Edit Profile (opens in new tab) Higham, Nicholas J. (b. 1961 d. 2024) Co-Author Distance Author ID: higham.nicholas-j Published as: Higham, Nicholas J.; Higham, N. J.; Higham, Nicholas; Higham, Nick more...less Homepage: https://nhigham.com/ External Links: MGP · ORCID · Wikidata · Google Scholar · Twitter · dblp · GND · IdRef · theses.fr Documents Indexed: 182 Publications since 1986, including 11 Books and 2 Additional arXiv Preprints 3 Contributions as Editor · 2 Further Contributions Biographic References: 1 Publication Co-Authors: 110 Co-Authors with 131 Joint Publications 2,562 Co-Co-Authors all top 5 Co-Authors 54 single-authored 18 Tisseur, Françoise 10 Higham, Desmond J. 10 Mary, Theo A. 9 Al-Mohy, Awad H. 7 Fasi, Massimiliano 6 Mackey, D. Steven 6 Pranesh, Srikara 5 Cheng, Sheung Hun 5 Lin, Lijing 5 Relton, Samuel D. 4 Carson, Erin Claire 4 Cox, Anthony J. 4 Davies, Philip I. 4 Dongarra, Jack J. 4 Guo, Chun-Hua 3 Blanchard, Pierre 3 Demmel, James Weldon 3 Knight, Philip A. 3 Mackey, Niloufer 3 Strabić, Nataša 3 Tomov, Stanimire Z. 2 Abdelfattah, Ahmad 2 Aprahamian, Mary 2 Bojanczyk, Adam W. 2 Borsdorf, Rüdiger 2 Connolly, Michael P. 2 Gates, Mark 2 Gautschi, Walter 2 Haidar, Azzam 2 Kim, Hyunmin 2 Lettington, Matthew C. 2 Lopez, Florent 2 Luszczek, Piotr 2 Mehrmann, Volker 2 Mikaitis, Mantas 2 Nakatsukasa, Yuji 2 Papadimitriou, Pythagoras 2 Patel, Harikrishna 2 Schreiber, Robert S. 2 Sherwood, Dennis 2 Stewart, Gilbert Wright 2 Zounon, Mawussi 1 Amestoy, Patrick R. 1 Anzt, Hartwig 1 Bai, Zhaojun 1 Bayraktar, Harun H. 1 Benzi, Michele 1 Betcke, Timo 1 Bini, Dario Andrea 1 Björk, Åke 1 Boman, Erik G. 1 Braconnier, Thierry 1 Brezinski, Claude 1 Buttari, Alfredo 1 Chan, Raymond Hon-Fu 1 Cojean, Terry 1 Corless, Robert Malcolm 1 Costa, Timothy B. 1 Deadman, Edvin 1 Dennis, Mark R. 1 Ding, Hui 1 Dingle, Nicholas J. 1 Du Croz, Jeremy J. 1 Elman, Howard C. 1 Garvey, Seamus D. 1 Glendinning, Paul Alexander 1 Golub, Gene Howard 1 Grammont, Laurence 1 Greenbaum, Anne 1 Greif, Chen 1 Grigori, Laura 1 Grützmacher, Thomas 1 Hale, Nicholas 1 Hammarling, Sven J. 1 Hargreaves, Gareth I. 1 Horn, Roger Alan 1 Iannazzo, Bruno 1 Jeffrey, David J. 1 Kandolf, Peter 1 Kenney, Charles S. 1 Kilmer, Misha Elena 1 Kurzak, Jakub 1 Laffey, Thomas J. 1 Laub, Alan J. 1 L’Excellent, Jean-Yves 1 Li, Rencang 1 Li, Sherry Xin 1 Lindquist, Neil 1 Loe, Jennifer A. 1 Martin, Paul Andrew 1 Mehl, Christian 1 Meini, Beatrice 1 Nadukandi, Prashanth 1 Nayak, Pratik 1 Noferini, Vanni 1 O’Leary, Dianne P. 1 Pan, Jianxin 1 Pothen, Alex 1 Pranesh, Sri 1 Puerta, Ferran ...and 21 more Co-Authors all top 5 Serials 52 SIAM Journal on Matrix Analysis and Applications 26 SIAM Journal on Scientific Computing 18 Linear Algebra and its Applications 9 IMA Journal of Numerical Analysis 9 ACM Transactions on Mathematical Software 8 BIT 8 Numerical Algorithms 4 SIAM Journal on Scientific and Statistical Computing 4 SIAM Review 3 Other Titles in Applied Mathematics 2 Mathematics of Computation 2 Numerische Mathematik 2 SIAM Journal on Numerical Analysis 2 Acta Numerica 2 London Mathematical Society. Newsletter 1 American Mathematical Monthly 1 International Journal for Numerical Methods in Engineering 1 Parallel Computing 1 Bulletin. The Institute of Mathematics and its Applications 1 Computational Statistics and Data Analysis 1 Numerical Linear Algebra with Applications 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Contemporary Mathematicians 1 Cambridge Tracts in Mathematics and Mathematical Physics all top 5 Fields 170 Numerical analysis (65-XX) 75 