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author = "C. Brezinski",
title = "A unified approach to various orthogonalities",
journal = "Annales de la Facult{\'e} des Sciences de Toulouse: Math{\'e}matiques",
volume = "1",
number = "3",
year = "1992",
pages = "277-292" }
@techreport{br1995,
author = {C. Brezinski},
title = {Hybrid procedures and semi-iterative methods for linear systems},
year = {1995},
number = {?},
institution = {Universit{\'e} de Lille},
}
@article{br1996,
author = "C. Brezinski",
title = "The methods of {Vorobyev} and {Lanczos}",
journal = LAA,
volume = "234",
year = "1996",
pages = "21-41" }
@article{br1996b,
author = "C. Brezinski",
title = "Extrapolation algorithms and {Pad{\'e}} approximations: a historical survey",
journal = ANM,
volume = "20",
number = "3",
year = "1996",
pages = "299-318" }
@article{br1997,
author = "C. Brezinski",
title = "A transpose-free {Lanczos}/{Orthodir} algorithm for linear systems",
journal = CRAS,
volume = "324",
year = "1997",
pages = "349-354" }
@book{br1997b,
author = "C. Brezinski",
title = "Projection Methods for Systems of Equations",
publisher = "North-Holland",
address = "Amsterdam",
year = "1997" }
@incollection{br1998,
author = "C. Brezinski",
title = "Hybrid methods for solving systems of equations",
booktitle = "NATO ASI Series C Mathematical and Physical Sciences - Advanced Study Institute",
publisher = "NATO",
volume = "508",
year = "1998",
pages = "271-290" }
@article{br1999,
author = "C. Brezinski",
title = "Error estimates for the solution of linear systems",
journal = SISC,
volume = "21",
number = "2",
year = "1999",
pages = "764-781" }
@article{br1999b,
author = "C. Brezinski",
title = "{Krylov} subspace methods, biorthogonal polynomials and {Pad{\'e}}-type approximants",
journal = NUMALGO,
volume = "21",
year = "1999",
pages = "97-107" }
@article{br1999c,
author = "C. Brezinski",
title = "Multiparameter descent methods",
journal = LAA,
volume = "296",
number = "1-3",
year = "1999",
pages = "113-141" }
@article{br2000,
author = "C. Brezinski",
title = "The block {Lanczos} and {Vorobyev} methods",
journal = CRAS,
volume = "331",
year = "2000",
pages = "137-142" }
@inproceedings{br2002,
author = "C. Brezinski",
title = "Formal orthogonal polynomials",
booktitle = "Computational Aspects of Linear Control",
publisher = "Springer",
address = "Boston, MA",
year = "2002",
pages = "73-85" }
@techreport{br2002b,
author = "C. Brezinski",
title = "An introduction to formal orthogonality and some of its applications",
institution = "Universit{\'e} de Lille, France",
number = "ANO438",
year = "2002" }
@article{br2003,
author = "C. Brezinski",
title = "A tribute",
journal = NUMALGO,
volume = "33",
number = "1",
year = "2003",
pages = "3-9" }
@article{br2005,
author = "C. Brezinski",
title = "La m{\'{e}}thode de {Cholesky}",
journal = RHM,
volume = "11",
year = "2005",
pages = "205-238" }
@article{br2006,
author = "C. Brezinski",
title = "The life and work of {Andr\'{e} Cholesky}",
journal = NUMALGO,
volume = "43",
year = "2006",
pages = "279-288" }
@book{br2006b,
author = "C. Brezinski",
title = "Histoires de Sciences. Inventions, D{\'e}couvertes et Savants",
publisher = "L'Harmattan",
address = "Paris",
year = "2006" }
@article{br2010,
author = "C. Brezinski",
title = "From numerical quadrature to {Pad{\'e}} approximation",
journal = ANM,
volume = "60",
number = "12",
year = "2010",
pages = "1209-1220" }
@book{br2010b,
author = "C. Brezinski",
title = "Les Images de la Terre. Cosmographie, G{\'e}od{\'e}sie, Topographie et Cartographie {\`a} Travers les Si{\`e}cles",
publisher = "L'Harmattan",
address = "Paris",
year = "2010" }
@article{br2019,
author = "C. Brezinski",
title = "Reminiscences of {Peter Wynn}",
journal = NUMALGO,
volume = "80",
number = "1",
year = "2019",
pages = "5-10" }
@article{brci2022,
author = "C. Brezinski and P. G. Ciarlet",
title = "{Richard Steven Varga}, 1928-2022",
journal = NUMALGO,
volume = "90",
year = "2022",
pages = "1-2" }
@article{bcrs2021,
author = "C. Brezinski and S. Cipolla and M. Redivo-Zaglia and Y. Saad",
title = "Shanks and {A}nderson-type acceleration techniques for systems of nonlinear equations",
journal = IMAJNA,
volume = "drab061",
year = "2021" }
@article{bfm2012,
author = "C. Brezinski and P. Fika and M. Mitrouli",
title = "Estimations of the trace of powers of positive self-adjoint operators by extrapolation of the moments",
journal = ETNA,
volume = "39",
year = "2012",
pages = "144-155" }
@article{bfm2012b,
author = "C. Brezinski and P. Fika and M. Mitrouli",
title = "Moments of a linear operator, with applications to the trace of the inverse of matrices and the solution of equations",
journal = NLAA,
volume = "19",
number = "6",
year = "2012",
pages = "937-953" }
@article{bgc2005,
author = {C. Brezinski and M. {Gross-Cholesky}},
journal = {Bull. Soc. Amis. Bib. \'Ec. Polytech.},
title = {La vie et les travaux d'{Andr\'e-Louis Cholesky}},
year = {2005},
pages = {7-32},
volume = {39},
}
@book{bmrz2022,
author = "C. Brezinski and G. Meurant and M. {Redivo-Zaglia}",
title = "A Journey Through the History of Numerical Linear Algebra",
publisher = "SIAM",
year = "2022" }
@article{bnrz2021,
author = "C. Brezinski and F. A. Norman and M. Redivo-Zaglia",
title = "The Legacy of {Peter Wynn}",
journal = "Mathematics",
volume = "9",
number = "11",
year = "2021",
pages = "1240-1285" }
@article{bnorz2012,
author = "C. Brezinski and P. Novati and M. Redivo-Zaglia",
title = "A rational {Arnoldi} approach for ill-conditioned linear systems",
journal = JCAM,
volume = "236",
number = "8",
year = "2012",
pages = "2063-2077" }
@article{brra2007,
author = "C. Brezinski and M. Raydan",
title = "Cauchy-{Schwarz} and {Kantorovich} type inequalities for scalar and matrix moment sequences",
journal = ADCM,
volume = "26",
number = "1",
year = "2007",
pages = "71-80" }
@inproceedings{brz1994c,
author = "C. Brezinski and M. Redivo-Zaglia",
title = "Breakdowns in the computation of orthogonal polynomials",
booktitle = "Nonlinear Numerical Methods and Rational Approximation, {II}",
editor = "A. Cuyt",
publisher = "Kluwer",
address = "Dordrecht",
year = "1994",
pages = "49-59" }
@article{brz1994a,
author = "C. Brezinski and M. Redivo-Zaglia",
title = "Hybrid procedures for solving linear systems",
journal = NUMAT,
volume = "67",
year = "1994",
pages = "1-19" }
@article{brz1994b,
author = "C. Brezinski and M. Redivo-Zaglia",
title = "Treatment of near-breakdown in the {CGS} algorithm",
journal = NUMALGO,
volume = "7",
year = "1994",
pages = "33-73" }
@article{brz1995,
author = "C. Brezinski and M. Redivo-Zaglia",
title = "Look-ahead in {BiCGstab} and other methods for linear systems",
journal = BIT,
volume = "35",
year = "1995",
pages = "169-201" }
@article{brz1998,
author = "C. Brezinski and M. Redivo-Zaglia",
title = "Transpose-free {Lanczos}-type algorithms for nonsymmetric linear systems",
journal = NUMALGO,
volume = "17",
year = "1998",
pages = "67-103" }
@techreport{brz1999,
author = {C. Brezinski and M. Redivo-Zaglia},
title = {On the choice of the auxiliary vectors in {Lanczos}' method for linear systems},
year = {1999},
address = {France},
number = {ANO-402},
institution = {Universit{\'e} de Lille},
}
@Article{brz2000,
author = {C. Brezinski and M. Redivo-Zaglia},
journal = CALC,
title = {Variations on {Lanczos}' tridiagonalization process},
year = {2000},
pages = {159-179},
volume = {37},
}
@article{brz2003,
author = "C. Brezinski and M. Redivo-Zaglia",
title = "A {Schur} complement approach to a general extrapolation algorithm",
journal = LAA,
volume = "368",
year = "2003",
pages = "279-301" }
@article{brz2006,
author = "C. Brezinski and M. Redivo-Zaglia",
title = "The {PageRank} vector: properties, computation, approximation, and acceleration",
journal = SIMAX,
volume = "28",
number = "2",
year= "2006",
pages = "551-575" }
@article{brz2013,
author = "C. Brezinski and M. Redivo-Zaglia",
title = "Pad{\'e}-type rational and barycentric interpolation",
journal = NUMAT,
volume = "125",
number = "1",
year = "2013",
pages = "89-113" }
@article{brz2015,
author = "C. Brezinski and M. Redivo-Zaglia",
title = "Convergence acceleration of {Kaczmarz}'s method",
journal = "J. Eng. Math.",
volume = "93",
year = "2015",
pages = "3-19" }
@article{brz2015b,
author = "C. Brezinski and M. Redivo-Zaglia",
title = "New representations of {Pad{\'e}}, {Pad{\'e}}-type, and partial {Pad{\'e}} approximants",
journal = JCAM,
volume = "284",
year = "2015",
pages = "69-77" }
@article{brz2019,
author = "C. Brezinski and M. Redivo-Zaglia",
title = "The genesis and early developments of {A}itken's process, {Shanks} transformation, the $\varepsilon$-algorithm,
and related fixed point methods",
journal = NUMALGO,
volume = "80",
year = "2019",
pages = "11-133" }
@book{brz2020,
author = "C. Brezinski and M. Redivo-Zaglia",
title = "Extrapolation and rational approximation. {T}he works of the main contributors",
publisher = "Springer Nature",
address = "Switzerland",
year = "2020" }
@article{brz2020b,
author = "C. Brezinski and M. Redivo-Zaglia",
title = "Some unusual results on extrapolation methods",
journal = NUMALGO,
volume = "84",
number = "4",
year = "2020",
pages = "1241-1264" }
@article{brz2023,
author = "C. Brezinski and M. Redivo-Zaglia",
title = "On the kernel of vector $\varepsilon$-algorithm and related topics",
journal = NUMALGO,
volume = "92",
number = "1",
year = "2023",
pages = "207-221" }
@article{brz2023b,
author = "C. Brezinski and M. Redivo-Zaglia",
title = "Reuben {Louis Rosenberg} (1909-1986) and the {Stein-Rosenberg} theorem",
journal = ETNA,
volume = "58",
year = "2023",
pages = "A1-A38" }
@article{brrs1998,
author = "C. Brezinski and M. Redivo-Zaglia and G. Rodriguez and S. Seatzu",
title = "Extrapolation techniques for ill-conditioned linear systems",
journal = NUMAT,
volume = "81",
number = "1",
year = "1998",
pages = "1-29" }
@article{brrs2003,
author = "C. Brezinski and M. Redivo-Zaglia and G. Rodriguez and S. Seatzu",
title = "Multi-parameter regularization techniques for ill-conditioned linear systems",
journal = NUMAT,
volume = "94",
number = "2",
year = "2003",
pages = "203-228" }
@article{brsa2018,
author = "C. Brezinski and M. Redivo-Zaglia and Y. Saad",
title = "Shanks sequence transformations and {A}nderson acceleration",
journal = SIREV,
volume = "60",
number = "3",
year = "2018",
pages = "646-669" }
@article{brs1991,
author = "C. Brezinski and M. Redivo-Zaglia and H. Sadok",
title = "Avoiding breakdown and near-breakdown in {Lanczos} type algorithms",
journal = NUMALGO,
volume = "1",
year = "1991",
pages = "261-284" }
@article{brs1992,
author = "C. Brezinski and M. Redivo-Zaglia and H. Sadok",
title = "A breakdown-free {Lanczos} type algorithm for solving linear systems",
journal = NUMAT,
volume = "63",
year = "1992",
pages = "29-38" }
@article{brs1991b,
author = {C. Brezinski and M. Redivo-Zaglia and H. Sadok},
journal = NUMALGO,
title = {Addendum to ``{A}voiding breakdown and near-breakdown in {Lanczos} type algorithms''},
year = {1992},
pages = {133-136},
volume = {2},
}
@article{brs1997,
author = "C. Brezinski and M. Redivo-Zaglia and H. Sadok",
title = "Breakdowns in the implementation of the {Lanczos} method for solving linear systems",
journal = CMA,
volume = "33",
number = "1",
year = "1997",
pages = "31-44" }
@misc{brs1998,
author = "C. Brezinski and M. Redivo-Zaglia and H. Sadok",
title = "Problems of breakdown and near-breakdown in {Lanczos}-based algorithms",
howpublished = "NATO ASI Series C Mathematical and Physical Sciences-Advanced Study Institute 508",
year = "1998",
pages = "255-270" }
@article{brs1999,
author = "C. Brezinski and M. Redivo-Zaglia and H. Sadok",
title = "New look-ahead {Lanczos}-type algorithms for linear systems",
journal = NUMAT,
volume = "83",
number = "1",
year = "1999",
pages = "53-85" }
@article{brs2000,
author = "C. Brezinski and M. Redivo-Zaglia and H. Sadok",
title = "The matrix and polynomial approaches to {Lanczos}-type algorithms",
journal = JCAM,
volume = "123",
number = "1-2",
year = "2000",
pages = "241-260" }
@article{brs2002,
author = "C. Brezinski and M. Redivo-Zaglia and H. Sadok",
title = "A review of formal orthogonality in {Lanczos}-based methods",
journal = JCAM,
volume = "140",
number = "1",
year = "2002",
pages = "81-98" }
@article{brse2008,
author = "C. Brezinski and G. Rodriguez and S. Seatzu",
title = "Error estimates for linear systems with applications to regularization",
journal = NUMALGO,
volume = "49",
number = "1-4",
year = "2008",
pages = "85-104" }
@article{brse2009,
author = "C. Brezinski and G. Rodriguez and S. Seatzu",
title = "Error estimates for the regularization of least squares problems",
journal = NUMALGO,
volume = "51",
number = "1",
year = "2009",
pages = "61-76" }
@article{bs1991,
author = "C. Brezinski and H. Sadok",
title = "Avoiding breakdown in the {CGS} algorithm",
journal = NUMALGO,
volume = "1",
year = "1991",
pages = "199-206" }
@article{bs1993,
author = "C. Brezinski and H. Sadok",
title = "Lanczos-type algorithms for solving systems of linear equations",
journal = ANM,
volume = "11",
year = "1993",
pages = "443-473" }
@article{bsrz1994,
author = "C. Brezinski and H. Sadok and M. Redivo-Zaglia",
title = "Orthogonal polynomials and the {Lanczos} method",
journal = "Banach Center Publications",
volume = "29",
number = "1",
year = "1994",
pages = "19-33" }
@book{brt2014,
author = "C. Brezinski and D. Tourn{\`e}s",
title = "Andr{\'{e}}{-}{L}ouis {Cholesky} (1875-1918), {M}athematician, {T}opographer and {A}rmy {O}fficer",
publisher = "Birkh{\"a}user",
address = "Basel",
year = "2014" }
@book{bt2014,
author = "C. Brezinski and D. Tourn{\`e}s",
title = "{Andr{\'e}-Louis Cholesky}, mathematician, topographer and army officer",
publisher = "Birkh{\"a}user",
year = "2014" }
@inproceedings{bw2001,
author = "C. Brezinski and L. Wuytack",
title = "Numerical analysis in the twentieth century",
booktitle = "Numerical analysis: {H}istorical Developments in the 20th Century",
editor = "C. Brezinski and L. Wuytack",
publisher = "North-Holland",
address = "Amsterdam",
year = "2001",
pages = "1-40" }
@article{blss2007,
author = "F. Brezzi and K. Lipnikov and M. Shashkov and V. Simoncini",
title = "A new discretization methodology for diffusion problems on generalized polyhedral meshes",
