Iterative procedure based on use of the approximate
                 inverse / 130 \\
                 Numerical example / 131 \\
                 Sensitivity of the eigenvalues of a matrix / 134 \\
                 Sensitivity of individual eigenvalues / 137 \\
                 Example of ill-conditioned eigenvalues / 138 \\
                 A posteriori estimates for a computed eigenvalue and
                 eigenvector of a real symmetric matrix / 139 \\
                 Calculation of the eigenvectors of a symmetric
                 tri-diagonal matrix / 142 \\
                 Effect of rounding errors / 143 \\
                 Calculation of the eigenvalues of a lower Hessenberg
                 matrix / 147 \\
                 Calculation of $f(\lambda)$ using floating-point
                 accumulation / 149 \\
                 Perturbation of the eigenvalues / 150 \\
                 Numerical example / 151 \\
                 Additional comments / 155 \\
                 Bibliography / 157 \\
                 Index / 159",
}

@Proceedings{Rall:1965:EDCa,
  editor =       "L. B. Rall",
  booktitle =    "Error in Digital Computation",
  title =        "Error in Digital Computation",
  volume =       "1",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "338",
  year =         "1965",
  MRclass =      "65.80",
  MRnumber =     "MR0189284 (32 \#6711)",
  MRreviewer =   "J. M. Ortega",
  bibdate =      "Tue Aug 15 18:20:34 MDT 1995",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/moore-ramon-e.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Proceedings of an advanced seminar conducted by the
                 Mathematics Research Center, United States Army, at the
                 University of Wisconsin, Madison, October 5--7, 1964.",
  tableofcontents = "1. The problem of error in digital computation /
                 Todd \\
                 2. Techniques for automatic error monitoring and
                 control / Ashenhurst \\
                 3. The automatic analysis and control of error in
                 digital computing based on the use of interval numbers
                 / Moore \\
                 4. Error in digital solution of linear problems /
                 Albasiny \\
                 5. The propagation of error in the digital integration
                 of ordinary differential equations / Henrici \\
                 6. Bibliography on error in digital computation (114
                 pp.)",
}

@Proceedings{Rall:1965:EDCb,
  editor =       "L. B. Rall",
  booktitle =    "Error in Digital Computation",
  title =        "Error in Digital Computation",
  volume =       "2",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "288",
  year =         "1965",
  MRclass =      "65.80",
  MRnumber =     "MR0189284 (32 \#6711)",
  MRreviewer =   "J. M. Ortega",
  bibdate =      "Tue Aug 15 18:20:34 MDT 1995",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/moore-ramon-e.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Proceedings of an advanced seminar conducted by the
                 Mathematics Research Center, United States Army, at the
                 University of Wisconsin, Madison, October 5--7, 1964.",
  tableofcontents = "1. Experimental investigation of unnormalize1
                 arithmetic / Ashenhurst \\
                 2. Error bounds for computations with continued
                 fractions / Henrici \\
                 3. Error bounds for asymptotic expansions of special
                 functions in the complex plane / Olver \\
                 4. Error analysis for transformations based on the use
                 of matrices of the form $I -2 w w^H$. / Wilkinson \\
                 5. Automatic local coordinate transformations to reduce
                 the growth of error bounds in interval computation of
                 solutions of ordinary differential equations / Moore
                 \\
                 6. Differential inequalities and error bounds /
                 Schroder \\
                 7. Discrete representations of partial differential
                 operators / Young and Dauwalder \\
                 8. Upper and lower bounds for solutions of integral
                 equations / Brown \\
                 9. Convergence ana error bounds for approximate
                 solutions of integral and operator equations / Anselone
                 \\
                 10. Applications of functional analysis to error
                 estimation / Collatz \\
                 11. Error in the solution of linear programming
                 problems / Wolfe",
}