Linear and multilinear algebra; matrix theory (15-XX) 8 Computer science (68-XX) 7 General and overarching topics; collections (00-XX) 7 Statistics (62-XX) 6 Operations research, mathematical programming (90-XX) 4 History and biography (01-XX) 2 Combinatorics (05-XX) 2 Ordinary differential equations (34-XX) 2 Approximations and expansions (41-XX) 2 Mechanics of deformable solids (74-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Systems theory; control (93-XX) 1 Number theory (11-XX) 1 Special functions (33-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX) 1 Mathematics education (97-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 171 Publications have been cited 6,023 times in 3,852 Documents Cited by ▼ Year ▼ Accuracy and stability of numerical algorithms. 2nd ed. Zbl 1011.65010 Higham, Nicholas J. 844 2002 Functions of matrices. Theory and computation. Zbl 1167.15001 Higham, Nicholas J. 793 2008 Accuracy and stability of numerical algorithms. Zbl 0847.65010 Higham, Nicholas J. 320 1996 Computing the nearest correlation matrix – a problem from finance. Zbl 1006.65036 Higham, Nicholas J. 172 2002 Computing a nearest symmetric positive semidefinite matrix. Zbl 0649.65026 Higham, Nicholas J. 162 1988 Computing the action of the matrix exponential, with an application to exponential integrators. Zbl 1234.65028 Al-Mohy, Awad H.; Higham, Nicholas J. 147 2011 NLEVP, a collection of nonlinear eigenvalue problems. Zbl 1295.65140 Betcke, Timo; Higham, Nicholas J.; Mehrmann, Volker; Schröder, Christian; Tisseur, Françoise 141 2013 The scaling and squaring method for the matrix exponential revisited. Zbl 1081.65037 Higham, Nicholas J. 129 2005 The numerical stability of barycentric Lagrange interpolation. Zbl 1067.65016 Higham, Nicholas J. 111 2004 A new scaling and squaring algorithm for the matrix exponential. Zbl 1194.15021 Al-Mohy, Awad H.; Higham, Nicholas J. 98 2010 Computing the polar decomposition - with applications. Zbl 0607.65014 Higham, Nicholas J. 87 1986 Computing \(A^\alpha, \log(A)\), and related matrix functions by contour integrals. Zbl 1176.65053 Hale, Nicholas; Higham, Nicholas J.; Trefethen, Lloyd N. 79 2008 Symmetric linearizations for matrix polynomials. Zbl 1137.15006 Higham, Nicholas J.; Mackey, D. Steven; Mackey, Niloufer; Tisseur, Françoise 73 2006 Matrix nearness problems and applications. Zbl 0681.65029 Higham, N. J. 71 1989 Computing real square roots of a real matrix. Zbl 0625.65032 Higham, Nicholas J. 62 1987 The scaling and squaring method for the matrix exponential revisited. Zbl 1178.65040 Higham, Nicholas J. 58 2009 Bounds for eigenvalues of matrix polynomials. Zbl 1055.15030 Higham, Nicholas J.; Tisseur, Françoise 56 2003 A Schur-Parlett algorithm for computing matrix functions. Zbl 1052.65031 Davies, Philip I.; Higham, Nicholas J. 54 2003 Structured pseudospectra for polynomial eigenvalue problems, with applications. Zbl 0996.65042 Tisseur, Françoise; Higham, Nicholas J. 53 2001 Structured backward error and condition of generalized eigenvalue problems. Zbl 0935.65032 Higham, Desmond J.; Higham, Nicholas J. 52 1998 A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra. Zbl 0959.65061 Higham, Nicholas J.; Tisseur, Françoise 51 2000 Newton’s method for the matrix square root. Zbl 0614.65045 Higham, Nicholas J. 49 1986 The conditioning of linearizations of matrix polynomials. Zbl 1131.65034 Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise 48 2006 Iterative solution of a nonsymmetric algebraic Riccati equation. Zbl 1146.65035 Guo, Chun-Hua; Higham, Nicholas