journal = CMAME,
volume = "196",
number = "37-40",
year = "2007",
pages = "3682-3692" }
@article{bsv2012,
author = "M. Briani and A. Sommariva and M. Vianello",
title = "Computing {Fekete} and {Lebesgue} points: simplex, square, disk",
journal = JCAM,
volume = "236",
number = "9",
year = "2012",
pages = "2477-2486" }
@article{bck1961,
author = "L. Brickman",
title = "On the field of values of a matrix",
journal = PAMS,
volume = "12",
number = "1",
year = "1961",
pages ="61-66" }
@article{brha2000,
author = "D. Bridges and R. Havea",
title = "A constructive analysis of a proof that the numerical range is convex",
journal = "LMS J. Comput. Math.",
volume = "3",
year = "2000",
pages = "191-206" }
@article{brgr2006,
author = "R. Bridson and C. Greif",
title = "A multipreconditioned conjugate gradient algorithm",
journal = SIMAX,
volume = "27",
number = "4",
year = "2006",
pages = "1056-1068" }
@book{brg1987,
author = "W. L. Briggs",
title = "A Multigrid Tutorial",
year = "1987",
publisher = "SIAM" }
@article{brh1990,
author = "W. L. Briggs and V. E. Henson",
title = "{FFT} as a multigrid algorithm",
journal = SIREV,
volume = "32",
year = "1990",
pages = "252-261" }
@article{brh1993,
author = "W. L. Briggs and V. E. Henson",
title = "Wavelets and multigrid",
journal = SISC,
volume = "14",
year = "1993",
pages = "506–510" }
@book{bhmc2000,
author = "W. L. Briggs and V. E. Henson and S. F. McCormick",
title = "A Multigrid Tutorial",
edition = "2nd",
publisher = "SIAM",
year = "2000" }
@article{brp1998,
author = "S. Brin and L. Page",
title = "The anatomy of a large-scale hypertextual web search engine",
journal = "Comput. Networks ISDN Syst.",
volume = "30",
year = "1998",
pages = "107-117" }
@phdthesis{brk1984,
author = "S. Brinkkemper",
title = "Two classes of preconditioning matrices",
school = "Dept. of Informatics, Catholic University of Nijmegen",
year = "1984" }
@techreport{brk1985,
author = {S. Brinkkemper},
title = {A class of incomplete block factorization methods},
year = {1985},
number = {71},
institution = {Catholic University of Nijmegen},
}
@book{bri1854b,
author = "F. Brioschi",
title = "La Teorica dei Determinanti e le sue Principali Applicazioni",
publisher = "Bizzoni",
year = "1854" }
@article{bri1854,
author = "F. Brioschi",
title = "Note sur un th{\'{e}}or{\`e}me relatif aux d{\'{e}}terminants gauches",
journal = JMPA,
volume = "19",
year = "1854",
pages = "253-256" }
@book{bri1856,
author = "F. Brioschi",
title = "Th{\'{e}}orie des D{\'{e}}terminants et leurs Principales Applications",
publisher = "Mallet-Bachelier",
address = "Paris",
year = "1856" }
@article{bgp1987,
author = "M. O. Bristeau and R. Glowinski and J. P{\'e}riaux",
title = "Numerical methods for the {Navier-Stokes} equations",
journal = CPR,
volume = "6",
year = "1987",
pages = "73-187" }
@article{brbu2007,
author = "C. Brittin and M. I. Bueno",
title = "Numerical properties of shifted tridiagonal {LU} factorizations",
journal = MJM,
volume = "4",
number = "3",
year = "2007",
pages = "277-290" }
@article{brgr2002,
author = "O. Br{\"{o}}ker and M. J. Grote",
title = "Sparse approximate inverse smoothers for geometric and algebraic multigrid",
journal = ANM,
volume = "41",
number = "1",
year = "2002",
pages = "61-80" }
@article{bs1956,
author = "R. A. Brooker and F. H. Sumner",
title = "The method of {Lanczos} for calculating the characteristic roots and vectors of a real symmetric matrix",
journal = "Proc. Instn. Elect. Engrs B.",
volume = "103",
year = "1956",
pages = "114-119" }
@article{brks2006,
author = "B. P. Brooks",
title = "The coefficients of the characteristic polynomial in terms of the eigenvalues and the elements of an $n\times n$ matrix",
journal = AML,
volume = "19",
number = "6",
year = "2006",
pages = "511-515" }
@inproceedings{batd2020,
author = "C. Brown and A. Abdelfattah and S. Tomov and J. J. Dongarra",
title = "Design, optimization, and benchmarking of dense linear algebra algorithms on {AMD GPUs}",
booktitle = "IEEE High Performance Extreme Computing Conference",
publisher = "IEEE",
year = "2020",
pages = "1-7" }
@article{brsp2004,
author = "E. S. Brown and I. M. Spitkovsky",
title = "On flat portions on the boundary of the numerical range",
journal = LAA,
volume = "390",
year = "2004",
pages = "75-109" }
@article{brow1991,
author = "P. N. Brown",
title = "A theoretical comparison of the {Arnoldi} and {GMRES} algorithms",
journal = SISSC,
volume = "12",
number = "1",
year = "1991",
pages = "58-78" }
@article{bh1989,
author = "P. N. Brown and A. C. Hindmarsh",
title = "Reduced storage matrix methods in stiff {ODE} systems",
journal = AMC,
volume = "31",
year = "1989",
pages = "40-91" }
@article{bw1997,
author = "P. N. Brown and H. F. Walker",
title = "{GMRES} on (nearly) singular systems",
journal = SIMAX,
volume = "18",
number = "1",
year = "1997",
pages = "37-51" }
@article{bro1930,
author = "E. T. Browne",
title = "The characteristic roots of a matrix",
journal = BAMS,
volume = "36",
number = "10",
year = "1930",
pages = "705-710" }
@article{bro1939,
author = "E. T. Browne",
title = "Limits to the characteristic roots of a matrix",
journal = AMM,
volume = "46",
number = "5",
year = "1939",
pages = "252-265" }
@article{bdghm2000,
author = "S. Browne and J. Dongarra and N. Garner and G. Ho and P. Mucci",
title = "A portable programming interface for performance evaluation on modern processors",
journal = IJHSC,
volume = "14",
number = "3",
year = "2000",
pages = "189-204" }
@article{bry1964,
author = "C. G. Broyden",
title = "Some generalisations of the theory of successive over-relaxation",
journal = NUMAT,
volume = "6",
number = "1",
year = "1964",
pages = "269-284" }
@article{bry1973,
author = "C. G. Broyden",
title = "Some condition number bounds for the {Gauss}ian elimination process",
journal = JIMA,
volume = "12",
year = "1973",
pages = "273-286" }
@incollection{bry1991,
author = "C. G. Broyden",
title = "Classical methods for linear equations",
booktitle = "Computer Algorithms for Solving Linear Algebraic Equations. NATO ASI Series, vol 77",
editor = "E. Spedicato",
publisher = "Springer",
year = "1991",
pages = "1-26",
note = "NATO ASI F, volume 77" }
@article{brfo1999,
author = "C. G. Broyden and P. Foschi",
title = "Duality in conjugate gradient methods",
journal = NUMALGO,
volume = "22",
year = "1999",
pages = "113-128" }
@article{brve2001,
author = "C. G. Broyden and M. T. Vespucci",
title = "On the convergence of {Krylov} linear equation solvers",
journal = OMS,
volume = "16",
number = "1-4",
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author = {E. C. Carson and J. W. Demmel},
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year = {2014},
address = {Berkeley, CA},
number = {UCB/EECS-2014-18},
institution = {EECS Department, University of California},
}
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author = {E. C. Carson and J. W. Demmel},
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year = {2014},
address = {Berkeley, CA},
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author = {A. Cegielski},
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@techreport{ce1937b,
author = "L. Cesari",
title = "Sulla risoluzione dei sistemi di equazioni lineari per approssimazioni successive",
institution = "Istituto per le applicazioni del calcolo, Consiglio Nazionale delle Richerche",
address = "Roma",
number = "12",
year = "1937" }
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year = "1937",
pages = "285-296" }
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volume = "25",
year = "1937",
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author = "J. L. Chabert",
title = "Gauss et la m{\'{e}}thode des moindres carr{\'{e}}s",
journal = RHS,
volume = "42",
number = "1-2",
year = "1989",
pages = "5-26" }
@book{cha1999,
author = "J. L. Chabert",
title = "A History of Algorithms. From the Pebble to the Microchip",
publisher = "Springer-Verlag",
address = "Berlin, Heidelberg",
year = "1999" }
@book{chac1929,
author = "A. B. Chace",
title = "The Rhind Mathematical Papyrus, {V}olume {I}",
publisher = "Mathematical Association of America",
year = "1929" }
@book{chac1929b,
author = "A. B. Chace and L. Bull and H. P. Manning",
title = "The Rhind Mathematical Papyrus, {V}olume {II}",
publisher = "Mathematical Association of America",
year = "1929" }
@techreport{cc1995,
author = {F. Chaitin-Chatelin},
title = {Le calcul qualitatif. {C}omment donner un sens {\`a} des r{\'e}sultats faux ?},
year = {1995},
number = {TR/PA/95/10},
institution = {CERFACS},
}
@book{ccf1996,
author = "F. Chaitin-Chatelin and V. Frayss{\'{e}}",
title = "Lectures on Finite Precision Computations",
publisher = "SIAM",
year = "1996" }
@inproceedings{ctp2000,
author = "F. Chaitin-Chatelin and E. Traviesas and L. Planti{\'e}",
title = "Understanding {Krylov} methods in finite precision",
booktitle = "International Conference on Numerical Analysis and Its Applications",
publisher = "Springer",
address = "Berlin, Heidelberg",
year = "2000" }
@incollection{cct2005,
author = "F. Chaitin-Chatelin and E. Traviesas-Cassan",
title = "{PRECISE} and the quality of reliable numerical software",
booktitle = "Accuracy and Reliability in Scientific Computing",
publisher = "SIAM",
year = "2005",
pages = "95-108" }
@incollection{cct2005b,
author = "F. Chaitin-Chatelin and E. Traviesas-Cassan",
title = "Qualitative computing",
booktitle = "Accuracy and Reliability in Scientific Computing",
publisher = "SIAM",
year = "2005",
pages = "77-92" }
@techreport{cbn1986,
author = "R. M. Chamberlain",
title = "An algorithm for {LU} factorization with partial pivoting on the hypercube",
institution = "Chr. Michelsen Institute",
number = "CCS 86/11",
year = "1986" }
@incollection{cbn1987,
author = "R. M. Chamberlain",
title = "An alternative view of {LU} factorization with partial pivoting on a hypercube multiprocessor",
booktitle = "Hypercube Multiprocessors 1987",
editor = "M. T. Heath",
publisher = "SIAM",
year = "1987",
pages = "569-575" }
@article{ccgsst2020,
author = "E. Y. Chan and R. M. Corless and L. {Gonzalez-Vega} and J. R. Sendra and J. Sendra and S. E. Thornton",
title = "Upper {Hessenberg} and {Toeplitz} bohemians",
journal = LAA,
volume = "601",
year = "2020",
pages = "72-100" }
@book{cgl2007,
author = "R. H. Chan and C. Greif and D. P. {O'~Leary}",
title = "Milestones in Matrix Computation: The Selected Works of {Gene H. Golub} with Commentaries",
publisher = "Oxford University Press",
address = "Oxford",
year = "2007" }
@article{ch1982,
author = "T. F. Chan",
title = "An improved algorithm for computing the singular value decomposition",
journal = TOMS,
volume = "8",
number = "1",
year = "1982",
pages = "72-83" }
@article{ch1984,
author = "T. F. Chan",
title = "On the existence and computation of {LU} factorizations with small pivots",
journal = MATCOMP,
volume = "42",
number = "168",
year = "1984",
pages = "535-547" }
@article{ch1987,
author = "T. F. Chan",
title = "Analysis of preconditioners for domain decomposition",
journal = SINUM,
volume = "24",
number = "2",
year = "1987",
pages = "382-390" }
@article{ch1987b,
author = "T. F. Chan",
title = "Rank revealing {QR} factorizations",
journal = LAA,
volume = "88-89",
year = "1987",
pages = "67-82" }
@inproceedings{ch1989,
author = "T. F. Chan",
title = "Domain decomposition algorithms and computational fluid dynamics",
booktitle = "Parallel Computing: Issues in Applied Research and Development",
editor = "J. J. Dongarra and I. S. Duff and P. Gaffney and S. McKee",
publisher = "Ellis Horwood",
year = "1989",
pages = "65-82" }
@article{cha1991,
author = "T. F. Chan",
title = "Fourier analysis of relaxed incomplete factorization preconditioners",
journal = SISSC,
volume ="12",
year = "1991",
pages = "668-680" }
@misc{chch2000,
author = "T. F. Chan and K. Chen",
title = "Two-stage preconditioners using wavelet band splitting and sparse approximation",
howpublished = "Dpt. of Mathematics, University of California, Los Angeles",
year = "2000" }
@article{chch2002,
author = "T. F. Chan and K. Chen",
title = "On two variants of an algebraic wavelet preconditioner",
journal = SISC,
volume = "24",
number = "1",
year = "2002",
pages = "260-283" }
@article{ce1989,
author = "T. F. Chan and H. C. Elman",
title = "Fourier analysis of iterative methods for elliptic problems",
journal = SIREV,
volume = "31",
number = "1",
year = "1989",
pages = "20-49" }
@article{cf1988,
author = "T. F. Chan and D. E. Foulser",
title = "Effectively well conditioned linear systems",
journal = SISSC,
volume = "9",
year = "1988",
pages = "963-969" }
@article{cgsst1994,
author = "T. F. Chan and E. Gallopoulos and V. Simoncini and T. Szeto and C. H. Tong",
title = "A quasi-minimal residual variant of the {Bi-CGStab} algorithm for nonsymmetric systems",
journal = SISC,
volume = "15",
number = "2",
year = "1994",
pages = "338-347" }
@techreport{cgt1995,
author = {T. F. Chan and J. R. Gilbert and S.-H. Teng},
title = {Geometric spectral partitioning},
year = {1995},
number = {?},
institution = {Xerox Parc, Palo Alto},
}
@book{cgpw1988,
author = "T. F. Chan and R. Glowinski and J. P{\'e}riaux and O. B. Widlund Eds.",
title = "Second International Symposium on Domain Decomposition Methods for Partial Differential Equations",
publisher = "SIAM",
year = "1989" }
@book{cgpw1990,
author = "T. F. Chan and R. Glowinski and J. P{\'e}riaux and O. B. Widlund Eds.",
title = "Third International Symposium on Domain Decomposition Methods for Partial Differential Equations",
publisher = "SIAM",
year = "1990" }
@misc{cgz1997,
author = "T. F. Chan and S. Go and L. Zikatanov",
title = "Lecture notes on multilevel methods for elliptic problems on unstructured grids",
howpublished = "Department of Mathematics, University of California, Los Angeles",
year = "1997" }
@techreport{cgo1988,
author = {T. F. Chan and D. Goovaerts},
title = {{Schwarz=Schur}: overlapping versus non overlapping domain decomposition},
year = {1988},
number = {CAM 88-21},
institution = {Dept.of Mathematics, UCLA},
}
@article{cgo1990,
author = "T. F. Chan and D. Goovaerts",
title = "A note on the efficiency of domain decomposed incomplete factorizations",
journal = SISSC,
volume = "11",
number = "4",
year = "1990",