@Book{Wilkinson:1971:LA,
  editor =       "James H. Wilkinson and Christian Reinsch",
  booktitle =    "Linear Algebra",
  title =        "Linear Algebra",
  volume =       "II",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 439",
  year =         "1971",
  ISBN =         "0-387-05414-6, 3-540-05414-6",
  ISBN-13 =      "978-0-387-05414-8, 978-3-540-05414-6",
  LCCN =         "QA251 .W67",
  bibdate =      "Wed Dec 15 18:44:50 1993",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/gnu.bib;
                 http://www.math.utah.edu/pub/tex/bib/master.bib;
                 http://www.math.utah.edu/pub/tex/bib/nummath.bib",
  series =       "Handbook for Automatic Computation, Editors: {F. L.
                 Bauer, A. S. Householder, F. W. J. Olver, H.
                 Rutishauser, K. Samelson and E. Stiefel}",
  tableofcontents = "Part I: Linear systems, least squares and linear
                 programming \\
                 J. H. Wilkinson / Introduction to Part I / 1--8 \\
                 1. Introduction \\
                 2. List of procedures \\
                 3. Positive definite symmetric matrices \\
                 4. Non-positive definite symmetric matrices \\
                 5. Non-Hermitian matrices \\
                 6. Least squares and related problems \\
                 7. The linear programming problem \\
                 R. S. Martin, G. Peters and J. H. Wilkinson / Symmetric
                 decomposition of a positive definite matrix / 9--30 \\
                 Martin, Peters and Wilkinson / Iterative refinement of
                 the solution of a positive definite system of equations
                 / 31--44 \\
                 F. L. Bauer and C. Reinsch / Inversion of positive
                 definite matrices by the Gauss-Jordan method / 45--49
                 \\
                 Martin and Wilkinson / Symmetric decomposition of
                 positive definite band matrices / 50--56 \\
                 T. Ginsburg / The conjugate gradient method / 57--69
                 \\
                 Martin and Wilkinson / Solution of symmetric and
                 unsymmetric band equations and the calculation of
                 eigenvectors of band matrices / 70--92 \\
                 H. J. Bowdler, Martin, Peters and Wilkinson / Solution
                 of real and complex systems of linear equations /
                 93--110 \\
                 P. Businger and G. H. Golub / Linear least squares
                 solutions by Householder transformations / 111--118 \\
                 Bauer / Elimination with weighted row combinations for
                 solving linear equations and least squares problems /
                 119--133 \\
                 Golub and Reinsch / Singular value decomposition and
                 least squares solutions / 134--151 \\
                 R. H. Bartels, J. Stoer and Ch. Zenger / A realization
                 of the simplex method based on triangular
                 decompositions / 152--190) \\
                 Part II: The algebraic eigenvalue problem \\
                 Wilkinson / Introduction to Part II / 191--201 \\
                 1. Introduction \\
                 2. List of procedures \\
                 3. Real, dense, symmetric matrices \\
                 4. Symmetric band matrices \\
                 5. Simultaneous determination of dominant eigenvalues
                 and eigenvectors of a symmetric sparse matrix \\
                 6. The generalized symmetric eigenvalue problems $A x =
                 \lambda B x$ and $A B x = \lambda x$ \\
                 7. Hermitian matrices \\
                 8. Real dense unsymmetric matrices \\
                 9. Unsymmetric band matrices \\
                 10. Dense unsymmetric matrices with complex elements,
                 H. Rutishauser / The Jacobi method for real symmetric
                 matrices / 202--211 \\
                 Martin, Reinsch and Wilkinson / Householder's
                 tridiagonalization of a symmetric matrix / 212--226 \\
                 H. Bowdler, Martin, Reinsch and Wilkinson / The $QR$
                 and $QL$ algorithms for symmetric matrices / 227--240
                 \\
                 A. Dubrulle, Martin and Wilkinson / The implicit $QL$
                 algorithm / 241--248 \\
                 W. Barth, Martin, and Wilkinson / Calculation of the
                 eigenvalues of a symmetric tridiagonal matrix by the
                 method of bisection / 249--256 \\
                 Reinsch and Bauer / Rational $QR$ transformation with
                 Newton shift for symmetric tridiagonal matrices /
                 257--265 \\
                 Martin, Reinsch and Wilkinson / The $QR$ algorithm for
                 band symmetric matrices / 266--272 \\
                 H. R. Schwarz / Tridiagonalization of a symmetric band
                 matrix / 273--283 \\
                 Rutishauser / Simultaneous iteration method for
                 symmetric matrices / 284--302 \\
                 Martin and Wilkinson / Reduction of the symmetric
                 eigenproblem $A x = \lambda B x$ and related problems
                 to standard form / 303--314 \\
                 B. N. Parlett and Reinsch / Balancing a matrix for
                 calculation of eigenvalues and eigenvectors / 315--326
                 \\
                 P. J. Eberlein and J. Boothroyd / Solution to the
                 eigenproblem by a norm reducing Jacobi type method /
                 327--338 \\
                 Martin and Wilkinson / Similarity reduction of a
                 general matrix to Hessenberg form / 339--358 \\
                 Martin, Peters and Wilkinson / The $QR$ algorithm for
                 real Hessenberg matrices / 359--371 \\
                 Peters and Wilkinson / Eigenvectors of real and complex
                 matrices by $LR$ and $QR$ triangularizations / 372--395
                 \\
                 Martin and Wilkinson / The modified $LR$ algorithm for
                 complex Hessenberg matrices / 396--403 \\
                 Eberlein / Solution to the complex eigenproblem by a
                 norm reducing Jacobi type method / 404--417 \\
                 Peters and Wilkinson / The calculation of specified
                 eigenvectors by inverse iteration / 418--439",
}

@Proceedings{Evans:1974:SNM,
  editor =       "D. J. Evans",
  title =        "Software for Numerical Mathematics",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xi + 451",
  year =         "1974",
  ISBN =         "0-12-243750-0",
  ISBN-13 =      "978-0-12-243750-2",
  LCCN =         "QA297 .S591",
  bibdate =      "Tue Aug 15 18:38:31 1995",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Proceedings of the IMA Conference, Loughborough
                 University of Technology, 1973.",
}