J. 46 2007 Numerical analysis of a quadratic matrix equation. Zbl 0966.65040 Higham, Nicholas J.; Kim, Hyun-Min 46 2000 Backward error of polynomial eigenproblems solved by linearization. Zbl 1159.65042 Higham, Nicholas J.; Li, Ren-Cang; Tisseur, Françoise 46 2008 \(J\)-orthogonal matrices: Properties and generation. Zbl 1034.65026 Higham, Nicholas J. 45 2003 Backward error and condition of structured linear systems. Zbl 0747.65028 Higham, Desmond J.; Higham, Nicholas J. 44 1992 The accuracy of floating point summation. Zbl 0788.65053 Higham, Nicholas J. 40 1993 A survey of condition number estimation for triangular matrices. Zbl 0635.65049 Higham, Nicholas J. 39 1987 Computing matrix functions. Zbl 1242.65090 Higham, Nicholas J.; Al-Mohy, Awad H. 39 2010 A survey of componentwise perturbation theory in numerical linear algebra. Zbl 0815.65062 Higham, Nicholas J. 37 1994 Stable iterations for the matrix square root. Zbl 0884.65035 Higham, Nicholas J. 37 1997 FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimations. Zbl 0665.65043 Higham, Nicholas J. 36 1988 Accelerating the solution of linear systems by iterative refinement in three precisions. Zbl 1453.65067 Carson, Erin; Higham, Nicholas J. 34 2018 Solving a quadratic matrix equation by newton’s method with exact line searches. Zbl 1017.65038 Higham, Nicholas J.; Kim, Hyun-Min 34 2001 Algorithms for the matrix \(p\)th root. Zbl 1103.65046 Bini, Dario A.; Higham, Nicholas; Meini, Beatrice 34 2005 Error analysis of the Björck-Pereyra algorithms for solving Vandermonde systems. Zbl 0595.65029 Higham, Nicholas J. 34 1987 The symmetric Procrustes problem. Zbl 0641.65034 Higham, Nicholas J. 32 1988 A preconditioned Newton algorithm for the nearest correlation matrix. Zbl 1188.65055 Borsdorf, Rüdiger; Higham, Nicholas J. 32 2010 Detecting a definite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems. Zbl 1004.65045 Higham, Nicholas J.; Tisseur, Françoise; Van Dooren, Paul M. 32 2002 Perturbation theory and backward error for \(AX - XB = C\). Zbl 0781.65034 Higham, Nicholas J. 31 1993 A Schur-Newton method for the matrix \(p\)th root and its inverse. Zbl 1128.65030 Guo, Chun-Hua; Higham, Nicholas J. 30 2006 A Schur-Padé algorithm for fractional powers of a matrix. Zbl 1242.65091 Higham, Nicholas J.; Lin, Lijing 29 2011 Computing the Fréchet derivative of the matrix exponential, with an application to condition number estimation. Zbl 1180.65049 Al-Mohy, Awad H.; Higham, Nicholas J. 29 2009 Solving the indefinite least squares problem by hyperbolic QR factorization. Zbl 1036.65035 Bojanczyk, Adam; Higham, Nicholas J.; Patel, Harikrishna 29 2003 The matrix sign decomposition and its relation to the polar decomposition. Zbl 0816.15012 Higham, Nicholas J. 29 1994 More on pseudospectra for polynomial eigenvalue problems and applications in control theory. Zbl 1004.65046 Higham, Nicholas J.; Tisseur, Françoise 29 2002 An improved Schur-Padé algorithm for fractional powers of a matrix and their Fréchet derivatives. Zbl 1279.65050 Higham, Nicholas J.; Lin, Lijing 29 2013 Functions preserving matrix groups and iterations for the matrix square root. Zbl 1079.65053 Higham, Nicholas J.; Mackey, D. Steven; Mackey, Niloufer; Tisseur, Françoise 28 2005 Approximating the logarithm of a matrix to specified accuracy. Zbl 0989.65057 Cheng, Sheung Hun; Higham, Nicholas J.; Kenney, Charles S.; Laub, Alan J. 28 2001 A new approach to probabilistic rounding error analysis. Zbl 07123205 Higham, Nicholas J.; Mary, Theo 28 2019 Stability of block. Zbl 0834.65010 Demmel, James