pages = "794-803" }
@article{cgo1990b,
author = "T. F. Chan and D. Goovaerts",
title = "On the relationship between overlapping and nonoverlapping domain decomposition methods",
journal = SIMAX,
volume = "13",
year = "1990",
pages = "663-670" }
@techreport{cho1990,
author = {T. F. Chan and T. Y. Hou},
title = {Domain decomposition interface preconditioners for general second order elliptic problems},
year = {1990},
number = {CAM 88-16},
institution = {Dept. of Mathematics, UCLA},
}
@article{chl1991,
author = "T. F. Chan and T. Y. Hou and P. L. Lions",
title = "Geometry related convergence results for domain decomposition algorithms",
journal = SINUM,
volume = "28",
number = "2",
year = "1991",
pages = "378–391" }
@article{cjz1983,
author = "T. F. Chan and K. R. Jackson and B. Zhu",
title = "Alternating direction incomplete factorizations",
journal = SINUM,
volume = "20",
number = "2",
year = "1983",
pages = "239-257" }
@inproceedings{chk1990,
author = "T. F. Chan and D. E. Keyes",
title = "Interface preconditionings for domain decomposed convection-diffusion operators",
booktitle = "Third International Symposium on Domain Decomposition Methods for Partial Differential Equations",
editor = "T. F. Chan and R. Glowinski and J. P{\'e}riaux and O. B. Widlund",
publisher = "SIAM",
year = "1990",
pages = "245-262" }
@article{ckt1989,
author = "T. F. Chan and C. C. J. Kuo and C. Tong",
title = "Parallel elliptic preconditioners: {Fourier} analysis and performance on the {Connection} {Machine}",
journal = CPC,
volume = "53",
year = "1989",
pages = "237–252" }
@article{ckt1990,
author = "T. F. Chan and C. C. J. Kuo and C. Tong",
title = "Multilevel filtering preconditioners",
journal = SIMAX,
volume = "11",
number = "3",
year = "1990",
pages = "403-429" }
@article{cmv1997,
author = "T. F. Chan and S. D. Margenov and P. S. Vassilevski",
title = "Performance of block-{ILU} factorization preconditioners based on block-size reduction for {2D} elasticity systems",
journal = SISC,
volume = "18",
number = "5",
year = "1997",
pages = "1355-1366" }
@inproceedings{cma1991,
author = "T. F. Chan and T. Mathew",
title = "An application of the probing technique to the vertex space method in domain decomposition",
booktitle = "Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations",
editor = "R. Glowinski and Y. A. Kuznetsov and G. Meurant and J. P{\'e}riaux and O. B. Widlund",
publisher = "SIAM",
year = "1991",
pages = "101-111" }
@inproceedings{cma1992b,
author = "T. F. Chan and T. Mathew",
title = "Fourier and probe variants of the vertex space domain decomposition algorithm",
booktitle = "Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations",
editor = "D. E. Keyes and T. F. Chan and G. Meurant and J. S. Scroggs and R. G. Voigt",
publisher = "SIAM",
year = "1992",
pages = "236-249" }
@article{cma1992,
author = "T. F. Chan and T. Mathew",
title = "The interface probing in domain decomposition",
journal = SIMAX,
volume = "13",
year = "1992",
pages = "212-238" }
@article{chm1994,
author = "T. F. Chan and T. Mathew",
title = "Domain decomposition algorithms",
journal = ACTNUM,
volume = "3",
year = "1994",
pages = "61-143" }
@techreport{cm1990,
author = "T. F. Chan and G. Meurant",
title = "Fourier analysis of block preconditioners",
institution = "University of California, Los Angeles",
number = "CAM 90-04",
year = "1990" }
@techreport{cpv1991,
author = {T. F. Chan and L. {De Pillis} and H. van der Vorst},
institution = {Dpt. of Mathematics, UCLA},
title = {A transpose-free squared {Lanczos} algorithm and application to solving nonsymmetric linear systems},
year = {1991},
number = {91-17 CAM},
}
@article{cpv1998,
author = "T. F. Chan and L. {De Pillis} and H. van der Vorst",
title = "Transpose-free formulations of {Lanczos}-type methods for nonsymmetric linear systems",
journal = NUMALGO,
volume = "17",
number = "1",
year = "1998",
pages = "51-66" }
@techreport{cre1985,
author = {T. F. Chan and D. C. Resasco},
title = {A survey of preconditioners for domain decomposition},
year = {1985},
number = {YALEU/DCS/RR-414},
institution = {Dept. of Computer Science, Yale University},
}
@article{cre1986,
author = "T. F. Chan and D. C. Resasco",
title = "Generalized deflated block elimination",
journal = SINUM,
volume = "23",
number = "5",
year = "1986",
pages = "913-924" }
@article{cre1987b,
author = "T. F. Chan and D. C. Resasco",
title = "A domain-decomposed fast {Poisson} solver on a rectangle",
journal = SISSC,
volume = "8",
number = "1",
year = "1987",
pages = "s14-s26",
note = "Errata, SISSC, 8(3), p.~457" }
@inproceedings{cre1987,
author = "T. F. Chan and D. C. Resasco",
title = "Analysis of domain decomposition preconditioners on irregular regions",
booktitle = "Proceedings of the Sixth IMACS Int'l Symp. on Computer Methods for Partial Differential Equations",
editor = "R. Vichnevetsky and R. Stepleman",
publisher = "IMACS",
year = "1987",
pages = "317-322" }
@inproceedings{cre1988,
author = "T. F. Chan and D. C. Resasco",
title = "A framework for the analysis and construction of domain decomposition preconditioners",
booktitle = "First International Symposium on Domain Decomposition Methods for Partial Differential Equations",
editor = "R. Glowinski and G. H. Golub and G. Meurant and J. P{\'e}riaux",
publisher = "SIAM",
year = "1988",
pages = "217-230" }
@inproceedings{csm1994,
author = "T. F. Chan and B. F. Smith",
title = "Domain decomposition and multigrid algorithms for elliptic problems on unstructured meshes",
booktitle = "Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International
Conference on Domain Decomposition",
editor = "D. E. Keyes and J. Xu",
publisher = "American Mathematical Society",
year = "1994",
pages = "175-189." }
@article{cs1994,
author = "T. F. Chan and T. Szeto",
title = "A composite step conjugate gradients squared algorithm for solving nonsymmetric linear systems",
journal = NUMALGO,
volume = "7",
number = "1",
year = "1994",
pages = "17-32" }
@article{cs1996,
author = "T. F. Chan and T. Szeto",
title = "Composite step product methods for solving nonsymmetric linear systems",
journal = SISC,
volume = "17",
number = "6",
year = "1996",
pages = "1491-1508" }
@article{ctw1997,
author = "T. F. Chan and W. P. Tang and W. L. Wan",
title = "Wavelet sparse approximate inverse preconditioners",
journal = BITNM,
volume = "37",
number = "3",
year = "1997",
pages = "644-660" }
@techreport{ctu1989,
author = {T. F. Chan and R. S. Tuminaro},
title = {Analysis of a parallel multigrid algorithm},
year = {1989},
number = {CAM 89-29},
institution = {University of California, Los Angeles},
}
@inproceedings{chva2000,
author = "T. F. Chan and P. Vanek",
title = "Detection of strong coupling in algebraic multigrid solvers",
booktitle = "Multigrid Methods VI",
editor = " E. Dick and K. Riemslagh and J. Vierendeels",
publisher = "Springer",
address = "Berlin, Heidelberg",
year = "2000",
pages = "11-23" }
@article{chv1995,
author = "T. F. Chan and P. S. Vassilevski",
title = "A framework for block {ILU} factorizations using block-size reduction",
journal = MATCOMP,
volume = "64",
number = "209",
year = "1995",
pages = "129-156" }
@techreport{cvdv1994,
author = {T. F. Chan and H. A. {van der Vorst}},
title = {Approximate and incomplete factorizations},
year = {1994},
number = {871},
institution = {Dept. of Mathematics, University of Utrecht},
}
@article{cw1997,
author = "T. F. Chan and W. L. Wan",
title = "Analysis of projection methods for solving linear systems with multiple right-hand sides",
journal = SISC,
volume = "18",
number = "6",
year = "1997",
pages = "1698-1721" }
@article{cwy1997,
author = "T. F. Chan and Q. Ye",
title = "A mixed product {Krylov} subspace method for solving nonsymmetric linear systems",
journal = AJM,
volume = "1",
number = "3",
year = "1997",
pages = "422-434" }
@article{chzo1996,
author = "T. F. Chan and J. Zou",
title = "A convergence theory of multilevel additive {Schwarz} methods on unstructured meshes",
journal = NUMALGO,
volume = "13",
number = "2",
year = "1996",
pages = "365-398" }
@article{cg1980,
author = "W. M. Chan and A. George",
title = "A linear time implementation of the {Reverse Cuthill-McKee} algorithm",
journal = BITNM,
volume = "20",
number = "1",
year = "1980",
pages = "8-14" }
@phdthesis{ch1978,
author = "R. Chandra",
title = "Conjugate gradient methods for partial differential equations",
school = "Dpt. of Computer Science, Yale University",
note = "Report 129",
year = "1978" }
@inproceedings{ces1975,
author = "R. Chandra and S. C. Eisenstat and M. H. Schultz",
title = "Conjugate gradient methods for partial differential equations",
booktitle = "Computer Methods for Partial Differential Equations",
editor = "R. Vichnevetsky",
publisher = "AICA",
year = "1975",
pages = "60-64" }
@inproceedings{ces1977,
author = "R. Chandra and S. C. Eisenstat and M. H. Schultz",
title = "The modified conjugate residual method for partial differential equations",
booktitle = "Advances in Computer Methods for Partial Differential Equations {II}",
editor = "R. Vichnevetsky",
year = "1977",
pages = "13-19" }
@article{cgsxz2007,
author = "S. Chandrasekaran and M. Gu and X. Sun and J. Xia and J. Zhu",
title = "A superfast algorithm for {Toeplitz} systems of linear equations",
journal = SIMAX,
volume = "29",
number = "4",
year = "2007",
pages = "1247-1266" }
@incollection{cgxz2007,
author = "S. Chandrasekaran and M. Gu and J. Xia and J. Zhu",
title = "A fast {QR} algorithm for companion matrices",
booktitle = "Recent Advances in Matrix and Operator Theory",
publisher = "Birkh{\"{a}}user",
address = "Basel",
year = "2007",
pages = "111-143" }
@misc{cip1992,
author = "S. Chandrasekaran and I. C. F. Ipsen",
title = "On the singular value decomposition of triangular matrices",
howpublished = "Proceedings of the 1992 Shanghai International Numerical Algebra and its Applications Conference",
year = "1992" }
@article{cip1994,
author = "S. Chandrasekaran and I. C. F. Ipsen",
title = "On rank-revealing factorisations",
journal = SIMAX,
volume = "15",
number = "2",
year = "1994",
pages = "592-622" }
@article{cip1995,
author = "S. Chandrasekaran and I. C. F. Ipsen",
title = "On the sensitivity of solution components in linear systems of equations",
journal = SIMAX,
volume = "16",
number = "1",
year = "1995",
pages = "93-112" }
@article{cip1995b,
author = "S. Chandrasekaran and I. C. F. Ipsen",
title = "Analysis of a {QR} algorithm for computing singular values",
journal = SIMAX,
volume = "16",
number = "2",
year = "1995",
pages = "520-535" }
@article{chl1985,
author = "K. M. Chandy and L. Lamport",
title = "Distributed snapshots: determining global states of distributed systems",
journal = "ACM Trans. Comput. Syst.",
volume = "3",
number = "1",
year = "1985",
pages = "63-75" }
@inproceedings{cha1969,
author = "A. Chang",
title = "Application of sparse matrix methods in electric power system analysis",
booktitle = "Proceedings of the Symposium on Sparse Matrices and their Applications",
editor = "R. A. Willoughby",
publisher = "IBM, Thomas J. Watson Research Center",
year = "1969",
pages = "113-122" }
@article{chfc2016,
author = "F. C. Chang",
title = "Matrix inverse as by-product of determinant",
journal = "British J. Math. Comput. Sci.",
volume = "12",
number = "4",
year = "2016",
pages = "1-21" }
@article{cxw2002,
author = "{X.-W.} Chang",
title = "Some features of {Gaussian} elimination with rook pivoting",
journal = BITNM,
volume = "42",
number = "1",
year = "2002",
pages = "66-83" }
@article{cxw2012,
author = "{X.-W.} Chang",
title = "On the perturbation of the {Q}-factor of the {QR} factorization",
journal = LAA,
volume = "19",
number = "3",
year = "2012",
pages ="607-619" }
@article{cgp2008,
author = "{X.-W.} Chang and G. H. Golub and C. C. Paige",
title = "Towards a backward perturbation analysis for data least squares problems",
journal = SIMAX,
volume = "30",
number = "4",
year = "2008",
pages = "1281-1301" }
@article{cp1998,
author = "{X.-W.} Chang and C. C. Paige",
title = "On the sensitivity of the {LU} factorization",
journal = BITNM,
volume = "38",
number = "3",
year ="1998",
pages = "486-501" }
@article{cp2001,
author = {{X.-W.} Chang and C. C. Paige},
journal = NUMAT,
title = {Componentwise perturbation analyses for the {QR} factorization},
year = {2001},
number = {2},
pages = {319-345},
volume = {88},
}
@article{cp2007,
author = "{X.-W.} Chang and C. C. Paige",
title = "Euclidean distances and least squares problems for a given set of vectors",
journal = ANM,
volume = "57",
year = "2007",
pages = "1240-1244" }
@article{cps1996,
author = "{X.-W.} Chang and C. C. Paige and G. W. Stewart",
title = "New perturbation analyses for the {Cholesky} factorization",
journal = IMAJNA,
volume = "16",
number = "4",
year = "1996",
pages ="457-484" }
@article{cpt2008,
author = "{X.-W.} Chang and C. C. Paige and D. Titley-P{\'e}loquin",
title = "Characterizing matrices that are consistent with given solutions",
journal = SIMAX,
volume = "30",
number = "4",
year = "2008",
pages = "1406-1420" }
@article{cptp2021,
author = "{X.-W.} Chang and C. C. Paige and D. {Titley-Peloquin}",
title = "Structure in loss of orthogonality",
journal = LAA,
volume = "623",
year = "2021",
pages = "149-167" }
@article{chst2010,
author = "{X.-W.} Chang and D. Stehl{\'e}",
title = "Rigorous perturbation bounds of some matrix factorizations",
journal = SIMAX,
volume = "31",
number = "5",
year = "2010",
pages = "2841-2859" }
@article{chtp2009,
author = "{X.-W.} Chang and D. {Titley-Peloquin}",
title = "Backward perturbation analysis for scaled total least-squares problems",
journal = NLAA,
volume = "16",
number = "8",
year = "2009",
pages = "627-648" }
@article{chba2000,
author = "D. Chapelle and {K.-J.} Bathe",
title = "The mathematical shell model underlying general shell elements",
journal = IJNME,
volume = "48",
number = "2",
year = "2000",
pages = "289-313" }
@article{cs1997,
author = "A. Chapman and Y. Saad",
title = "Deflated and augmented {Krylov} subspace techniques",
journal = NLAA,
volume = "4",
year = "1997",
pages = "43-66" }
@article{csw2000,
author = "A. Chapman and Y. Saad and L. Wigton",
title = "High order {ILU} preconditioners for {CFD} problems",
journal = "Int. J. Numer. Methods Fluids",
volume = "33",
number = "6",