@Proceedings{ICM:1974:PIC,
  key =          "ICM'74",
  title =        "Proceedings of the International Congress of
                 Mathematicians, Vancouver, Canada, August 21--29,
                 1974",
  publisher =    "Canadian Mathematical Congress",
  address =      "Montr{\'{e}}al, Qu{\'e}bec, Canada",
  year =         "1975",
  ISBN =         "0-8218-3059-7",
  ISBN-13 =      "978-0-8218-3059-8",
  LCCN =         "QA3 .A572",
  bibdate =      "Wed Aug 16 08:54:12 1995",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@Book{Scaife:1974:SNA,
  editor =       "B. K. P. (Brendan Kevin Patrick) Scaife",
  booktitle =    "Studies in numerical analysis: papers in honour of
                 {Cornelius Lanczos}",
  title =        "Studies in numerical analysis: papers in honour of
                 {Cornelius Lanczos}",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xxii + 333",
  year =         "1974",
  ISBN =         "0-12-621150-7",
  ISBN-13 =      "978-0-12-621150-4",
  LCCN =         "QA297 .S86",
  bibdate =      "Wed Jun 8 14:07:51 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Published for the Royal Irish Academy.",
  URL =          "http://catalog.hathitrust.org/Record/000575557",
  acknowledgement = ack-nhfb,
  subject =      "Numerical analysis; Lanczos, Cornelius; Bibliography",
  subject-dates = "1893--1974",
  tableofcontents = "Contributors / v \\
                 Editor's Foreword / vii \\
                 Cornelius Lanczos --- A Biographical Note / ix \\
                 List of Publications by Cornelius Lanczos / xii \\
                 \\
                 Table-making at the National Bureau of Standards /
                 Gertrude Blanch and Ida Rhodes / 1 \\
                 \\
                 Vignette of a Cultural Episode / Wilhelm Magnus / 7 \\
                 \\
                 The Physicist as Poet / Janice Bireline / 15 \\
                 \\
                 Conservation Laws in Einstein's General Theory of
                 Relativity / William R. Davis / 29 \\
                 \\
                 I Introduction / 29 \\
                 II Historical Comments --- Field Conservation Laws
                 proposed for General Relativity 1916--1959 / 31 \\
                 III Properties of General Covariant Field Theories / 34
                 \\
                 IV Remarks on Symmetry Properties and Invariance
                 Principles in Physical Theories / 37 \\
                 V Conservation Laws of Particle Mechanics in Riemannian
                 Spacetime / 40 \\
                 VI Particle Conservation Laws for Symmetry Properties
                 not representable by Point Deformations / 41 \\
                 VII Field Conservation Law Generators in General
                 Relativity / 43 \\
                 VIII Comments on Application of Conservation Laws for
                 Physically Closed Systems / 45 \\
                 IX Tensorial Tetrad Conservation Law Generators / 47
                 \\
                 X Conservation Laws for Curve Congruences with Special
                 Kinematical and Symmetry Properties / 50 \\
                 XI Other Integral Conservation Expressions / 52 \\
                 XII Conclusions / 54 \\
                 \\
                 An elementary procedure for the evaluation of electric
                 networks / L. Janossy / 65 \\
                 \\
                 Canonical Polynomials in the Lanczos Tau Method ---
                 Eduardo L. Ortiz / 73 \\
                 \\
                 I Introduction / 73 \\
                 II Mathematical Tables and Machine Tables / 74 \\
                 III The Tau Method / 76 \\
                 IV The Canonical Polynomials / 77 \\
                 V The Recursive Form of the Tau Method / 78 \\
                 VI Algebraic Formulation / 81 \\
                 VII Integrated Forms of the Tau Method / 82 \\
                 VIII Expansion of the Approximate Solution in More
                 General Bases / 86 \\
                 IX Eigenvalue Problems / 90 \\
                 \\
                 Rational Approximations from Chebyshev Series --- C. W.
                 Clenshaw and K. Lord / 95 \\
                 \\
                 I Introduction / 95 \\
                 II The Generalized Pad{\'e} Approximation / 98 \\
                 III The Chebyshev--Pad{\'e} Table / 98 \\
                 IV The Calculation of $S_{m,n}(x)$ / 101 \\
                 V An Example / 102 \\
                 VI Case of Slow Convergence / 104 \\
                 VII Computational Aspects / 105 \\
                 VIII Numerical Results / 107 \\
                 \\
                 Accuracy of Computed Eigensystems and Invariant
                 Subspaces / G. Peters and J. H. Wilkinson / 115 \\
                 \\
                 I Introduction / 115 \\
                 II Summary of Perturbation Theory for Normal Matrices /
                 115 \\
                 III Perturbation Theory for Non-Normal Matrices / 119
                 \\
                 IV Eigenvector Perturbations / 123 \\
                 V Computation of Orthogonal Bases for an Invariant
                 Subspace / 124 \\
                 VI Numerical Example / 127 \\
                 VII Attainable Accuracy / 129 \\
                 VIII Low Relative Errors in Small Eigenvalues / 132 \\
                 \\
                 Buckling of a Beam under Axial Compression with Elastic
                 Support / A. P. Gallagher / 137 \\
                 \\
                 I Introduction / 137 \\
                 II Formulation of the Integro--Differential Equation /
                 139 \\
                 III Analysis of the Even Modes of Buckling / 140 \\
                 IV Analysis of the Odd Modes of Buckling / 142 \\
                 V Numerical Results / 143 \\
                 \\
                 The Frequency Approach to Numerical Analysis / R. W.
                 Hamming / 151 \\
                 \\
                 I Introduction / 151 \\
                 II The effects of Sampling-Aliasing / 152 \\
                 III The Finite Fourier Series / 154 \\
                 IV The Nyquist Interval and the Sampling Theorem / 158
                 \\
                 V The Difference Table and Noise / 160 \\
                 VI A Quick Look at Integration / 162 \\
                 VII Smoothing / 163 \\
                 VIII The Gibbs Phenomenon / 166 \\
                 IX Elementary Filter Theory / 169 \\
                 X More Advanced Filter Theory / 172 \\
                 \\
                 Detouring around Computational Roadblocks --- A Tale of
                 Two Integrals / Forman S. Acton / 177 \\
                 \\
                 The Hypercircle Method / J. L. Synge / 201 \\
                 \\
                 I Simplification / 201 \\
                 II An Example: The Dirichlet Problem / 203 \\
                 III The Pay-Off in the Dirichlet Problem / 207 \\
                 IV More General View. The Hypercircle / 209 \\
                 V Historical Note / 212 \\
                 VI The Significance of a Small Hypersphere / 213 \\
                 VII Vertices / 215 \\
                 \\
                 Lower Bounds for the Dirichlet Integral / J. J. McMahon
                 / 219 \\
                 \\
                 I The Problem / 219 \\
                 II Essential Inequality / 220 \\
                 III Method of Constructing Normally-Continuous
                 Divergent-Free Vector-Fields / 221 \\
                 IV A Class of Functions and Vector-Fields / 223 \\
                 V Properties of $P''_{\rho \sigma}$ / ??? \\
                 VI Formulae for the Three Fundamental Vector-Fields /
                 225 \\
                 VII Integrals of Vector-Fields / 228 \\
                 VIII Use of Symmetry / 230 \\
                 IX A Calculation with Lattice Edge $a = 1$ / 231 \\
                 \\
                 The Koenig--Hadamard Theorem again / Alston S.
                 Householder / 235 \\
                 \\
                 Significance Arithmetic --- On the Algebra of Binary
                 Strings / N. Metropolis and Gian-Carlo Rota / 241 \\
                 \\
                 I Introduction / 241 \\
                 II The Arithmetic of Binary Strings / 243 \\
                 III Multiplication / 247 \\
                 IV Binary Functions / 250 \\
                 \\
                 Practical Algorithms for Finding the Type of a
                 Polynomial / John J. H. Miller / / 253 \\
                 \\
                 I Introduction / 253 \\
                 II The Type of a Polynomial Relative to the Unit Circle
                 / 254 \\
                 III The Type of a Polynomial Relative to the Imaginary
                 Axis / 256 \\
                 IV Examples / 260 \\
                 \\
                 The Edge-Function Method in Elastostatics / P. M.
                 Quinlan / 265 \\
                 \\
                 Introduction / 265 \\
                 I The Elastostatic Problem / 266 \\
                 II Edge-Functions for a Polygonal Region / 267 \\
                 III Derived Edge-Functions / 269 \\
                 IV Some Particular Integrals / 271 \\
                 V Polygonal Beam: The Boundary Identity Problem / 272
                 \\
                 VI Trapezoidal Beam --- Illustration Examples / 276 \\
                 VII Polar Elasto-Functions / 278 \\
                 VIII Singular Loadings / 282 \\
                 IX Singular Loadings on Boundary / 284 \\
                 X Symmetrical Functions / 286 \\
                 XI Symmetrical Singular Loadings / 287 \\
                 XII Applications / 288 \\
                 \\
                 Generalised Lobatto Quadrature Formulas for Contour
                 Integrals / S. J. Maskell and R. A. Sack / 295 \\
                 \\
                 I Introduction / 295 \\
                 II General Formulas for the Coefficients / 298 \\
                 I II Generalized Lobatto- Mehler Quadrature / 300 \\
                 IV Numerical Tests / 303 \\
                 V Conclusions / 308 \\
                 \\
                 Spline Functions and Differential Equations --- First
                 Order Equations / I. J. Schoenberg / 311 \\
                 \\
                 I A Remark Due to C. Lanczos / 311 \\
                 II The Spline Approximations of Higher Degree / 313 \\
                 III The Construction of the Spline Approximation $S(x)$
                 / 314 \\
                 IV The Unique Existence of $S_n(x)$ and on Error
                 Estimate / 316 \\
                 V All Derivatives of $S(x)$ Approximate those of $y(x)$
                 / 320 \\
                 VI Examples / 321",
}