W.; Higham, Nicholas J.; Schreiber, Robert S. 27 1995 Efficient algorithms for the matrix cosine and sine. Zbl 1084.65039 Hargreaves, Gareth I.; Higham, Nicholas J. 27 2005 Stability analysis of algorithms for solving confluent Vandermonde-like systems. Zbl 0724.65025 Higham, Nicholas J. 27 1990 Numerically stable generation of correlation matrices and their factors. Zbl 0969.65036 Davies, Philip I.; Higham, Nicholas J. 26 2000 A new analysis of iterative refinement and its application to accurate solution of ill-conditioned sparse linear systems. Zbl 1379.65019 Carson, Erin; Higham, Nicholas J. 26 2017 Fast solution of Vandermonde-like systems involving orthogonal polynomials. Zbl 0666.65025 Higham, Nicholas J. 25 1988 Computing the Fréchet derivative of the matrix logarithm and estimating the condition number. Zbl 1362.65051 Al-Mohy, Awad H.; Higham, Nicholas J.; Relton, Samuel D. 25 2013 A modified Cholesky algorithm based on a symmetric indefinite factorization. Zbl 0949.65022 Cheng, Sheung Hun; Higham, Nicholas J. 23 1998 Factorizing complex symmetric matrices with positive definite real and imaginary parts. Zbl 0909.65016 Higham, Nicholas J. 23 1998 Improved inverse scaling and squaring algorithms for the matrix logarithm. Zbl 1252.15027 Al-Mohy, Awad H.; Higham, Nicholas J. 23 2012 Matlab guide. 2nd ed. Zbl 1067.68180 Higham, Desmond J; Higham, Nicholas J. 21 2005 New algorithms for computing the matrix sine and cosine separately or simultaneously. Zbl 1315.65045 Al-Mohy, Awad H.; Higham, Nicholas J.; Relton, Samuel D. 21 2015 Anderson acceleration of the alternating projections method for computing the nearest correlation matrix. Zbl 1347.65074 Higham, Nicholas J.; Strabić, Nataša 21 2016 Large growth factors in Gaussian elimination with pivoting. Zbl 0681.65012 Higham, Nicholas J.; Higham, Desmond J. 20 1989 Exploiting fast matrix multiplication within the level 3 BLAS. Zbl 0900.65118 Higham, Nicholas J. 19 1990 Computing the field of values and pseudospectra using the Lanczos method with continuation. Zbl 0861.65033 Braconnier, Thierry; Higham, Nicholas J. 19 1996 On \(p\)th roots of stochastic matrices. Zbl 1223.15042 Higham, Nicholas J.; Lin, Lijing 19 2011 Detecting and solving hyperbolic quadratic eigenvalue problems. Zbl 1180.65042 Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Françoise 18 2009 Computing the polar decomposition and the matrix sign decomposition in matrix groups. Zbl 1066.65033 Higham, Nicholas J.; Mackey, D. Steven; Mackey, Niloufer; Tisseur, Françoise 18 2004 Estimating the matrix \(p\)-norm. Zbl 0741.65040 Higham, Nicholas J. 18 1992 Algorithm 694: A collection of test matrices in MATLAB. Zbl 0900.65120 Higham, Nicholas J. 18 1991 Squeezing a matrix into half precision, with an application to solving Linear systems. Zbl 1420.65017 Higham, Nicholas J.; Pranesh, Srikara; Zounon, Mawussi 18 2019 The complex step approximation to the Fréchet derivative of a matrix function. Zbl 1188.65054 Al-Mohy, Awad H.; Higham, Nicholas J. 17 2010 Computing the matrix cosine. Zbl 1033.65027 Higham, Nicholas J.; Smith, Matthew I. 17 2003 Accuracy and stability of the null space method for solving the equality constrained least squares problem. Zbl 0924.65033 Cox, Anthony J.; Higham, Nicholas J. 17 1999 Scaling, sensitivity and stability in the numerical solution of quadratic eigenvalue problems. Zbl 1166.74009 Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise; Garvey, Seamus D. 17 2008 Analysis of the Cholesky decomposition of a semi-definite matrix. Zbl 0721.65014 Higham, Nicholas