year = "2000",
pages = "767-788" }
@techreport{cdgky2020,
author = "A. Charara and J. J. Dongarra and M. Gates and J. Kurzak and A. {YarKhan}",
title = "{SLATE} mixed precision performance report",
institution = "University of Tennessee",
number = "SLATE Working Note ?",
year = "2020" }
@article{ckl2017,
author ="A. Charara and D. E. Keyes and H. Ltaief",
title = "A framework for dense triangular matrix kernels on various manycore architectures",
journal = CCPE,
volume = "29",
number = "15",
year = "2017",
pages = "e4187" }
@inproceedings{clk2016,
author ="A. Charara and H. Ltaief and D. E. Keyes",
title = "Redesigning triangular dense matrix computations on {GPUs}",
booktitle = "22nd International Conference on Parallel and Distributed Computing",
publisher = "Springer",
year = "2016",
pages = "477-489" }
@book{vch1910,
author = "G. {von Charasoff}",
title = "Das System des Marxismus. Darstellung und Kritik",
publisher = "Hans Bondy",
address = "Berlin",
year = "1910" }
@article{cbd2020,
author = "V. Charisopoulos and A. R. Benson and A. Damle",
title = "Entrywise convergence of iterative methods for eigenproblem",
journal = "Adv. Neural Inf. Process. Syst.",
volume = "33",
year = "2020",
pages = "5644-5655" }
@article{cro1989,
author = "P. Charrier and J. Roman",
title = "Algorithmique et calculs de complexit{\'e} pour un solveur de type dissection embo{\^\i}t{\'e}e",
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author = "P. I. Davies and N. J. Higham",
title = "Computing {$f(A)b$} for matrix functions $f$",
booktitle = "QCD and Numerical Analysis III",
editor = "A. Bori~i and A. Frommer and B. Jo{\'{o}} and A. Kennedy and B. Pendleton",
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author = "P. Davis and P. Rabinowitz",
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year = "1954",
pages = "183-191" }
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author = "P. Davis and P. Rabinowitz",
title = "Advances in orthonormalizing computation",
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year = "1961",
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author = "P. J. Davis",
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year = "2000" }
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author = "P. J. Davis and P. Rabinowitz",
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year = "1984" }
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author = "T. Davis",
title = "Forty two problems of first degree from {Diophantus}' {Arithmetica}",
school = "Wichita State University",
address = "USA",
year = "2010" }
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author = {T. A. Davis},
title = {Performance of an unsymmetric pattern multifrontal method for sparse {LU} factorization},
year = {1992},
number = {TR-92-014},
institution = {University of Florida},
}
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author = {T. A. Davis},
title = {Users' guide for the unsymmetric pattern multifrontal package},
year = {1993},
number = {TR-93-020},
institution = {University of Florida},
}
@techreport{dav1994,
author = {T. A. Davis},
title = {A combined unifrontal/multifrontal method for unsymmetric sparse matrices},
year = {1994},
number = {TR-94-005},
institution = {University of Florida},
}
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author = "T. A. Davis",
title = "A column pre-ordering strategy for the unsymmetric-pattern multifrontal method",
journal = TOMS,
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number = "2",
year = "2004",
pages = "165-195" }
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author = "T. A. Davis",
title = "Algorithm 832: {UMFPACK} V4.3 - an unsymmetric-pattern multifrontal method",
journal = TOMS,
volume = "30",
number = "2",
year = "2004",
pages = "196-199" }
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author = "T. A. Davis",
title = "Algorithm 849: {A} concise sparse {Cholesky} factorization package",
journal = TOMS,
volume = "31",
number = "4",
year = "2005",
pages = "587-591" }
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author = "T. A. Davis",
title = "Direct Methods for Sparse Linear Systems",
publisher = "SIAM",
year = "2006" }
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author = "T. A. Davis",
title = "Algorithm 915, {SuiteSparseQR}: {M}ultifrontal multithreaded rank-revealing sparse {QR} factorization",
journal = TOMS,
volume = "38",
number = "1",
year = "2011",
pages = "8:1-8:22" }
@article{dav2013,
author = "T. A. Davis",
title = "Algorithm 930, {FACTORIZE}: {A}n object-oriented linear system solver for {MATLAB}",
journal = TOMS,
volume = "39",
number = "4",
year = "2013",
pages = "1-18" }
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author = "T. A. Davis",
title = "Algorithm 1000: {SuiteSparse: GraphBLAS}: {G}raph algorithms in the language of sparse linear algebra",
journal = TOMS,
volume = "45",
number = "4",
year = "2019",
pages = "44:1-44:25" }
@article{dd1997,
author = "T. A. Davis and I. S. Duff",
title = "An unsymmetric{-}pattern multifrontal method for sparse {LU} factorization",
journal = SIMAX,
volume = "18",
number = "1",
year = "1997",
pages = "140-158" }
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author = "T. A. Davis and I. S. Duff",
title = "A combined unifrontal/multifrontal method for unsymmetric sparse matrices",
journal = TOMS,
volume = "25",
number = "1",
year = "1999",
pages = "1-20" }
@article{ddn2020,
author = "T. A. Davis and I. S. Duff and S. Nakov",
title = "Design and implementation of a parallel {Markowitz} threshold algorithm",
journal = SIMAX,
volume = "41",
number = "2",
year = "2020",
pages = "573-590" }
@article{dgln2004,
author = "T. A. Davis and J. R. Gilbert and S. I. Larimore and E. G. Ng",
title = "A column approximate minimum degree ordering algorithm",
journal = TOMS,
volume = "30",
number = "3",
year = "2004",
pages = "353-376" }
@article{daha1999,
author = "T. A. Davis and W. H. Hager",
title = "Modifying a sparse {Cholesky} factorization",
journal = SIMAX,
volume = "20",
number = "3",
year = "1999",
pages = "606-627" }
@article{daha2005,
author = "T. A. Davis and W. H. Hager",
title = "Row modifications of a sparse {Cholesky} factorization",
journal = SIMAX,
volume = "26",
number = "3",
year = "2005",
pages = "621-639" }
@article{dh2011,
author = "T. A. Davis and Y. Hu",
title = "{The University of Florida} sparse matrix collection",
journal = TOMS,
volume = "38",
number = "1",
year = "2011",
pages = "1-25" }
@article{dpn2010,
author = "T. A. Davis and E. Palamadai Natarajan",
title = "Algorithm 907: {KLU}, a direct sparse solver for circuit simulation problems",
journal = TOMS,
volume = "37",
number = "3",
year = "2010",
pages = "1-17" }
@article{drs2016,
author = "T. A. Davis and S. Rajamanickam and W. M. {Sid-Lakhdar}",
title = "A survey of direct methods for sparse linear systems",
journal = ACTNUM,
volume = "25",
year = "2016",
pages = "383-566" }
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journal = SIMAX,
volume = "11",
year = "1990",
pages = "383-402" }
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pages = "448-449" }
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number = "2",
year = "2011",
pages = "287-304" }
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year = "2017",
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year = "2019",
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institution = "University of Tennessee",
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note = "Also CS-89-87, Department of Computer Science, University of Tennessee" }
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author = {J. W. Demmel},
title = {Open problems in numerical linear algebra},
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number = {CS-92-164},
institution = {University of Minnesota},
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booktitle = "Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations",
editor = "D. E. Keyes and T. F. Chan and G. Meurant and J. S. Scroggs and R. G. Voigt",
publisher = "SIAM",
year = "1992",
pages = "151-194" }
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author = "Q. V. Dinh and R. Glowinski and J. P{\'e}riaux",
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@misc{ddrs2022,
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@techreport{dol1991,
author = "S. Doi and A. Lichnewsky",
title = "A graph-theory approach for analyzing the effects of ordering on {ILU} preconditionning",
institution = "INRIA",
address = "Rocquencourt, France",
number = "RR-1452",
year = "1991" }
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author = "S. Doi and T. Washio",
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year = "1999",
pages = "1995-2014" }
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author = "V. Dolean and M. J. Gander and A. Kyriakis",
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author = "V. Dolej{\v{s}\'{\i}} and P. Tich{\'{y}}",
title = "On efficient numerical solution of linear algebraic systems arising in goal-oriented error estimates",
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year = "2020",
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author = "J. M. Donato",
title = "Iterative methods for scalar and coupled systems of elliptic equations",
school = "Dept. of Mathematics, UCLA",
year = "1991" }
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author = "J. M. Donato and T. F. Chan",
title = "Fourier analysis of incomplete factorization preconditioners for {3D} anisotropic problems",
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year = "1992",
pages = "319-338" }
@techreport{ddfgkl2013,
author = "S. Donfack and J. J. Dongarra and M. Faverge and M. Gates and J. Kurzak and P. Luszczek",
title = "On algorithmic variants of parallel {Gaussian} elimination: {C}omparison of implementations in terms of performance and numerical properties",
institution = "INRIA",
number = "hal-00867837",
year = "2013",
note = "Also LAWN 280" }
@article{ddfgk2015,
author = "S. Donfack and J. J. Dongarra and M. Faverge and M. Gates and J. Kurzak and P. Luszczek and I. Yamazaki",
title = "A survey of recent developments in parallel implementations of {Gauss}ian elimination",
journal = CPE,
volume = "27",
number = "5",
year = "2015",
pages = "1292-1309" }
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author = "S. Dong and K. Liu",
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@techreport{don1980,
author = "J. J. Dongarra",
title = "{LINPACK} working note 3, {Fortran} {BLAS} timing",
institution = "Argonne National Laboratory",
number = "ANL-80-24. CM-P00068636",
year = "1980" }
@misc{don2022,
author = "J. J. Dongarra",
title = "A not so simple matter of software; {T}he evolution of mathematical software: {S}oftware and algorithms follow the hardware",
howpublished = "ACM, to be published",
year = "2022" }
@techreport{don2023,
author = "J. J. Dongarra and al.",
title = "Can the {United States} maintain its leadership in high-performance computing?",
institution = "Department of Energy, Office of Science",
year ="2023" }
@techreport{dbms1977,
author = "J. J. Dongarra and J. R. Bunch and C. B. Moler and G. W. Stewart",
title = "Preliminary {Linpack} user{'}s guide",
institution = "Argonne National Laboratory",
number = "ANL-AMD-TM-313",
note = "Linpack working note \# 9",
year = "1977" }
@book{dbms1979,
author = "J. J. Dongarra and J. R. Bunch and C. B. Moler and G. W. Stewart",
title = "Linpack User{'}s Guide",
publisher = "SIAM",
address = "Philadelphia",
year = "1979" }
@article{ddhd1990,
author = "J. J. Dongarra and J. {Du Croz} and S. Hammarling and I. S. Duff",
title = "Algorithm 679: {A} set of level 3 basic linear algebra subprograms: model implementation and test programs",
journal = TOMS,
volume = "16",
number ="1",
year = "1990",
pages = "18-28" }
@article{ddhh1988b,
author = "J. J. Dongarra and J. {Du Croz} and S. Hammarling and R. J. Hanson",
title = "Algorithm 656: An extended set of {FORTRAN} basic linear algebra subprograms",
journal = TOMS,
volume = "14",
number ="1",
year = "1988",
pages = "18-32" }
@article{ddhh1988,
author = "J. J. Dongarra and J. {Du Croz} and S. Hammarling and R. J. Hanson",
title = "An extended set of {FORTRAN} basic linear algebra subprograms",
journal = TOMS,
volume = "14",
number ="1",
year = "1988",
pages = "1-17" }
@article{dod1991,
author = "J. J. Dongarra and J. W. Demmel",
title = "{LAPACK}: a portable high-performance numerical library for linear algebra",
journal = "Supercomputer",
volume = "46",
year = "1991",
pages = "33-38" }
@book{ddgm1989,
author = "J. J. Dongarra and I. S. Duff and P. Gaffney and S. McKee Eds.",
title = "Vector and Parallel Computing, Issues in Applied Research and Development",
publisher = "Ellis Horwood",
year = "1989" }
@techreport{ddgh2018,
author = "J. J. Dongarra and I. S. Duff and M. Gates and A. Haidar and S. Hammarling and N. J. Higham and
J. Hogg and P. Valero Lara and P. Luszczek and M. Zounon and S. D. Relton and S. Tomov and T. Costa and S. Knepper",
title = "Batched {BLAS (Basic Linear Algebra Subprograms)} 2018 specification",
institution = "Innovative Computing Laboratory, University of Tennessee",
number = "ICL-UTK-1170-2018",
year = "2018" }
@book{ddsvdv1991,
author = "J. J. Dongarra and I. S. Duff and D. C. Sorensen and H. A. {van der Vorst}",
title = "Solving Linear Systems on Vector and Shared Memory Computers",
publisher = "SIAM",
year = "1991" }
@book{ddsv1998,
author = "J. J. Dongarra and I. S. Duff and D. C. Sorensen and H. A. van der Vorst",
title = "Numerical linear algebra for high-performance computers",
publisher = "SIAM",
year = "1998" }
@techreport{doei2003,
author = "J. J. Dongarra and V. Eijkhout",
title = "Finite-choice algorithm optimization in conjugate gradients",
institution = "University of Tennessee, Knoxville",
number = "UT-CS-03-502",
year = "2003" }
@article{deli2001,
author = "J. J. Dongarra and V. Eijkhout and P. Łuszczek",
title = "Recursive approach in sparse matrix {LU} factorization",
journal = "Sci. Program.",
volume = "9",
number = "1",
year = "2001",
pages = "51-60" }
@article{doe1984,
author = "J. J. Dongarra and S. C. Eisenstat",