@InBook{Evans:1976:IJH,
  author =       "Christopher Evans",
  title =        "Interview with {J. H. Wilkinson}",
  number =       "10",
  publisher =    "Science Museum",
  address =      "London, UK",
  pages =        "??--??",
  year =         "1976",
  bibdate =      "Thu Nov 10 10:17:31 GMT 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
  series =       "Pioneers of Computing, 60-Minute Recordings of
                 Interviews",
  acknowledgement = ack-nhfb,
  mynote =       "Recorded Teddington 1976. He moved to NPL May 1946.
                 Half time with Turing, half in Desk Computing section
                 w/Goodwin and Fox. Moved from 32 to 40 bit words in
                 version 7 of ACE design. Side 1, [112]: ``Turing is a
                 very impressive mathematician ... He was a lousy
                 computer ... One of the worst performers on a desk
                 computer it's ever been my misfortune to work with.''
                 JHW thinks they produced the first fl. pt. programs
                 ([32] of side 2) and regrets not writing them up in his
                 1948 progress report. ([245] of Side 2): Pilot ACE did
                 fl. pt. multiply in 3 millisecs - very fast for the
                 time (many millisecs on EDASC)!, This meant NPL got
                 practical fl. pt. experience before anyone else,
                 leading to error analysis developments.",
}

@Proceedings{Hartnell:1976:PFM,
  editor =       "B. L. Hartnell and H. C. Williams",
  title =        "Proceedings of the Fifth Manitoba Conference on
                 Numerical Mathematics, October 1--4, 1975",
  number =       "16",
  publisher =    pub-UMP,
  address =      pub-UMP:adr,
  pages =        "vi + 658",
  year =         "1976",
  ISBN =         "0-919628-16-8",
  ISBN-13 =      "978-0-919628-16-8",
  LCCN =         "QA297 .M33 1975",
  bibdate =      "Tue Aug 15 18:42:33 1995",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  series =       "Congressus numerantium",
}

@Proceedings{Jacobs:1976:SAN,
  editor =       "David A. H. Jacobs",
  title =        "The state of the art in numerical analysis:
                 Proceedings of the Conference on the State of the Art
                 in Numerical Analysis held at the University of York,
                 April 12th--15th, 1976",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xix + 978",
  year =         "1976",
  ISBN =         "0-12-378650-9",
  ISBN-13 =      "978-0-12-378650-0",
  LCCN =         "QA297 .C6461 1976",
  bibdate =      "Tue Aug 15 18:46:30 1995",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}