J. 17 1990 A framework for analyzing nonlinear eigenproblems and parametrized linear systems. Zbl 1288.65049 Grammont, Laurence; Higham, Nicholas J.; Tisseur, Françoise 17 2011 An improved arc algorithm for detecting definite Hermitian pairs. Zbl 1202.65054 Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Françoise 17 2010 Definite matrix polynomials and their linearization by definite pencils. Zbl 1232.65059 Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise 16 2009 Iterative refinement enhances the stability of \(QR\) factorization methods for solving linear equations. Zbl 0736.65016 Higham, Nicholas J. 16 1991 Componentwise perturbation theory for linear systems with multiple right- hand sides. Zbl 0801.65043 Higham, Desmond J.; Higham, Nicholas J. 16 1992 Iterative refinement for linear systems and LAPACK. Zbl 0887.65034 Higham, Nicholas J. 16 1997 Simulating low precision floating-point arithmetic. Zbl 07124603 Higham, Nicholas J.; Pranesh, Srikara 16 2019 Bounding the error in Gaussian elimination for tridiagonal systems. Zbl 0716.65025 Higham, Nicholas J. 15 1990 Improved error bounds for undetermined system solvers. Zbl 0770.65025 Demmel, James W.; Higham, Nicholas J. 15 1993 Stable and efficient spectral divide and conquer algorithms for the symmetric eigenvalue decomposition and the SVD. Zbl 1326.65049 Nakatsukasa, Yuji; Higham, Nicholas J. 15 2013 The canonical generalized polar decomposition. Zbl 1222.15018 Higham, Nicholas J.; Mehl, Christian; Tisseur, Françoise 15 2010 The equality constrained indefinite least squares problem: Theory and algorithms. Zbl 1050.65035 Bojanczyk, Adam; Higham, Nicholas J.; Patel, Harikrishna 14 2003 Experience with a matrix norm estimator. Zbl 0752.65036 Higham, Nicholas J. 14 1990 Stability of methods for matrix inversion. Zbl 0748.65021 Du Croz, Jeremy J.; Higham, Nicholas J. 14 1992 An algorithm for the matrix Lambert \(W\) function. Zbl 1317.65116 Fasi, Massimiliano; Higham, Nicholas J.; Iannazzo, Bruno 14 2015 Computing a nearest correlation matrix with factor structure. Zbl 1213.65022 Borsdorf, Rüdiger; Higham, Nicholas J.; Raydan, Marcos 13 2010 Efficient algorithms for computing the condition number of a tridiagonal matrix. Zbl 0599.65026 Higham, Nicholas J. 13 1986 Fast polar decomposition of an arbitrary matrix. Zbl 0711.65024 Higham, Nicholas J.; Schreiber, Robert S. 13 1990 Stability of block algorithms with fast level-3 BLAS. Zbl 0892.65016 Demmel, James W.; Higham, Nicholas J. 13 1992 The Princeton companion to applied mathematics. Zbl 1327.00002 13 2015 The accuracy of solutions to triangular systems. Zbl 0683.65029 Higham, Nicholas J. 12 1989 Probabilistic rounding error analysis of Householder QR factorization. Zbl 1520.65019 Connolly, Michael P.; Higham, Nicholas J. 1 2023 Matrix multiplication in multiword arithmetic: error analysis and application to GPU tensor cores. Zbl 1511.65040 Fasi, Massimiliano; Higham, Nicholas J.; Lopez, Florent; Mary, Theo; Mikaitis, Mantas 1 2023 Mixed precision algorithms in numerical linear algebra. Zbl 1512.65081 Higham, Nicholas J.; Mary, Theo 7 2022 Solving block low-rank linear systems by LU factorization is numerically stable. Zbl 1511.65024 Higham, Nicholas J.; Mary, Theo 4 2022 Anymatrix: an extensible MATLAB matrix collection. Zbl 1492.65002 Higham, Nicholas J.; Mikaitis, Mantas 4 2022 Arbitrary precision algorithms for computing the matrix cosine and its Fréchet derivative. Zbl 1508.65044 Al-Mohy, Awad H.; Higham, Nicholas J.; Liu, Xiaobo 3 2022 Optimizing and factorizing the Wilson matrix. Zbl 