title = "Squeezing the most out of an algorithm in {CRAY FORTRAN}",
journal = TOMS,
volume = "10",
number = "3",
year = "1984",
pages = "219-230" }
@inproceedings{dfll2012,
author = "J. J. Dongarra and M. Faverge and H. Ltaief and P. Luszczek",
title = "Exploiting fine-grain parallelism in recursive {LU} factorization",
booktitle = "Applications, Tools and Techniques on the Road to Exascale Computing",
publisher = "IOS Press",
year = "2012",
pages = "429-436" }
@article{dfll2014,
author = "J. J. Dongarra and M. Faverge and H. Ltaief and P. Luszczek",
title = "Achieving numerical accuracy and high performance using recursive tile {LU} factorization with partial pivoting",
journal = CCPE,
volume = "16",
number = "7",
year = "2014",
pages = "1408-1431" }
@article{dghkl2019,
author = "J. J. Dongarra and M. Gates and A. Haidar and J.Kurzak and P. Luszczek and al.",
title = "{PLASMA}: {P}arallel linear algebra software for multicore using {OpenMP}",
journal = TOMS,
volume = "45",
number = "2",
year = "2019",
pages = "16:1-16:35" }
@techreport{doge2022,
author = "J. J. Dongarra and A. Geist",
title = "Report on the {Oak Ridge National Laboratory's Frontier} system",
institution = "University of Tennessee",
number = "ICL-UT-22-05",
year = "2022" }
@article{dggmm2008,
author = "J. J. Dongarra and G. H. Golub and E. Grosse and C. B. Moler and K. Moore",
title = "Netlib and {NA-Net}: {B}uilding a scientific computing community",
journal = IEAHC,
volume = "30",
number = "2",
year = "2008",
pages = "30-41" }
@article{dg1985,
author = "J. J. Dongarra and E. Grosse",
title = "Distribution of mathematical software via electronic mail",
journal = "ACM SIGNUM Newsletter",
volume = "20",
number = "3",
year = "1985",
pages = "45-47" }
@article{dg1987,
author = "J. J. Dongarra and E. Grosse",
title = "Distribution of mathematical software via electronic mail",
journal = CACM,
volume = "30",
number = "5",
year = "1987",
pages = "403-407" }
@article{dgk1984,
author = "J. J. Dongarra and F. G. Gustavson and A. Karp",
title = "Implementing linear algebra algorithms for dense matrices on a vector pipeline machine",
journal = SIREV,
volume = "26",
number = "1",
year = "1984",
pages = "91-112" }
@inproceedings{dhp1997,
author = "J. J. Dongarra and S. Hammarling and A. Petitet",
title = "Case studies on the development of {ScaLAPACK} and the {NAG} numerical {PVM} library",
booktitle = "Quality of Numerical Software",
editor = "R. F. Boisvert",
publisher = "Springer",
address = "Boston, MA",
year = "1997",
pages = "236-248" }
@article{dhl2016,
author = "J. J. Dongarra and M. A. Heroux and P. Luszczek",
title = "High{-}performance conjugate{-}gradient benchmark: {A} new metric for ranking high{-}performance computing systems",
journal = "The International Journal of High Performance Computing Applications",
volume = "30",
number = "1",
year = "2016",
pages = "3-10" }
@article{doh1986,
author = "J. J. Dongarra and T. Hewitt",
title = "Implementing dense linear algebra algorithms using multitasking on the Cray {X–MP–4} (or approaching the {Gigaflop})",
journal = SISSC,
volume = "7",
number = "1",
year = "1986",
pages = "347-305" }
@article{dh1979,
author = "J. J. Dongarra and A. R Hinds",
title ="Unrolling loops in {Fortran}",
journal = SPE,
volume = "9",
number = "3",
year = "1979",
pages = "219-226" }
@article{dld2003,
author = "J. J. Dongarra and P. Luszczek and A. Petitet",
title = "The {LINPACK} benchmark: past, present and future",
journal = CCPE,
volume = "15",
number = "9",
year = "2003",
pages = "803-820" }
@article{dms1997,
author = "J. J. Dongarra and H. W. Meuer and E. Strohmaier",
title = "{TOP500} supercomputer sites",
journal = "Supercomputer",
volume = "13",
year = "1997",
pages = "89-111" }
@misc{dmss2000,
author = "J. J. Dongarra and H. W. Meuer and H. D. Simon and E. Strohmaier",
title = "High performance computing today",
howpublished = "Lawrence Berkeley National Laboratory",
year = "2000" }
@techreport{dm1980,
author = "J. J. Dongarra and C. B. Moler",
title = "Implementation guide for {Linpack}",
institution = "Argonne National Laboratory",
number = "ANL-80-105",
note = "Linpack working note \# 13",
year = "1980" }
@inproceedings{dm1984,
author = "J. J. Dongarra and C. B. Moler",
title = "Eispack: A package for solving matrix eigenvalue problems",
booktitle = "Sources and Development of Mathematical Software",
editor = "W. R. Cowell",
publisher = "Prentice-Hall",
address = "Englewood Cliffs, NJ",
year = "1984",
pages = "68-87" }
@misc{dora2000,
author = "J. J. Dongarra and P. Raghavan",
title = "A new recursive implementation of sparse {Cholesky} factorization",
howpublished = "Proceedings of the 16th IMACS World Congress on Scientific Computing, Applications, Mathematics, and Simulation",
year = "2000" }
@article{dos1984,
author = "J. J. Dongarra and A. H. Sameh",
title = "On some parallel banded system solvers",
journal = PARCOMP,
volume = "1",
year = "1984",
pages = "223-235" }
@article{dso1987,
author = "J. J. Dongarra and D. C. Sorensen",
title = "A fully parallel algorithm for the symmetric eigenvalue problem",
journal = SISSC,
volume = "8",
year = "1987",
pages = "139-154" }
@techreport{ds1982,
author = "J. J. Dongarra and G. W. Stewart",
title = "Linpack - {A} package for solving linear systems",
note = "Linpack working note 15",
institution = "Argonne National Laboratory",
number = "ANL-82-30",
year = "1982" }
@article{dtlkgyaha2017,
author = "J. Dongarra and S. Tomov and P. Luszczek and J. Kurzak and M. Gates and I. Yamazaki and H. Anzt and A. Haidar and A. Abdelfattah",
title = "With extreme computing the rules have changed",
journal = CSE,
volume = "19",
number = "3",
note = "IEEE",
year = "2017",
pages = "52-62" }
@article{dw1996,
author = "J. J. Dongarra and D. Walker",
title = "{MPI}: {A} standard message passing interface",
journal = "Supercomputer",
volume = "12",
number = "1",
year = "1996",
pages = "56-68" }
@techreport{dow1993,
author = {J. J. Dongarra and D. W. Walker},
title = {The design of linear algebra libraries for high performance computers},
year = {1993},
number = {ORNL/TM-12404},
institution = {Oak Ridge National Lab.},
}
@article{dw2000,
author = "J. J. Dongarra and J. Wa\'{s}niewski",
title = "LAPACK95 {-} high performance linear algebra package",
journal = "Math. Model. Anal.",
volume = "5",
number = "1",
year = "2000",
pages = "44-54" }
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author = "M. H. Doolittle",
booktitle = "Report of the Superintendant of the U.S. Coast and Geodetic Survey showing the progress of the work during fiscal year ending June 1878",
title = "Explanations and illustrations of method employed in the office in solution of normal equations and the adjustment of a triangulation",
publisher = "Government Publishing Office",
address = "Washington",
year = "1881",
pages = "115-120" }
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author = "F. M. Dopico and J. M. Molera",
title = "Perturbation theory for factorizations of {LU} type through series expansions",
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year = "2005",
pages = "561-581" }
@article{dkmo2009,
author = "F. M. Dopico and P. Koev and J. M. Molera",
title = "Implicit standard {Jacobi} gives high relative accuracy",
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year = "2009",
pages = "519-553" }
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author = "F. M. Dopico and F. Uhlig",
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pages = "590-622" }
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volume = "202",
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@misc{dor1990,
author = "J. L. Dorier",
title = "Analyse historique de l'{\'{e}}mergence des concepts {\'{e}}l{\'{e}}mentaires d'alg{\`e}bre lin{\'{e}}aire",
howpublished = "hal-02138152",
year = "1990" }
@article{dor1993,
author = "J. L. Dorier",
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volume = "3",
year = "1993",
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@article{dor1995,
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author = "F. W. Dorr",
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@article{drr1975,
author = "F. W. Dorr",
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@article{do1988,
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@techreport{degr1985,
author = "I. S. Duff and A. M. Erisman and C. W. Gear and J. K. Reid",
title = "Some remarks on inverses of sparse matrices",
institution = "Argonne National Lab.",
number = "ANL/MCS-TM-51",
year = "1985" }
@article{degr1988,
author = "I. S. Duff and A. M. Erisman and C. W. Gear and J. K. Reid",
title = "Sparsity structure and {Gauss}ian elimination",
journal = "ACM Signum newsletter",
volume = "23",
number = "2",
year = "1988",
pages = "2-8" }
@article{der1976,
author = "I. S. Duff and A. M. Erisman and J. K. Reid",
title = "On {George}'s nested dissection method",
journal = SINUM,
volume = "13",
number = "5",
year = "1976",
pages = "686-695" }
@book{der2017,
author = "I. S. Duff and A. M. Erisman and J. K. Reid",
title = "Direct Methods for Sparse Matrices",
edition = "2nd",
publisher = "Oxford University Press",
note = "First edition 1987",
year = "2017" }
@techreport{dgl1987,
author = {I. S. Duff and N. I. Gould and M. Lescrenier and J. K. Reid},
title = {The multifrontal method in a parallel environment},
year = {1987},
number = {CSS 211},
institution = {Harwell Laboratory},
}
@inproceedings{dgl1990,
author = "I. S. Duff and N. I. Gould and M. Lescrenier and J. K. Reid",
title = "The multifrontal method in a parallel environment",
booktitle = "Reliable Numerical Computation",
editor = "M. G. Cox and S. Hammarling",
publisher = "Oxford University Press",
address = "London",
year = "1990",
pages = "93-111" }
@article{dgrst1990,
author = "I. S. Duff and N. I. Gould and J. K. Reid and J. A. Scott and K. Turner",
title = "The factorization of sparse symmetric indefinite matrices",
journal = IMAJNA,
volume = "11",
number = "2",
year = "1990",
pages = "181-204" }
@article{dgl1989,
author = "I. S. Duff and R. G. Grimes and J. G. Lewis",
title = "Sparse matrix test problems",
journal = TOMS,
volume = "15",
number = "1",
year = "1989",
pages = "1-14" }
@techreport{dgl1997,
author = "I. S. Duff and R. G. Grimes and J. G. Lewis",
title = "The {Rutherford-Boeing} sparse matrix collection",
institution = "Rutherford Appleton Laboratory",
number = "RAL-TR-97-031",
year = "1997" }
@article{dgrz2015,
author = "I. S. Duff and R. Guivarch and D. Ruiz and M. Zenadi",
title = "The augmented block {Cimmino} distributed method",
journal = SISC,
volume = "37",
number = "3",
year = "2015",
pages = "A1248-A1269" }
@article{dhp2002,
author = "I. S. Duff and M. A. Heroux and R. Pozo",
title = "An overview of the sparse basic linear algebra subprograms: {T}he new standard from the {BLAS} technical forum",
journal = TOMS,
volume = "28",
number = "2",
year = "2002",
pages = "239-267" }
@article{dhl2020,
author = "I. S. Duff and J. Hogg and F. Lopez",
title = "A new sparse {$LDL^T$} solver using a posteriori threshold pivoting",
journal = SISC,
volume = "42",
number = "2",
year = "2020",
pages = "C23-C42" }
@inproceedings{duj1989,
author = "I. S. Duff and S. L. Johnson",
title = "Node ordering and concurrency in structurally symmetric sparse problems",
booktitle = "Parallel Supercomputing: Methods, Algorithms and Applications",
editor = "G. F. Carey",
publisher = "John Wiley and Sons",
year = "1989",
pages = "?-?" }
@article{duko1999,
author = "I. S. Duff and J. Koster",
title = "The design and use of algorithms for permuting large entries to the diagonal of sparse matrices",
journal = SIMAX,
volume = "20",
number = "4",
year = "1999",
pages = "889-901" }
@article{duko2001,
author = "I. S. Duff and J. Koster",
title = "On algorithms for permuting large entries to the diagonal of a sparse matrix",
journal = SIMAX,
volume = "22",
number = "4",
year = "2001",
pages = "973-996" }
@article{dllt1987,
author = "I. S. Duff and J. Laminie and A. Lichnewsky and F. Thomasset",
title = "An experiment with arithmetic precision in linear algebra computations",
journal = "Int. J. Num. Meth. Fluids",
volume = "7",
number = "10",
year = "1987",
pages = "1077-1092" }
@techreport{dmr1992,
author = "I. S. Duff and M. Marrone and G. Radicati",
title = "A proposal for user level sparse {BLAS}",
institution = "Rutherford Appleton Laboratory",
number = "RAL-92-087",
year = "1992" }
@article{dmrv1997,
author = "I. S. Duff and M. Marrone and G. Radicati and C. Vittoli",
title = "Level 3 basic linear algebra subprograms for sparse matrices: a user-level interface",
journal = TOMS,
volume = "23",
number = "3",
year = "1997",
pages = "379-401" }
@article{dm1989,
author = "I. S. Duff and G. Meurant",
title = "The effect of ordering on preconditioned conjugate gradients",
journal = BIT,
volume = "29",
year = "1989",
pages = "635-657" }
@article{dupr2005,
author = "I. S. Duff and S. Pralet",
title = "Strategies for scaling and pivoting for sparse symmetric indefinite problems",
journal = SIMAX,
volume = "27",
number = "2",
year = "2005",
pages = "313-340" }
@article{dr1974,
author = "I. S. Duff and J. K. Reid",
title = "A comparison of sparsity orderings for obtaining a pivotal sequence in {Gauss}ian elimination",
journal = JIMA,
volume = "14",
year = "1974",
pages = "281-291" }
@article{dr1978b,
author = "I. S. Duff and J. K. Reid",
title = "Algorithm 529: {P}ermutations to block triangular form",
journal = TOMS,
volume = "4",
number = "2",
year = "1978",
pages = "189-192" }
@article{dr1978,
author = "I. S. Duff and J. K. Reid",
title = "An implementation of {Tarjan}'s algorithm for the block triangularization of a matrix",
journal = TOMS,
volume = "4",
number = "2",
year = "1978",
pages = "137-147" }
@article{dr1979,
author = "I. S. Duff and J. K. Reid",
title = "Some design features of a sparse matrix code",
journal = TOMS,
volume = "5",
number = "1",
year = "1979",
pages = "18-35" }
@article{dr1983,
author = "I. S. Duff and J. K. Reid",
title = "The multifrontal solution of indefinite sparse symmetric linear equations",
journal = TOMS,
volume = "9",
number = "3",
year = "1983",
pages = "302-325" }
@article{dr1984,
author = "I. S. Duff and J. K. Reid",
title = "The multifrontal solution of unsymmetric sets of linear equations",