@Proceedings{Powell:1977:CDJ,
  editor =       "M. J. D. Powell",
  title =        "The Contribution of Dr. {J}. {H}. Wilkinson to
                 numerical analysis: Proceedings of a symposium \ldots{}
                 held in London on July 6th, 1977",
  number =       "19",
  publisher =    pub-IMA,
  address =      pub-IMA:adr,
  pages =        "viii + 91",
  year =         "1977",
  LCCN =         "QA297.C66 1978",
  bibdate =      "Tue Aug 15 18:51:43 1995",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  series =       "IMA Symposium Proceedings",
  xxISBN =       "none",
}

@Proceedings{deBoor:1978:RAN,
  editor =       "Carl de Boor and Gene H. Golub",
  title =        "Recent advances in numerical analysis: proceedings of
                 a symposium conducted by the Mathematics Research
                 Center, the University of Wisconsin--Madison, May
                 22--24, 1978",
  volume =       "41",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "ix + 270",
  year =         "1978",
  ISBN =         "0-12-208360-1",
  ISBN-13 =      "978-0-12-208360-0",
  LCCN =         "QA297 S994 1978",
  bibdate =      "Tue Aug 15 18:49:19 1995",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  series =       "Publ. Math. Res. Center Univ. Wisconsin",
}

@Proceedings{Jacobs:1978:NSN,
  editor =       "D. A. H. Jacobs",
  title =        "Numerical software, needs and availability:
                 proceedings of the Conference on Applications of
                 Numerical Software, Needs and Availability, held at the
                 University of Sussex, September 19th--22nd, 1977",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xvii + 408",
  year =         "1978",
  ISBN =         "0-12-378660-6",
  ISBN-13 =      "978-0-12-378660-9",
  LCCN =         "QA297 C74 1977",
  bibdate =      "Tue Aug 15 18:54:26 1995",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  price =        "UK\pounds 11.60",
}

@Proceedings{Metropolis:1980:HCT,
  editor =       "Nicholas Metropolis and Jack Howlett and Gian-Carlo
                 Rota",
  booktitle =    "A History of Computing in the {Twentieth Century}: {A}
                 Collection of Essays",
  title =        "A History of Computing in the {Twentieth Century}: {A}
                 Collection of Essays",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xix + 659",
  year =         "1980",
  ISBN =         "0-12-491650-3",
  ISBN-13 =      "978-0-12-491650-0",
  LCCN =         "QA75.5 .I63 1976",
  bibdate =      "Tue Aug 15 18:57:33 1995",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Original versions of these papers were presented at
                 the International Research Conference on the History of
                 Computing, held at the Los Alamos Scientific
                 Laboratory, 10--15 June 1976.",
  acknowledgement = ack-nhfb,
  remark =       "This book contains the edited versions of the papers
                 presented at the international research Conference on
                 the History of Computing, held at the Los Alamos
                 Scientific Laboratory, 10--15 June 1976. The book
                 provides an account of the development of the first
                 large-scale computers in the first half of the
                 twentieth century. Each chapter describes one phase of
                 the development and is written by either a participant
                 or a witness to these events. The treatment is
                 narrative and factual and is meant to give a first
                 exposition of the res gestae. The Exposition is
                 accessible to anyone interested in the subject and
                 requires no technical background.",
}

@Proceedings{Meek:1981:PTM,
  editor =       "D. S. Meek and Hugh C. Williams",
  title =        "Proceedings of the tenth Manitoba Conference on
                 Numerical Mathematics and Computing, October 1--4,
                 1980",
  volume =       "30--31",
  publisher =    pub-UMP,
  address =      pub-UMP:adr,
  year =         "1981",
  ISBN =         "0-919628-30-3 (vol.~1) 0-919628-31-1 (vol.~2)",
  ISBN-13 =      "978-0-919628-30-4 (vol.~1) 978-0-919628-31-1
                 (vol.~2)",
  ISSN =         "0384-9864",
  bibdate =      "Wed Aug 16 09:03:40 1995",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  series =       "Congressus Numerantium",
}