1489.15012 Higham, Nicholas J.; Lettington, Matthew C. 1 2022 Stochastic rounding and its probabilistic backward error analysis. Zbl 1462.65050 Connolly, Michael P.; Higham, Nicholas J.; Mary, Theo 11 2021 A multiprecision derivative-free Schur-Parlett algorithm for computing matrix functions. Zbl 1476.65067 Higham, Nicholas J.; Liu, Xiaobo 7 2021 Exploiting lower precision arithmetic in solving symmetric positive definite linear systems and least squares problems. Zbl 1467.65023 Higham, Nicholas J.; Pranesh, Srikara 6 2021 Random matrices generating large growth in LU factorization with pivoting. Zbl 1459.65036 Higham, Desmond J.; Higham, Nicholas J.; Pranesh, Srikara 5 2021 Accurately computing the log-sum-exp and softmax functions. Zbl 1509.65019 Blanchard, Pierre; Higham, Desmond J.; Higham, Nicholas J. 4 2021 Generating extreme-scale matrices with specified singular values or condition number. Zbl 1462.65041 Fasi, Massimiliano; Higham, Nicholas J. 2 2021 Matrices with tunable infinity-norm condition number and no need for pivoting in LU factorization. Zbl 1467.65035 Fasi, Massimiliano; Higham, Nicholas J. 2 2021 Integer matrix factorisations, superalgebras and the quadratic form obstruction. Zbl 1467.15009 Higham, Nicholas J.; Lettington, Matthew C.; Schmidt, Karl Michael 2 2021 A set of batched basic linear algebra subprograms and LAPACK routines. Zbl 07467952 Abdelfattah, Ahmad; Costa, Timothy; Dongarra, Jack; Gates, Mark; Haidar, Azzam; Hammarling, Sven; Higham, Nicholas J.; Kurzak, Jakub; Luszczek, Piotr; Tomov, Stanimire; Zounon, Mawussi 2 2021 The mathematics of floating-point arithmetic. Zbl 1477.65276 Higham, Nicholas J. 1 2021 Sharper probabilistic backward error analysis for basic linear algebra kernels with random data. Zbl 1452.65090 Higham, Nicholas J.; Mary, Theo 11 2020 Mixed precision block fused multiply-add: error analysis and application to GPU tensor cores. Zbl 1452.65425 Blanchard, Pierre; Higham, Nicholas J.; Lopez, Florent; Mary, Theo; Pranesh, Srikara 9 2020 Three-precision GMRES-based iterative refinement for least squares problems. Zbl 1461.65032 Carson, Erin; Higham, Nicholas J.; Pranesh, Srikara 9 2020 A class of fast and accurate summation algorithms. Zbl 1471.65035 Blanchard, Pierre; Higham, Nicholas J.; Mary, Theo 9 2020 Mixed-precision iterative refinement using tensor cores on GPUs to accelerate solution of linear systems. Zbl 1472.65174 Haidar, Azzam; Bayraktar, Harun; Tomov, Stanimire; Dongarra, Jack; Higham, Nicholas J. 6 2020 Numerical algorithms for high-performance computational science. Zbl 1462.65231 Dongarra, Jack; Grigori, Laura; Higham, Nicholas J. 4 2020 A new approach to probabilistic rounding error analysis. Zbl 07123205 Higham, Nicholas J.; Mary, Theo 28 2019 Squeezing a matrix into half precision, with an application to solving Linear systems. Zbl 1420.65017 Higham, Nicholas J.; Pranesh, Srikara; Zounon, Mawussi 18 2019 Simulating low precision floating-point arithmetic. Zbl 07124603 Higham, Nicholas J.; Pranesh, Srikara 16 2019 A new preconditioner that exploits low-rank approximations to factorization error. Zbl 1408.65013 Higham, Nicholas J.; Mary, Theo 12 2019 An arbitrary precision scaling and squaring algorithm for the matrix exponential. Zbl 1437.65033 Fasi, Massimiliano; Higham, Nicholas J. 6 2019 Accelerating the solution of linear systems by iterative refinement in three precisions. Zbl 1453.65067 Carson, Erin; Higham, Nicholas J. 34 2018 Multiprecision algorithms for computing the matrix logarithm. Zbl 1390.15073 Fasi, Massimiliano; Higham, Nicholas J. 8 2018 Computing the wave-kernel matrix functions. Zbl 1403.65020 Nadukandi, Prashanth; Higham, Nicholas J. 5 2018 A new analysis of iterative refinement and its application to accurate solution of ill-conditioned sparse linear systems. Zbl 1379.65019 Carson, Erin; Higham, Nicholas J. 26 2017 Matlab guide. 