journal = SISSC,
volume = "5",
number = "3",
year = "1984",
pages = "633-641" }
@techreport{dr1993,
author = {I. S. Duff and J. K. Reid},
title = {{MA48}, a {Fortran} code for direct solution of sparse unsymmetric linear systems of equations},
year = {1993},
number = {RAL–93–072},
institution = {Rutherford Appleton Laboratory},
}
@techreport{dr1995,
author = {I. S. Duff and J. K. Reid},
title = {{MA47}, a {Fortran} code for direct solution of indefinite sparse symmetric linear systems},
year = {1995},
number = {RAL–95–001},
institution = {Rutherford Appleton Laboratory},
}
@article{dr1996,
author = "I. S. Duff and J. K. Reid",
title = "The design of {MA48}: a code for the direct solution of sparse unsymmetric linear systems of equations",
journal = TOMS,
volume = "22",
number = "2",
year = "1996",
pages = "187-226" }
@article{drmn1979,
author = "I. S. Duff and J. K. Reid and N. Munksgaard and B. Nielsen",
title = "Direct solution of sets of linear equations whose matrix is sparse, symmetric and indefinite",
journal = JIMA,
volume = "23",
year = "1979",
pages = "235-250" }
@article{drs1989,
author = "I. S. Duff and J. K. Reid and J. A. Scott",
title = "The use of profile reduction algorithms with a frontal code",
journal = IJNME,
volume = "28",
year = "1989",
pages = "2555-2568" }
@techreport{ds1993,
author = {I. S. Duff and J. A. Scott},
title = {{MA42}- {A} new frontal code for solving sparse unsymmetric systems},
year = {1993},
number = {RAL-93-064},
institution = {Rutherford Appleton Laboratory},
}
@techreport{ds1994,
author = {I. S. Duff and J. A. Scott},
title = {The use of multiple fronts in {Gauss}ian elimination},
year = {1994},
number = {RAL-94-040},
institution = {Rutherford Appleton Laboratory},
}
@article{ds1996,
author = "I. S. Duff and J. A. Scott",
title = "The design of a new frontal code for solving sparse unsymmetric systems",
journal = TOMS,
volume = "22",
number = "1",
year ="1996",
pages = "30-45" }
@book{ds1979,
author = "I. S. Duff and G. W. Stewart",
title = "Sparse Matrix Proceedings, 1978",
publisher = "SIAM",
year = "1979" }
@article{dufu2010,
author = "I. S. Duff and B. U{\c{c}}ar",
title = "On the block triangular form of symmetric matrices",
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number = "3",
year = "2010",
pages = "455-470" }
@incollection{dufu2012,
author = "I. S. Duff and B. U{\c{c}}ar",
title = "Combinatorial problems in solving linear systems",
booktitle = "Combinatorial Scientific Computing",
editor = "U. Naumann and O. Schenk",
publisher = "Chapman and Hall, CRC Press",
year = "2012",
pages = "21-68" }
@article{dv2002,
author = "I. S. Duff and C. V{\"{o}}mel",
title = "Algorithm 818: {A} reference model implementation of the {S}parse {BLAS} in {Fortran} 95",
journal = TOMS,
volume = "28",
number = "2",
year = "2002",
pages = "268-283" }
@article{dv2002b,
author = "I. S. Duff and C. V{\"{o}}mel",
title = "Incremental norm estimation for dense and sparse matrices",
journal = BIT,
volume = "42",
number = "2",
year = "2002",
pages = "300-322" }
@article{dvdv1999,
author = "I. S. Duff and H. A. {van der Vorst}",
title = "Developments and trends in the parallel solution of linear systems",
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year = "1999",
pages = "1931-1970" }
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volume = "71",
year = "1964",
pages = "65-87" }
@inproceedings{dufu2018,
author = "E. Dufrechou and P. Ezzatti",
title = "Solving sparse triangular linear systems in modern {GPUs}: {A} synchronization-free algorithm",
booktitle = "26th Euromicro International Conference on Parallel, Distributed and Network-based Processing",
publisher = "IEEE",
year = "2018",
pages = "196-203" }
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author = "J. W. Duke",
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@misc{dvri2016,
author = "M. Dukhan and R. Vuduc and J. Riedy",
title = "Wanted: {F}loating-point add round-off error instruction",
howpublished = "ArXiv preprint arXiv:1603.00491",
year = "2016" }
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author = "A. L. Dulmage and N. S. Mendelsohn",
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author = "A. L. Dulmage and N. S. Mendelsohn",
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@article{dm1963,
author = "A. L. Dulmage and N. S. Mendelsohn",
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author = "{J.-G.} Dumas and T. Gautier and C. Pernet and J. L. Roch and Z. Sultan",
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author = "{J.-G.} Dumas and C. Pernet and Z. Wan",
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booktitle = "Proceedings of the 2005 International Symposium on Symbolic and Algebraic Computation",
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@phdthesis{du2012,
author = "S. Duminil",
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year = "2012" }
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author = {D. B. Duncan and J. F. Kenney},
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author = "J. A. George and E. G. Ng",
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publisher = "IEEE",
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author = "G. H. Golub",
title = "Least squares, singular values and matrix approximations",
journal = "Aplikace Matematiky",
volume = "13",
number = "1",
year = "1968",
pages = "44-51" }
@article{go1973,
author = "G. H. Golub",
title = "Some modified matrix eigenvalue problems",
journal = SIREV,
volume = "15",
number = "2",
year = "1973",
pages = "318-334" }
@article{go1974,
author = "G. H. Golub",
title = "Bounds for matrix moments",
journal = RMJM,
volume = "4",
number = "2",
year = "1974",
pages = "207-211" }
@inproceedings{go1995,
author = "G. H. Golub",
title = "Matrix computation and the theory of moments",
booktitle = "Proceedings of the International Congress of Mathematicians, Z{\"u}rich, Switzerland 1994",
editor = "S. D. Chatterji",
publisher = "Birkh{\"a}user",
address = "Basel",
year = "1995",
pages = "1440-1448" }
@article{gof1992,
author = "G. H. Golub and B. Fischer",
title = "How to generate unknown orthogonal polynomials out of known orthogonal polynomials",
journal = JCAM,
volume = "43",
year = "1992",
pages = "99-115" }
@article{gog1990,
author = "G. H. Golub and M. H. Gutknecht",
title = "Modified moments for indefinite weight functions",
journal = NUMAT,
volume = "57",
year = "1990",
pages = "607-624" }
@article{ghol1999,
author = "G. H. Golub and P. C. Hansen and D. P. {O'Leary}",
title = "Tikhonov regularization and total least squares",
journal = SIMAX,
volume = "21",
number = "1",
year = "1999",
pages = "185-194" }
@article{ghw1979,
author = "G. H. Golub and M. Heath and G. Wahba",
title = "Generalized cross-validation as a method to choosing a good ridge parameter",
journal = TEC,
volume = "21",
number = "2",
year = "1979",
pages = "215-223" }
@article{ghs1987,
author = "G. H. Golub and A. Hoffman and G. W. Stewart",
title = "A generalization of the {Eckart-Young-Mirsky} matrix approximation theorem",
journal = LAA,
volume = "88",
year = "1987",
pages = "317-327" }
@article{gk1965,
author = "G. H. Golub and W. Kahan",
title = "Calculating the singular values and pseudo-inverse of a matrix",
journal = SINUM,
volume = "2",
number = "2",
year = "1965",
pages = "205-224" }
@article{gok1986,
author = "G. H. Golub and R. Kannan",
title = "Convergence of a two-stage {Richardson} process for non linear equations",
journal = BITNM,
volume = "26",
number = "2",
year = "1986",
pages = "209-216" }
@article{gok1983,
author = "G. H. Golub and J. Kautsky",
title = "Calculation of {Gauss} quadratures with multiple free and fixed knots",
journal = NUMAT,
volume = "41",
year = "1983",
pages = "147-163" }
@article{goke1989,
author = "G. H. Golub and M. D. Kent",
title = "Estimates of eigenvalues for iterative methods",
journal = MATCOMP,
volume = "53",
number = "188",
year = "1989",
pages = "619-626" }
@techreport{gks1976,
author = "G. H. Golub and V. Klema and G. W. Stewart",
title = "Rank degeneracy and least squares problems",
institution = "Stanford University, Dept. of Computer Science",
number = "STAN-CS-76-559",
year = "1976" }
@article{gv1979,
author = "G. H. Golub and C. F. {Van Loan}",
title = "Unsymmetric positive definite linear systems",
journal = LAA,
volume = "28",
year = "1979",
pages = "85-97" }
@article{gvl1980,
author = "G. H. Golub and C. F. {Van Loan}",
title = "An analysis of the total least squares problem",
journal = SINUM,
volume = "17",
number = "6",
year = "1980",
pages = "883-893" }
@book{gvl1989,
author = "G. H. Golub and C. F. {Van Loan}",
title = "Matrix {C}omputations",
edition = "2nd",
publisher = "Johns Hopkins University Press",
address = "Baltimore",
year = "1989" }
@book{gvl1996,
author = "G. H. Golub and C. F. {Van Loan}",
title = "Matrix {C}omputations",
edition = "3rd",
publisher = "Johns Hopkins University Press",
address = "Baltimore",
year = "1996" }
@book{gvl2013,
author = "G. H. Golub and C. F. {Van Loan}",
title = "Matrix {C}omputations",
edition = "4th",
publisher = "Johns Hopkins University Press",
address = "Baltimore",
year = "2013" }
@inproceedings{golu1976,
author = "G. H. Golub and F. T. Luk",
title = "Singular value decomposition: {A}pplications and computations",
booktitle = "Transactions of the Twenty-Second Conference of Army Mathematicians",
publisher = "US Army Research Office",
year = "1976",
pages = "577-605" }
@article{gvm1991,
author = "G. H. Golub and U. {von Matt}",
title = "Quadratically constrained least squares and quadratic problems",
journal = NUMAT,
volume = "59",
year = "1991",
pages = "561-580" }
@inproceedings{gvm1997,
author = "G. H. Golub and U. {von Matt}",
title = "Generalized cross-validation for large scale problems",
booktitle = "Recent Advances in Total Least Squares Techniques and Errors-in-variable Modelling",
editor = "S. {van Huffel}",
publisher = "SIAM",
address = "Philadelphia",
year = "1997",
pages = "139-148" }
@inproceedings{gvm1997b,
author = "G. H. Golub and U. {von Matt}",
title = "Tikhonov regularization for large scale problems",
booktitle = "Scientific Computing",
editor = "G. H. Golub and S. H. Lui and F. Luk and R. Plemmons",
publisher = "Springer",
address = "Berlin",
year = "1997",
pages = "3-26" }
@inproceedings{gma1984,
author = "G. H. Golub and D. Mayers",
title = "The use of preconditioning over irregular regions",
booktitle = "Computing Methods in Applied Science and Engineering VI",
editor = "R. Glowinski and J. L. Lions",
publisher = "North-Holland",
year = "1984",
pages = "3-14" }
@article{gomo2001,
author = "G. H. Golub and H. Melb\o",
title = "A stochastic approach to error estimates for iterative linear solvers, part 1",
journal = BITNM,
volume = "41",
number = "5",
year = "2001",
pages = "977-985" }
@techreport{gomo2001b,
author = {G. H. Golub and H. Melb\o},
title = {A stochastic approach to error estimates for iterative linear solvers, part 2},
year = {2001},
number = {SCCM-01-05},
institution = {Stanford University, Computer Science Dept.},
}
@book{gom1983,
author = "G. H. Golub and G. Meurant",
title = "R{\'e}solution Num{\'e}rique des Grands Syst{\`e}mes Lin{\'e}aires",
publisher = "Eyrolles",
year = "1983" }
@inproceedings{gm1994,
author = "G. H. Golub and G. Meurant",
title = "Matrices, moments and quadrature",
booktitle = "Numerical Analysis 1993",
editor = "D. F. Griffiths and G. A. Watson",
series = "Pitman Research Notes in Mathematics",
volume = "303",
publisher = "Longman Sci. Tech.",
year = "1994",
pages = "105-156",
note = "Reprinted in \cite{cgl2007}" }
@article{gme1997,
author = "G. H. Golub and G. Meurant",
title = "Matrices, moments and quadrature {II} or how to compute the norm of the error in iterative methods",
journal = BITNM,
volume = "37",
number = "3",
year = "1997",
pages = "687-705" }
@book{gme2010,
author = "G. H. Golub and G. Meurant",
title = "Matrices, Moments and Quadrature with Applications",
publisher = "Princeton University Press",
year = "2010" }
@article{gom1987,
author = "G. H. Golub and C. B. Moler",
title = "Dedication to {J}. {H}. {Wilkinson}",
journal = LAA,
volume = "88/89",
number = "1-3",
year = "1987",
pages = "1-3" }
@article{gnv1979,
author = "G. H. Golub and S. Nash and C. Van Loan",
title = "A {Hessenberg}-{Schur} method for the problem {$AX+XB=C$}",
journal = ITAC,
volume = "24",
number = "6",
year = "1979",
pages = "909-913" }
@article{gol1989,
author = "G. H. Golub and D. P. {O{'}Leary}",
title = "Some history of the conjugate gradient and {Lanczos} algorithms: 1948-1976",
journal = SIREV,
volume = "31",
number = "1",
year = "1989",
pages = "50-102" }
@book{goo1992,
author = "G. H. Golub and J. M. Ortega",
title = "Scientific Computing and Differential Equations, an Introduction to Numerical Methods",
publisher = "Academic Press",
year = "1992" }
@techreport{gov1981,
author = {G. H. Golub and M. L. Overton},
title = {Convergence of a two-stage {Richardson} iterative procedure for solving systems of linear equations},
year = {1981},
number = {NA-81-17},
institution = {Computer Science Dept., Stanford University},
}
@article{gov1988,
author = "G. H. Golub and M. L. Overton",
title = "The convergence of inexact {Chebyshev} and {Richardson} iterative methods for solving linear systems",
journal = NUMAT,
volume = "53",
number = "5",
year = "1988",
pages = "571-593" }
@inproceedings{godp1990,
author = {G. H. Golub and J. E. {de Pillis}},
booktitle = {Iterative Methods for Large Linear Systems},
title = {Toward an effective two-parameter {SOR} method},
year = {1990},
editor = {D. R. Kincaid and L. J. Hayes},
pages = {107-119},
publisher = {Academic Press},
}
@article{gr1970,
author = "G. H. Golub and C. Reinsch",
title = "Singular value decomposition and least squares solutions",
journal = NUMAT,
volume = "14",
year = "1970",
pages = "403-420" }
@article{grt2007,
author = "G. H. Golub and D. Ruiz and A. Touhami",
title = "A hybrid approach combining {Chebyshev} filter and conjugate gradient for solving linear systems with multiple right-hand sides",
journal = SIMAX,
volume = "29",
number = "3",
year = "2007",
pages ="774-795" }
@article{gsvd2000,
author = "G. H. Golub and K. S{{\o}}lna and P. {Van Dooren}",