@Proceedings{Iserles:1987:SAN,
  editor =       "A. Iserles and M. J. D. Powell",
  booktitle =    "{State of the Art in Numerical Analysis. Proceedings
                 of the Joint IMA\slash SIAM Conference held at the
                 University of Birmingham, 14--18 April 1986}",
  title =        "{State of the Art in Numerical Analysis. Proceedings
                 of the Joint IMA\slash SIAM Conference held at the
                 University of Birmingham, 14--18 April 1986}",
  volume =       "9",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "x + 719",
  year =         "1987",
  ISBN =         "0-19-853614-3",
  ISBN-13 =      "978-0-19-853614-7",
  LCCN =         "QA297.J65 1986",
  bibdate =      "Mon Sep 9 14:56:14 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  series =       "The Institute of Mathematics and Its Applications
                 conference series; new series",
  URL =          "http://www.gbv.de/dms/hbz/toc/ht002967923.pdf;
                 http://zbmath.org/?q=an:0611.00024",
  ZMnumber =     "0611.00024",
  acknowledgement = ack-nhfb,
  confdate =     "14--18 April 1986",
  conflocation = "Birmingham, UK",
  confsponsor =  "Inst. Math. Appl.; SIAM",
  pubcountry =   "UK",
  tableofcontents = "Contributors / / xiii \\
                 1. Eigenvalue problems / J. H. Wilkinson / 1 \\
                 2. Numerical linear algebra in statistical computing /
                 N. J. Higham and G. W. Stewart / 41 \\
                 3. Sparse matrices / J. K. Reid / 59 \\
                 4. Multivariate approximation / Carl de Boor / 87 \\
                 5. Data approximation by splines in one and two
                 independent variables / M. G. Cox / 111 \\
                 6. Methods for best approximation and regression
                 problems / G. A. Watson / 139 \\
                 7. Branch cuts for complex elementary functions / W.
                 Kahan / 165 \\
                 8. Recent developments in linear and quadratic
                 programming / R. Fletcher / 213 \\
                 9. Solving systems of nonlinear equations by tensor
                 methods / R. B. Schnabel and P. D. Frank / 245 \\
                 10. Numerical methods for bifurcation problems / A. D.
                 Jepson and A. Spence / 273 \\
                 11. On the iterative solution of differential and
                 integral equations using secant updating techniques /
                 A. Griewank / 299 \\
                 12. Methods for nonlinear constraints in optimization
                 calculations / M. J. D. Powell / 325 \\
                 13. The influence of vector and parallel processors on
                 numerical analysis / I. S. Duff / 359 \\
                 14. Developments in stability theory for ordinary
                 differential equations / J. D. Lambert / 409 \\
                 15. Stiff ODE initial value problems and their solution
                 / A. R. Curtis / 433 \\
                 16. Order stars and stability / G. Wanner / 451 \\
                 17. The state of the art in the numerical treatment of
                 integral equations / C. T. H. Baker / 473 \\
                 18. Strongly elliptic boundary integral equations / W.
                 L. Wendland / 511 \\
                 19. Collocation methods for one-dimensional Fredholm
                 and Volterra integral equations / H. Brunner / 563 \\
                 20. Numerical methods for free and moving boundary
                 problems / C. W. Cryer / 601 \\
                 21. Multigrid methods for elliptic equations / J. Walsh
                 / 623 \\
                 22. Galerkin finite element methods and their
                 generalizations / K. W. Morton / 645 \\
                 23. Recent developments in the numerical solution of
                 nonlinear conservation laws / S. Osher and P. K. Sweby
                 / 681 \\
                 Index / 701",
}

@Book{Ashenhurst:1987:ATA,
  editor =       "Robert L. Ashenhurst",
  booktitle =    "{ACM Turing Award Lectures}: the first twenty years,
                 1966--1985",
  title =        "{ACM Turing Award Lectures}: the first twenty years,
                 1966--1985",
  publisher =    pub-ACM # " and " # pub-AW,
  address =      pub-ACM:adr # " and " # pub-AW:adr,
  pages =        "xviii + 483",
  year =         "1987",
  ISBN =         "0-201-07794-9",
  ISBN-13 =      "978-0-201-07794-0",
  LCCN =         "QA76.24 .A33 1987",
  bibdate =      "Tue Jun 21 11:01:04 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 http://www.math.utah.edu/pub/tex/bib/acm-turing-awards.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "ACM Press anthology series",
  acknowledgement = ack-nhfb,
  subject =      "Electronic data processing; Computers",
  tableofcontents = "The synthesis of algorithmic systems / Alan J.
                 Perlis \\
                 Computers then and now / Maurice V. Wilkes \\
                 One man's view of computer science / R. W. Hamming \\
                 Form and content in computer science / Marvin Minsky
                 \\
                 Some comments from a numerical analyst / J. H.
                 Wilkinson \\
                 Generality in artificial intelligence / John McCarthy
                 \\
                 The humble programmer / Edsger W. Dijkstra \\
                 The programmer as navigator / Charles W. Bachman \\
                 Computer programming as an art / Donald E. Knuth \\
                 Computer science as empirical inquiry: symbols and
                 search / Allen Newell and Herbert A. Simon \\
                 Complexity of computations / Michael O. Rabin \\
                 Logic and programming languages / Dana S. Scott \\
                 Can programming be liberated from the von Neumann
                 style?: a functional style and its algebra of programs
                 / John Backus \\
                 The paradigms of programming / Robert W. Floyd \\
                 Notation as a tool of thought / Kenneth E. Iverson \\
                 The emperor's old clothes / Charles Antony Richard
                 Hoare \\
                 Relational database: a practical foundation for
                 productivity / E. F. Codd \\
                 An overview of computational complexity / Stephen A.
                 Cook \\
                 Reflections on software research / Dennis M. Ritchie
                 \\
                 Reflections on trusting trust / Ken Thompson \\
                 From programming language design to computer
                 construction / Niklaus Wirth \\
                 Combinatorics, complexity, and randomness / Richard M.
                 Karp \\
                 Algorithm design / Robert E. Tarjan \\
                 Computer science: the emergence of a discipline / John
                 E. Hopcroft \\
                 The search for performance in scientific processors /
                 John Cocke \\
                 Micropipelines / Ivan E. Sutherland \\
                 On building systems that will fail / Fernando J.
                 Corbat{\'o} \\
                 Elements of interaction / Robin Milner \\
                 Turing Award Lecture: it's time to reconsider time /
                 Richard Edwin Stearns \\
                 Turing Award Lecture: on computational complexity and
                 the nature of computer science / Juris Hartmanis \\
                 How the `what' becomes the `how' / Edward A. Feigenbaum
                 \\
                 To dream the possible dream / Raj Reddy \\
                 The Eary Days of RSA: History and Lessons / Ronald L.
                 Rivest \\
                 Pre-RSA Days: History and Lessons / Leonard Adleman \\
                 Cryptography: State of the science / Adi Shamir \\
                 Turing Award Lecture / Alan Kay \\
                 Assessing the Internet: Lessons Learned, Strategies for
                 Evolution, and Future Possibilities / Vinton Cerf,
                 Robert E. Kahn \\
                 Computing vs. Human Thinking / Peter Naur \\
                 Compiling for Performance: A Personal Tour / Frances
                 Allen \\
                 Model checking: my 27-year quest to overcome the state
                 explosion problem / Edmund M. Clarke \\
                 Model checking: A Personal Perspective / E. Allen
                 Emerson \\
                 The Quest for Correctness Beyond Verification / Joseph
                 Sifakis \\
                 The Power of Abstraction / Barbara Liskov \\
                 Improving the Future by Examining the Past / Charles P.
                 Thacker",
}