3rd revised and updated edition. Zbl 1357.68001 Higham, Desmond J; Higham, Nicholas J. 9 2017 Computing the action of trigonometric and hyperbolic matrix functions. Zbl 1365.65135 Higham, Nicholas J.; Kandolf, Peter 7 2017 Anderson acceleration of the alternating projections method for computing the nearest correlation matrix. Zbl 1347.65074 Higham, Nicholas J.; Strabić, Nataša 21 2016 Restoring definiteness via shrinking, with an application to correlation matrices with a fixed block. Zbl 1386.15062 Higham, Nicholas J.; Strabić, Nataša; Šego, Vedran 11 2016 Matrix inverse trigonometric and inverse hyperbolic functions: theory and algorithms. Zbl 1388.15012 Aprahamian, Mary; Higham, Nicholas J. 10 2016 Testing matrix function algorithms using identities. Zbl 1347.65087 Deadman, Edvin; Higham, Nicholas J. 5 2016 An algorithm to compute the polar decomposition of a \(3 \times 3\) matrix. Zbl 1353.65020 Higham, Nicholas J.; Noferini, Vanni 4 2016 Estimating the largest elements of a matrix. Zbl 1352.65132 Higham, Nicholas J.; Relton, Samuel D. 4 2016 Bounds for the distance to the nearest correlation matrix. Zbl 1347.65075 Higham, Nicholas J.; Strabić, Nataša 3 2016 New algorithms for computing the matrix sine and cosine separately or simultaneously. Zbl 1315.65045 Al-Mohy, Awad H.; Higham, Nicholas J.; Relton, Samuel D. 21 2015 An algorithm for the matrix Lambert \(W\) function. Zbl 1317.65116 Fasi, Massimiliano; Higham, Nicholas J.; Iannazzo, Bruno 14 2015 The Princeton companion to applied mathematics. Zbl 1327.00002 13 2015 Matrix functions: a short course. Zbl 1332.15021 Higham, Nicholas J.; Lin, Lijing 2 2015 Higher order Fréchet derivatives of matrix functions and the level-2 condition number. Zbl 1308.65066 Higham, Nicholas J.; Relton, Samuel D. 11 2014 Covariance structure regularization via entropy loss function. Zbl 1506.62109 Lin, Lijing; Higham, Nicholas J.; Pan, Jianxin 10 2014 The matrix unwinding function, with an application to computing the matrix exponential. Zbl 1300.65024 Aprahamian, Mary; Higham, Nicholas J. 9 2014 Estimating the condition number of the Fréchet derivative of a matrix function. Zbl 1377.65054 Higham, Nicholas J.; Relton, Samuel D. 3 2014 NLEVP, a collection of nonlinear eigenvalue problems. Zbl 1295.65140 Betcke, Timo; Higham, Nicholas J.; Mehrmann, Volker; Schröder, Christian; Tisseur, Françoise 141 2013 An improved Schur-Padé algorithm for fractional powers of a matrix and their Fréchet derivatives. Zbl 1279.65050 Higham, Nicholas J.; Lin, Lijing 29 2013 Computing the Fréchet derivative of the matrix logarithm and estimating the condition number. Zbl 1362.65051 Al-Mohy, Awad H.; Higham, Nicholas J.; Relton, Samuel D. 25 2013 Stable and efficient spectral divide and conquer algorithms for the symmetric eigenvalue decomposition and the SVD. Zbl 1326.65049 Nakatsukasa, Yuji; Higham, Nicholas J. 15 2013 Reducing the influence of tiny normwise relative errors on performance profiles. Zbl 1298.65086 Dingle, Nicholas J.; Higham, Nicholas J. 6 2013 Improved inverse scaling and squaring algorithms for the matrix logarithm. Zbl 1252.15027 Al-Mohy, Awad H.; Higham, Nicholas J. 23 2012 Backward stability of iterations for computing the polar decomposition. Zbl 1252.65083 