title = "Computing the {SVD} of a general matrix product/quotient",
journal = SIMAX,
volume = "22",
number = "1",
year = "2000",
pages = "1-19" }
@article{gsw2008,
author = "G. H. Golub and M. Stoll and A. Wathen",
title = "Approximation of the scattering amplitude and linear systems",
journal = ETNA,
volume = "31",
year = "2008",
pages = "178-203" }
@article{gs1994,
author = "G. H. Golub and Z. Strako{\v{s}}",
title = "Estimates in quadratic formulas",
journal = NUMALGO,
volume = "8",
number = "2",
year = "1994",
pages = "241-268" }
@article{gu2009,
author = "G. H. Golub and F. Uhlig",
title = "The {QR} algorithm: 50 years later its genesis by {J}ohn {Francis} and {V}era {Kublanovskaya} and subsequent developments",
journal = IMAJNA,
volume = "29",
number = "3",
year = "2009",
pages = "467-485" }
@inproceedings{gu1977,
author = "G. H. Golub and R. Underwood",
title = "The block {Lanczos} method for computing eigenvalues",
booktitle = "Mathematical Software {III}, Proceedings of a Symposium conducted by the Mathematics Research Center, the University of Wisconsin-Madison, March 28{-}30, 1977",
editor = "J. Rice",
publisher = "Academic Press",
year = "1977",
pages = "361-377" }
@article{gov1974,
author = "G. H. Golub and J. M. Varah",
title = "On a characterization of the best $\ell_2$-scaling of a matrix",
journal = SINUM,
volume = "11",
number = "3",
year = "1974",
pages = "472-479" }
@article{go1961,
author = "G. H. Golub and R. S. Varga",
title = "{Chebyshev} semi-iterative methods, successive overrelaxation iterative Methods, and second order {Richardson} iterative methods. {I}",
journal = NUMAT,
volume = "3",
number = "1",
year = "1961",
pages = "147-156" }
@article{go1961b,
author = "G. H. Golub and R. S. Varga",
title = "{Chebyshev} semi-iterative methods, successive overrelaxation iterative Methods, and second order {Richardson} iterative methods. {II}",
journal = NUMAT,
volume = "3",
number = "1",
year = "1961",
pages = "157-168" }
@incollection{gvdv1997b,
author = "G. H. Golub and H. A. {van der Vorst}",
title = "150 years old and still alive: {E}igenproblems",
booktitle = "The State of the Art in Numerical Analysis",
editor = "I. S. Duff and G. A. Watson",
publisher = "Oxford University Press",
year = "1997",
pages = "93-119" }
@incollection{gvdv1997,
author = "G. H. Golub and H. A. {van der Vorst}",
title = "Closer to the solutions: {I}terative linear solvers",
booktitle = "The State of the Art in Numerical Analysis",
editor = "I. S. Duff and G. A. Watson",
publisher = "Oxford University Press",
year = "1997",
pages = "63-92" }
@article{gvdv1997c,
author = "G. H. Golub and H. A. {van der Vorst}",
title = "Eigenvalue computation in the 20th century",
journal = JCAM,
volume = "123",
number = "1-2",
year = "2000",
pages = "35-65" }
@inproceedings{gvdv2001,
author = "G. H. Golub and H. A. {van der Vorst}",
title = "Closer to the solutions: {I}terative linear solvers",
booktitle = "The State of the Art in Numerical Analysis",
editor = "I. S. Duff and G. A. Watson",
publisher = "Oxford University Press",
year = "2001",
pages = "63-92" }
@techreport{gw1967,
author = "G. H. Golub and J. H. Welsch",
title = "Calculation of {Gauss} quadrature rules",
institution = "Stanford University, Computer Science Dept.",
number = "CS 81",
year = "1967" }
@article{gw1969,
author = "G. H. Golub and J. H. Welsch",
title = "Calculation of {Gauss} quadrature rules",
journal = MATCOMP,
volume = "23",
number = "106",
year = "1969",
pages = "221-230" }
@article{gwi1976,
author = "G. H. Golub and J. H. Wilkinson",
title = "Ill-conditioned eigensystems and the computation of the {Jordan} canonical form",
journal = SIREV,
volume = "18",
number = "4",
year = "1976",
pages = "578-619" }
@article{gy1999,
author = "G. H. Golub and Q. Ye",
title = "Inexact preconditioned conjugate gradient method with inner-outer iteration",
journal = SISC,
volume = "21",
number = "4",
year = "1999",
pages = "1305-1320" }
@article{gye2000,
author = "G. H. Golub and Q. Ye",
title = "Inexact inverse iteration for generalized eigenvalue problems",
journal = BIT,
volume = "40",
number = "4",
year = "2000",
pages = "671-684" }
@article{gyzh1994,
author = "G. H. Golub and H. Zha",
title = "Perturbation analysis of the canonical correlations of matrix pairs",
journal = LAA,
volume = "210",
year = "1994",
pages = "3-28" }
@article{grt2008,
author = "M. Gomes-Ruggiero and V. Rocha Lopes and J. Toledo-Benavides",
title = "A safeguard approach to detect stagnation of {GMRES}(m) with applications in {Newton}-{Krylov} methods",
journal = COAM,
volume = "27",
number = "2",
year = "2008",
pages = "175-199" }
@phdthesis{gnn2009,
author = "P. Gonnet",
title = "Adaptive quadrature re-revisited",
school = "ETH Z{\"{u}}rich",
year = "2009" }
@article{gptr2011,
author = "P. Gonnet and R. Pach{\'{o}}n and L. N. Trefethen",
title = "Robust rational interpolation and least-squares",
journal = ETNA,
volume = "38",
year = "2011",
pages = "146-167" }
@article{ggtr2013,
author = "P. Gonnet and S. G{\"{u}}ttel and L. N. Trefethen",
title = "Robust {Pad{\'e}} approximation via {SVD}",
journal = SIREV,
volume = "55",
number = "1",
year = "2013",
pages = "101-117" }
@article{gosc2016,
author = "C. C. Gonzaga and R. M. Schneider",
title = "On the steepest descent algorithm for quadratic functions",
journal = "Comput. Optim. Appl.",
volume = "63",
number = "2",
year = "2016",
pages = "523-542" }
@article{gbc2018,
author = "S. L. Gonzaga de Oliveira and J. A. B. Bernardes and G. O. Chagas",
title = "An evaluation of reordering algorithms to reduce the computational cost of the incomplete {Cholesky}-conjugate gradient method",
journal = COAM,
volume = "37",
number = "3",
year = "2018",
pages = "2965-3004" }
@article{gcp2000,
author = "P. Gonz{\'{a}}lez and J. C. Cabaleiro and T. F. Pena",
title = "On parallel solvers for sparse triangular systems",
journal = "J. Syst. Archit.",
volume = "46",
number = "8",
year = "2000",
pages = "675-685" }
@phdthesis{goz1986,
author = "R. Gonzalez",
title = "Domain decomposition for two dimensional elliptic operators on vector and parallel machines",
school = "Rice University",
year = "1986" }
@article{gmtt2011,
author = "J. {Gonz{\'{a}}lez-Dom{\'\i}nguez} and M. J. Mart{\'\i}n and G. L. Taboada and J. Tourino",
title = "Dense triangular solvers on multicore clusters using {UPC}",
journal = PCS,
volume = "4",
year = "2011",
pages = "231-240" }
@article{grt2012,
author = "E. {Gonz{\'{a}}lez-Guti{\'e}rrez} and L. {Hern{\'{a}}ndez Rebollar} and M. I. Todorov",
title = "Relaxation methods for solving linear inequality systems: converging results",
journal = "TOP",
volume = "20",
year ="2012",
pages ="426-436" }
@article{goo1958,
author = "I. J. Good",
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journal = "J. Roy. Statist. Soc. Ser. B",
volume = "20",
year = "1958",
pages = "361-372" }
@article{goo1971,
author = "I. J. Good",
title = "The relationship between two {Fast Fourier Transforms}",
journal = ITCO,
volume = "20",
year = "1971",
pages = "310-317" }
@article{gmrs1995,
author = "T. N. T. Goodman and C. A. Micchelli and G. Rodriguez and S. Seatzu",
title = "On the {Cholesky} factorization of the {Gram} matrix of locally supported functions",
journal = BITNM,
volume = "35",
number = "2",
year = "1995",
pages = "233-257" }
@article{goo2020,
author = "J. R. Goodstein",
title = "Olga {Taussky-Todd}",
journal = NAMS,
volume = "67",
number = "3",
year = "2020",
pages = "345-353" }
@article{gor1999,
author = "S. Goossens and D. Roose",
title = "Ritz and harmonic {Ritz} values and the convergence of {FOM} and {GMRES}",
journal = NLAA,
volume = "6",
number = "4",
year = "1999",
pages = "281-293" }
@phdthesis{gvs1990,
author = "D. Goovaerts",
title = "Domain decomposition for elliptic partial differential equations",
school = "Katholieke Universiteit Leuven",
year = "1990" }
@article{gotr2019,
author = "A. Gopal and L. N. Trefethen",
title = "New {Laplace} and {Helmholtz} solvers",
journal = PNAS,
volume = "116",
number = "21",
year = "2019",
pages = "10223-10225" }
@article{gotr2019b,
author = "A. Gopal and L. N. Trefethen",
title = "Representation of conformal maps by rational functions",
journal = NUMAT,
volume = "142",
number = "2",
year = "2019",
pages = "359-382" }
@article{gor2005,
author = "D. Gordon",
title = "Parallel {ART} for image reconstruction in {CT} using processor arrays",
journal = "Int. J. Parallel Emergent Distrib. Syst.",
volume = "21",
year = "2005",
pages = "365-380" }
@article{gor2018,
author = "D. Gordon",
title = "The {Cimmino-Kaczmarz} equivalence and related results",
journal = "Appl. Anal. Optim.",
volume = "2",
year = "2018",
pages = "253-270" }
@article{gbh1970,
author = "R. Gordon and R. Bender and G. T. Herman",
title = "Algebraic reconstruction techniques {(ART)} for three-dimensional electron microscopy and x-ray photography",
journal = "J. Theor. Biol.",
volume = "29",
year = "1970",
pages = "471-481" }
@article{gcgmrl2019,
author = "C. Gorman and G. Ch{\'{a}}vez and P. Ghysels and T. Mary and F. H. Rouet and X. S. Li",
title = "Robust and accurate stopping criteria for adaptive randomized sampling in matrix-free hierarchically semiseparable construction",
journal = SISC,
volume = "41",
number = "5",
year = "2019",
pages = "S61-S85" }
@book{gos1577,
author = "G. Gosselin",
title = "De Arte Magna, seu de Occulta Parte Numerorum quae et {A}lgebra et {A}lmucabala Vulgo Dicitur",
publisher = "Gilles Bets",
address = "Paris",
year = "1577" }
@article{goto2008,
author = "C. Gotsman and S. Toledo",
title = "On the computation of null spaces of sparse rectangular matrices",
journal = SIMAX,
volume = "30",
number = "2",
year = "2008",
pages = "445-463" }
@incollection{gou1996,
author = "D. Gough",
title = "The success story of the transfer and development of methods from geophysics to helioseismology",
booktitle = "Inverse Methods",
editor = "B. H. Jacobsen and K. Mosegaard and P. Sibani",
publisher = "Springer",
address = "Berlin, Heidelberg",
year = "1996",
pages = "1-31" }
@article{gou1991,
author = "N. Gould",
title = "On growth in {Gauss}ian elimination with complete pivoting",
journal =SIMAX,
volume = "12",
number = "2",
year = "1991",
pages = "354-361" }
@techreport{gsc1995,
author = {N. I. Gould and J. A. Scott},
institution = {Rutherford Appleton Laboratory},
title = {On approximate inverse preconditioners},
year = {1995},
address = {UK},
number = {RAL-TR-95-026},
}
@article{gos1998,
author = "N. I. Gould and J. A. Scott",
title = "Sparse approximate-inverse preconditioners using norm-minimization techniques",
journal = SISC,
volume = "19",
number = "2",
year = "1998",
pages = "605-625" }
@article{gsh2007,
author = "N. I. Gould and J. A. Scott and Y. Hu",
title = "A numerical evaluation of sparse direct solvers for the solution of large sparse symmetric linear systems of equations",
journal = TOMS,
volume = "33",
number = "2",
year = "2007",
pages = "1-32" }
@article{goou1968,
author = "A. R. Gourlay",
title = "The acceleration of the {Peaceman-Rachford} method by {Chebyshev} polynomials",
journal = COMPJ,
volume = "10",
year = "1968",
pages = "378-382" }
@article{goou1970,
author = "A. R. Gourlay",
title = "On {Chebychev} acceleration procedures for alternating direction iterative methods",
journal = JIMA,
volume = "6",
year = "1970",
pages = "1-11" }
@article{gor2015,
author = "R. Gower and P. Richt{\'a}rik",
title = "Randomized iterative methods for linear systems",
journal = SIMAX,
volume = "36",
number = "4",
year = "2015",
pages = "1660-1690" }
@incollection{gow2011,
author = "T. Gowers",
title = "Is {M}athematics discoverd or invented?",
booktitle ="Meaning in Mathematics",
editor = "J. Polkinghorne",
publisher = "Oxford University Press",
year = "2011",
pages = "3-12" }
@misc{gaa2012,
author = "M. M. Gra{\c{c}}a",
title = "Quadrature as a least-squares and minimax problem",
howpublished = "ArXiv preprint arXiv:1206.0281",
year = "2012" }
@article{gra1972,
author = "W. B. Gragg",
title = "The {Pad{\'e}} table and its relation to certain algorithms of numerical analysis",
journal = SIREV,
volume = "14",
number = "1",
year = "1972",
pages ="1-62" }
@article{gra1974,
author = "W. B. Gragg",
title = "Matrix interpretations and applications of the continued fraction algorithm",
journal = RMJM,
volume = "4",
number = "2",
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author = "J. F. Grcar",
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address = "USA",
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institution = "Department of Information Technology, Uppsala University",
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pages = "179-213" }
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author = "M. H. Gutknecht",
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publisher = "ACM Press",
year = "1990",
pages = "301-313" }
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author = "M. H. Gutknecht",
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booktitle = "Proceedings of the Copper Mountain Conference on Iterative Methods",
year = "1990" }
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author = {M. H. Gutknecht},
title = {On certain types of $(k,l)$-step methods for solving linear systems of equations},
year = {1991},
number = {IPS-91-01},
institution = {ETH Z{\"{u}}rich},
}
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author = "M. H. Gutknecht",
title = "The pioneer days of scientific computing in {Switzerland}",
journal = "IPS Windows",
volume = "2",
year = "1991",
pages = "23-27",
note = "And {\it Crosscuts}, v~2 n~3 (1993), pp.~14-17" }
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author = "M. H. Gutknecht",
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year = "1992",
pages = "594-639" }
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author = "M. H. Gutknecht",
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journal = SINUM,
volume = "30",
year = "1993",
pages = "40-56" }
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author = "M. H. Gutknecht",
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journal = SISC,
volume = "14",
number = "5",
year = "1993",
pages = "1020-1033" }