@Article{Chatelin:1987:SVM,
  author =       "F. Chatelin and J. Dongarra and I. Duff",
  title =        "Special Volume in Memory of {James H. Wilkinson}",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "88--89",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "1987",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Mon Jan 02 09:49:28 2006",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  URL =          "http://www.sciencedirect.com/science/journal/00243795/88-89",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Proceedings{Cox:1990:RNC,
  editor =       "M. G. Cox and S. Hammarling",
  booktitle =    "Reliable numerical computation",
  title =        "Reliable numerical computation",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xvi + 339",
  year =         "1990",
  ISBN =         "0-19-853564-3",
  ISBN-13 =      "978-0-19-853564-5",
  LCCN =         "QA297 .R435 1990",
  MRclass =      "65-06",
  MRnumber =     "91k:65011",
  bibdate =      "Fri Dec 20 18:34:52 1996",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Based on papers from a conference in honour of the
                 late James Hardy Wilkinson (died Sunday 5th October
                 1986) held at National Physical Laboratory, Teddington,
                 Middlesex, UK, 8th--10th July 1987.",
  price =        "US\$75.00",
  abstract =     "Published to honor the late Jim Wilkinson, the
                 respected pioneer in numerical analysis, this book
                 includes contributions from his colleagues and
                 collaborators, leading experts in their own right. The
                 breadth of Wilkinson's research is reflected in the
                 topics covered, which include linear algebra, error
                 analysis and computer arithmetic algorithms, and
                 mathematical software. An invaluable reference, the
                 book is completely up-to-date with the latest
                 developments on the Lanczos algorithm,
                 QR-factorizations, error propagation models, parameter
                 estimation problems, sparse systems, and
                 shape-preserving splines. Reflecting the current growth
                 and vitality of this field, the volume is an essential
                 reference for all numerical analysts.",
  acknowledgement = ack-nhfb,
  tableofcontents = "List of contributors / / xv \\
                 Prologue. Reflections on Jim Wilkinson / Gene Golub / 1
                 \\
                 1. Misconvergence in the Lanczos algorithm / Beresford
                 Parlett / 7 \\
                 2. The Lanczos algorithm for a pure imaginary Hermitian
                 matrix / Charles L. Lawson and Kajal K. Gupta / 25 \\
                 3. Nearest defective matrices and the geometry of
                 ill-conditioning / James Demmel / 35 \\
                 4. Computational aspects of the Jordan canonical form /
                 Theo Beelen and Paul Van Dooren / 57 \\
                 5. Some aspects of generalized QR factorizations / C.
                 C. Paige / 73 \\
                 6. The multifrontal method in a parallel environment /
                 I. S. Duff, N. I. M. Gould, M. Lescrenier, and J. K.
                 Reid / 93 \\
                 7. A Schur-complement method for sparse quadratic
                 programming / Philip E. Gill, Walter Murray, Michael A.
                 Saunders, and Margaret H. Wright / 113 \\
                 8. A probabilistic round-off error propagation model.
                 Application to the eigenvalue problem / Francoise
                 Chatelin and Marie Christine Brunet / 139 \\
                 9. Analysis of the Cholesky decomposition of a
                 semi-definite matrix / Nicholas J. Higham / 161 \\
                 10. On the conditioning of parameter estimation
                 problems / James M. Varah / 187 \\
                 11. Rounding errors in algebraic process-in level-index
                 arithmetic / F. W J. Olver / 197 \\
                 12. Experiments in tearing large sparse systems / Mario
                 Arioli and lain S. Duff / 207 \\
                 13. The least-squares solution of linear equations with
                 block-angular observation matrix / M. G. Cox / 227 \\
                 14. An iterative method for solving linear inequalities
                 / G. W Stewart / 241 \\
                 15. Iterative refinement and reliable computing / Ake
                 Bjorck / 249 \\
                 16. Software for shape-preserving spline interpolation
                 / Christian H. Reinsch / 267 \\
                 17. Experiences with some software engineering
                 practices in numerical software / D. A. H. Jacobs and
                 G. Markham / 277 \\
                 18. Evolution of numerical software for dense linear
                 algebra / Jack Dongarra and Sven Hammarling / 297 \\
                 Epilogue. Jim Wilkinson: some after-dinner sentiments /
                 L. Fox / 329",
}

@InProceedings{Parlett:1990:CJH,
  author =       "B. N. Parlett",
  title =        "The Contribution of {J. H. Wilkinson} to Numerical
                 Analysis",
  crossref =     "Nash:1990:HSC",
  pages =        "17--30",
  year =         "1990",
  bibdate =      "Tue Mar 13 14:04:57 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Nash:1990:HSC,
  editor =       "Stephen G. Nash",
  booktitle =    "A History of Scientific Computing",
  title =        "A History of Scientific Computing",
  publisher =    pub-AW # " and " # pub-ACM,
  address =      pub-AW # " and " # pub-ACM:adr,
  pages =        "xix + 359",
  year =         "1990",
  ISBN =         "0-201-50814-1",
  ISBN-13 =      "978-0-201-50814-7",
  LCCN =         "QA76.17 .H59 1990",
  bibdate =      "Wed Dec 15 10:39:57 1993",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "ACM Press history series",
  remark =       "Based on papers presented at the Conference on the
                 History of Scientific and Numeric Computation, held in
                 Princeton, N.J., 1987.",
  subject =      "Electronic data processing; History; Science; Data
                 processing",
}

@Book{Wilkinson:1994:REA,
  author =       "J. H. Wilkinson",
  title =        "Rounding errors in algebraic processes",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "viii + 161",
  year =         "1994",
  ISBN =         "0-486-67999-3",
  ISBN-13 =      "978-0-486-67999-0",
  MRclass =      "65G05",
  MRnumber =     "MR1280465",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
  note =         "Reprint of the 1963 original [Prentice-Hall, Englewood
                 Cliffs, NJ; MR0161456 (28 \#4661)]",
  acknowledgement = ack-nhfb,
}

@Book{Copeland:2005:ATA,
  editor =       "B. Jack Copeland",
  booktitle =    "{Alan Turing}'s {Automatic Computing Engine}: the
                 master codebreaker's struggle to build the modern
                 computer",
  title =        "{Alan Turing}'s {Automatic Computing Engine}: the
                 master codebreaker's struggle to build the modern
                 computer",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xx + 553",
  year =         "2005",
  ISBN =         "0-19-856593-3 (hardcover)",
  ISBN-13 =      "978-0-19-856593-2 (hardcover)",
  LCCN =         "QA75 .A43 2005",
  bibdate =      "Sat Nov 19 18:33:05 MST 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 melvyl.cdlib.org:210/CDL90",
  URL =          "http://ukcatalogue.oup.com/product/9780198565932.do;
                 http://www.oxfordscholarship.com/oso/public/content/maths/9780198565932/toc.html",
  abstract =     "The mathematical genius Alan Turing (1912--1954) was
                 one of the greatest scientists and thinkers of the 20th
                 century. Now well known for his crucial wartime role in
                 breaking the ENIGMA code, he was the first to conceive
                 of the fundamental principle of the modern computer ---
                 the idea of controlling a computing machine's
                 operations by means of coded instructions, stored in
                 the machine's `memory'. In 1945, Turing drew up his
                 revolutionary design for an electronic computing
                 machine --- his Automatic Computing Engine (`ACE'). A
                 pilot model of the ACE ran its first programme in 1950
                 and the production version, the `DEUCE', went on to
                 become a cornerstone of the fledgling British computer
                 industry. The first `personal' computer was based on
                 Turing's ACE. This book describes Turing's struggle to
                 build the modern computer. It contains first-hand
                 accounts by Turing and by the pioneers of computing who
                 worked with him. The book describes the hardware and
                 software of the ACE and contains chapters describing
                 Turing's path-breaking research in the fields of
                 Artificial Intelligence (AI) and Artificial Life
                 (A-Life).",
  acknowledgement = ack-nhfb,
  remark =       "Originally published: New York; London: Springer,
                 2003",
  subject =      "Turing, Alan Mathison; Computers; Great Britain;
                 History; Computer engineering; Great Britain; History",
  subject-dates = "1912--1954",
  tableofcontents = "Foreword / Donald W. Davies \\
                 Introduction / B. Jack Copeland \par

                 Part I: The National Physical Laboratory and the ACE
                 Project \\
                 A Century of Measurement and Computation at the
                 National Physical Laboratory, 1900--2000 / Eileen
                 Magnello \\
                 The Creation of the NPL Mathematics Division / Mary
                 Croarken \\
                 The Origins and Development of the ACE Project / B.
                 Jack Copeland \\
                 The Pilot ACE at the National Physical Laboratory,
                 James H. Wilkinson \par

                 Part II: Turing and the History of Computing \\
                 The ACE and the Shaping of British Computing / Martin
                 Campbell-Kelly \\
                 Computer Architecture and the ACE Computers / Robert
                 Doran \\
                 Turing and the Computer / B. Jack Copeland and Diane
                 Proudfoot \\
                 From Turing Machine to ``Electronic Brain'' / Teresa
                 Numerico \par

                 Part III: The ACE Computers \\
                 The Pilot ACE Instruction Format / Henry John Norton
                 \\
                 Programming the Pilot ACE / J.G. Hayes \\
                 The Pilot ACE: from Concept to Reality / Robin A.
                 Vowels \\
                 The DEUCE --- a User's View / Robin A. Vowels \\
                 Applications of the Pilot ACE and the DEUCE / Tom
                 Vickers \\
                 The ACE Test Assembly, the Pilot ACE, the Big ACE, and
                 the Bendix G15 / Harry D. Huskey \\
                 The ACE Simulator and the Cybernetic Model / Michael
                 Woodger \\
                 The Pilot Model and the Big ACE on the Web / Benjamin
                 Wells \par

                 Part IV: Electronics \\
                 How Valves Work / David O. Clayden \\
                 Recollections of Early Vacuum Tube Circuits / Maurice
                 Wilkes \\
                 Circuit Design of the Pilot ACE and the Big ACE / David
                 O. Clayden \par

                 Part V: Technical Reports and Lectures on the ACE and
                 the Pilot ACE, 1945--1951 \\
                 Proposed Electronic Calculator (1945) / Alan M. Turing
                 \\
                 Notes on Memory (1945) / Alan M. Turing \\
                 The Turing--Wilkinson Lecture Series (1946--1947) /
                 Alan M. Turing and James H. Wilkinson \\
                 The State of the Art in Electronic Digital Computing in
                 Britain and the United States (1947) / Harry D.
                 Huskey",
}