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author = "M. H. Gutknecht",
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year = "1994",
pages = "15-58" }
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author = "M. H. Gutknecht",
title = "The {Lanczos} process and {Pad{\'e}} approximation",
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editor = "J. Brown and M. Chu and D. Ellison and R. J. Plemmons",
publisher = "SIAM",
year = "1994",
pages = "61-75" }
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author = "M. H. Gutknecht",
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journal = ACTNUM,
volume = "6",
year = "1997",
pages = "271-397" }
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author = {M. H. Gutknecht},
title = {A general framework for recursions for {Krylov} space solvers},
year = {2005},
address = {Z{\"u}rich},
number = {No. 2005-09},
institution = {ETH},
}
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author = "M. H. Gutknecht",
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volume = "10-15",
year = "2007" }
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author = "M. H. Gutknecht",
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booktitle = "Frontiers of Computational Science",
publisher = "Springer",
address = "Berlin, Heidelberg",
year = "2007",
pages = "53-62" }
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volume = "39",
year = "2012",
pages = "156-185" }
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author = "M. H. Gutknecht and B. N. Parlett",
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year = "2010",
pages = "741-754" }
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author = "M. H. Gutknecht and K. J. Ressel",
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year = "1998",
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author = "M. H. Gutknecht and K. J. Ressel",
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volume = "21",
number = "4",
year = "2000",
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author = "M. H. Gutknecht and S. R{\"{o}}llin",
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journal = PARCOMP,
volume = "28",
number = "2",
year = "2002",
pages = "263-283" }
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author = "M. H. Gutknecht and M. Rozlo\v{z}n{\'\i}k",
title = "By how much can residual minimization accelerate the convergence of orthogonal residual methods?",
journal = NUMALGO,
volume = "27",
year = "2001",
pages = "189-213" }
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author = "M. H. Gutknecht and M. Rozlo\v{z}n{\'\i}k",
title = "Residual smoothing techniques: {D}o they improve the limiting accuracy of iterative solvers?",
journal = BITNM,
volume = "41",
number = "1",
year = "2001",
pages = "86-114" }
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author = "M. H. Gutknecht and M. Rozlo\v{z}n{\'\i}k",
title = "A framework for generalized conjugate gradient methods - with special emphasis on contributions by {R}{\"u}diger {Weiss}",
journal = ANM,
volume = "41",
year = "2002",
pages = "7-22" }
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author = "M. H. Gutknecht and T. Schmelzer",
title = "Updating the {QR} decomposition of block tridiagonal and block {Hessenberg} matrices",
journal = ANM,
volume = "58",
number = "6",
year = "2008",
pages = "871-883" }
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author = "M. H. Gutknecht and T. Schmelzer",
title = "The block grade of a block {Krylov} space",
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volume = "430",
number = "1",
year = "2009",
pages = "174-185" }
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author = "M. H. Gutknecht and Z. Strako\v{s}",
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volume = "22",
number = "1",
year = "2000",
pages = "213-229" }
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author = "M. H. Gutknecht and L. N. Trefethen",
title = "Real polynomial {Chebyshev} approximation by the {Carath{\'e}odory-Fej{\'e}r} method",
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volume = "19",
number = "2",
year = "1982",
pages = "358-371" }
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author = "M. H. Gutknecht and L. N. Trefethen",
title = "Real and complex {Chebyshev} approximation on the unit disk and interval",
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year = "1983",
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author = "M. H. Gutknecht and J. P. M. Zemke",
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volume = "34",
number = "2",
year = "2013",
pages = "283-311" }
@phdthesis{gutt2010,
author = "S. G{\"u}ttel",
title = "Rational {Krylov} methods for operator functions",
school = "Technische Universit{\"a}t Bergakademi Freiberg",
address = "Freiberg, Germany",
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@article{hi1987,
author = "N. J. Higham",
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journal = SIREV,
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@article{hi1987b,
author = "N. J. Higham",
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journal = NUMAT,
volume = "50",
number = "5",
year = "1987",
pages = "613-632" }
@article{hi1988,
author = "N. J. Higham",
title = "Algorithm 674: {FORTRAN} codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation",
journal = TOMS,
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number = "4",
year = "1988",
pages = "381-396" }
@article{hi1988b,
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journal = LAA,
volume = "103",
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author = "N. J. Higham",
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journal = "Inst. Math. Appl. Conf. Ser. New Ser.",
volume = "22",
year = "1988",
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@article{hi1988d,
author = "N. J. Higham",
title = "Fast solution of {Vandermonde}-like systems involving orthogonal polynomials",
journal = IMAJNA,
volume = "8",
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author = "N. J. Higham",
title = "How accurate is {Gauss}ian elimination?",
booktitle = "Numerical Analysis 1989",
editor = "D. F. Griffiths and G. A. Watson",
publisher = "Longman Scientific and Technical",
year = "1989",
pages = "137-154",
note = "Vol. 228, Pitman research notes in mathematics series" }
@article{hi1989,
author = "N. J. Higham",
title = "The accuracy of solutions to triangular systems",
journal = SINUM,
volume = "26",
number = "5",
year = "1989",
pages = "252-265" }
@article{hi1990b,
author = "N. J. Higham",
title = "Bounding the error in {Gauss}ian elimination for tridiagonal systems",
journal = SIMAX,
volume = "11",
number = "4",
year = "1990",
pages = "521-530" }
@article{hi1990,
author = "N. J. Higham",
title = "Experience with a matrix norm estimator",
journal = SISSC,
volume = "11",
year = "1990",
pages = "804-809" }
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author = "N. J. Higham",
title = "Algorithm 694: {A} collection of test matrices in {MATLAB}",
journal = TOMS,
volume = "17",
number = "3",
year = "1991",
pages = "289-305" }
@article{hi1992,
author = "N. J. Higham",
title = "Estimating the matrox $p$-norm",
journal = NUMAT,
volume = "62",
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author = "N. J. Higham",
title = "A survey of componentwise perturbation theory in numerical linear algebra",
booktitle = "Mathematics of Computation 1943-1993: A Half-Century of Computational Mathematics",
editor = "W. Gautschi",
publisher = "American Mathematical Society",
year = "1994",
pages = "49-78" }
@article{hi1994,
author = "N. J. Higham",
title = "The matrix sign decomposition and its relation to the polar decomposition",
journal = LAA,
volume = "212",
year = "1994",
pages = "3-20" }
@techreport{hi1995,
author = {N. J. Higham},
title = {The test matrix toolbox for {Matlab}},
year = {1995},
number = {Numerical Analysis 276},
institution = {Dept. of Mathematics, University of Manchester},
}
@book{hi1996,
author = "N. J. Higham",
title = "Accuracy and Stability of Numerical Algorithms",
publisher = "SIAM",
address = "Philadelphia",
year = "1996" }
@inproceedings{hi1997,
author = "N. J. Higham",
title = "Testing linear algebra software",
booktitle = "The Quality of Numerical Software: Assessment and Enhancement",
editor = "R. Boisvert",
publisher = "Chapman and Hall",
year = "1997",
pages = "109-124" }
@article{hi1997b,
author = "N. J. Higham",
title = "Iterative refinement for linear systems and {LAPACK}",
journal = IMAJNA,
volume = "17",
number = "4",
year = "1997",
pages = "495-509" }
@book{hi1998,
author = "N. J. Higham",
title = "Handbook of Writing for the Mathematical Sciences",
publisher = "SIAM",
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year = "1998" }
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title = "{QR} factorization with complete pivoting and accurate computation of the {SVD}",
journal = LAA,
volume = "309",
year = "2000",
pages = "153-174" }
@book{hi2002,
author = "N. J. Higham",
title = "Accuracy and Stability of Numerical Algorithms",
edition = "2nd",
publisher = "SIAM",
address = "Philadelphia",
year = "2002" }
@article{hi2004,
author = "N. J. Higham",
title = "The numerical stability of barycentric {Lagrange} interpolation",
journal = IMAJNA,
volume = "24",
number = "4",
year = "2004",
pages = "547-556" }
@article{hi2008,
author = "N. J. Higham",
title = "Cayley, {Sylvester}, and early matrix theory",
journal = LAA,
volume = "428",
year = "2008",
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@book{hi2008b,
author = "N. J. Higham",
title = "Functions of Matrices: {T}heory and Computation",
publisher = "SIAM",
address = "Philadelphia",
year = "2008" }
@article{hi2009,
author = "N. J. Higham",
title = "Cholesky factorization",
journal = "Wiley Interdisciplinary Reviews: Computational Statistics",
volume = "1",
number = "2",
year = "2009",
pages = "251-254" }
@article{hi2011,
author = "N. J. Higham",
title = "Gaussian elimination",
journal = "Wiley Interdisciplinary Reviews: Computational Statistics",
volume = "3",
number = "3",
year = "2011",
pages = "230-238" }
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author = "N. J. Higham",
title = "Functions of matrices",
institution = "The University of Manchester",
number = "MIMS EPrint 2013.27",
year = "2013" }
@article{hi2014,
author = "N. J. Higham",
title = "Sylvester's influence on applied mathematics",
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volume = "50",
number = "4",
year = "2014",
pages = "202-206" }
@techreport{hi2015,
author = "N. J. Higham",
title = "Numerical linear algebra and matrix analysis",
institution = "The University of Manchester",
number = "MIMS EPrint 2015.103",
year = "2015" }
@techreport{hi2015b,
author = "N. J. Higham",
title = "Programming languages: {A}n applied mathematics view",
institution = "The University of Manchester",
number = "MIMS EPrint 2015.89",
year = "2015" }
@techreport{hi2019,
author = "N. J. Higham",
title = "Error analysis for standard and {GMRES}-based iterative refinement in two and three-precisions",
institution = "The University of Manchester",
number = "MIMS EPrint 2019.19",
year = "2019" }
@book{hi2020,
author = "N. J. Higham",
title = "Handbook of Writing for the Mathematical Sciences",
publisher = "SIAM",
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@techreport{hi2021b,
author = "N. J. Higham",
title = "Numerical stability of algorithms at extreme scale and low precisions",
institution = "The University of Manchester",
number = "MIMS EPrint 2021.14",
year = "2021" }
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author = "N. J. Higham",
title = "The mathematics of floating-point arithmetic",
journal = "LMS Newsletter",
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year = "2021",
pages = "35-41" }
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author = "N. J. Higham and A. {Al-Mohy}",
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author = "N. J. Higham and A. {Al-Mohy}",
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number = "1",
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author = "N. J. Higham and E. Deadman",
title = "A catalogue of software for matrix functions. {V}ersion 2.0.",
institution = "The University of Manchester",
number = "MIMS EPrint: 2016.3",
year = "2016" }
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author = "N. J. Higham and D. J. Higham",
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author = "N. J. Higham and D. J. Higham",
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author = "N. J. Higham and E. Hopkins",
title = "A catalogue of software for matrix functions. {V}ersion 3.0.",
institution = "The University of Manchester",
number = "MIMS EPrint: 2020.7",
year = "2020" }
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author = "N. J. Higham and L. Lijing",
title = "Matrix functions: {A} short course",
booktitle = "Matrix Functions and Matrix Equations",
editor = "Z. Bai and W. Gao and Y. Su",
publisher = "Higher Education Press",
year = "2013",
pages = "1-27" }
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author = "N. J. Higham and T. Mary",
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journal = SISC,
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author = "N. J. Higham and T. Mary",
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journal = SISC,
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year = "2019",
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author = "N. J. Higham and T. Mary",
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author = "N. J. Higham and T. Mary",
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author = "N. J. Higham and V. Noferini",
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author = "N. J. Higham and S. Pranesh",
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author = "N. J. Higham and S. Pranesh",
title = "Exploiting lower precision arithmetic in solving symmetric positive definite linear systems and least squares problems",
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author = "N. J. Higham and S. Pranesh and M. Zounon",
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