Nakatsukasa, Yuji; Higham, Nicholas J. 10 2012 Computing the action of the matrix exponential, with an application to exponential integrators. Zbl 1234.65028 Al-Mohy, Awad H.; Higham, Nicholas J. 147 2011 A Schur-Padé algorithm for fractional powers of a matrix. Zbl 1242.65091 Higham, Nicholas J.; Lin, Lijing 29 2011 On \(p\)th roots of stochastic matrices. Zbl 1223.15042 Higham, Nicholas J.; Lin, Lijing 19 2011 A framework for analyzing nonlinear eigenproblems and parametrized linear systems. Zbl 1288.65049 Grammont, Laurence; Higham, Nicholas J.; Tisseur, Françoise 17 2011 A new scaling and squaring algorithm for the matrix exponential. Zbl 1194.15021 Al-Mohy, Awad H.; Higham, Nicholas J. 98 2010 Computing matrix functions. Zbl 1242.65090 Higham, Nicholas J.; Al-Mohy, Awad H. 39 2010 A preconditioned Newton algorithm for the nearest correlation matrix. Zbl 1188.65055 Borsdorf, Rüdiger; Higham, Nicholas J. 32 2010 The complex step approximation to the Fréchet derivative of a matrix function. Zbl 1188.65054 Al-Mohy, Awad H.; Higham, Nicholas J. 17 2010 An improved arc algorithm for detecting definite Hermitian pairs. Zbl 1202.65054 Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Françoise 17 2010 The canonical generalized polar decomposition. Zbl 1222.15018 Higham, Nicholas J.; Mehl, Christian; Tisseur, Françoise 15 2010 Computing a nearest correlation matrix with factor structure. Zbl 1213.65022 Borsdorf, Rüdiger; Higham, Nicholas J.; Raydan, Marcos 13 2010 The scaling and squaring method for the matrix exponential revisited. Zbl 1178.65040 Higham, Nicholas J. 58 2009 Computing the Fréchet derivative of the matrix exponential, with an application to condition number estimation. Zbl 1180.65049 Al-Mohy, Awad H.; Higham, Nicholas J. 29 2009 Detecting and solving hyperbolic quadratic eigenvalue problems. Zbl 1180.65042 Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Françoise 18 2009 Definite matrix polynomials and their linearization by definite pencils. Zbl 1232.65059 Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise 16 2009 Functions of matrices. Theory and computation. Zbl 1167.15001 Higham, Nicholas J. 793 2008 Computing \(A^\alpha, \log(A)\), and related matrix functions by contour integrals. Zbl 1176.65053 Hale, Nicholas; Higham, Nicholas J.; Trefethen, Lloyd N. 79 2008 Backward error of polynomial eigenproblems solved by linearization. Zbl 1159.65042 Higham, Nicholas J.; Li, Ren-Cang; Tisseur, Françoise 46 2008 Scaling, sensitivity and stability in the numerical solution of quadratic eigenvalue problems. Zbl 1166.74009 Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise; Garvey, Seamus D. 17 2008 Iterative solution of a nonsymmetric algebraic Riccati equation. Zbl 1146.65035 Guo, Chun-Hua; Higham, Nicholas J. 46 2007 The solution of \(s\exp(s)=a\) is not always the Lambert \(w\) function of \(a\). Zbl 1190.34072 Corless, Robert M.; Ding, Hui; Higham, Nicholas J.; Jeffrey, David J. 7 2007 Milestones in matrix computation. The selected works of Gene H. Golub. With commentaries by Anne Greenbaum, Åke Björk, Nicholas Higham, Walter Gautschi and G. W. Stewart. Edited by Raymond H. Chan, Chen Greif, and Dianne P. O’Leary. Zbl 1121.65031 Golub, Gene H. 1 2007 Symmetric linearizations for matrix polynomials. Zbl 1137.15006 Higham, Nicholas J.; Mackey, D. Steven; Mackey, Niloufer; Tisseur, Françoise 73 2006 The conditioning of linearizations of matrix polynomials. Zbl 1131.65034 Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise 48 2006 A Schur-Newton method for the matrix \(p\)th root and its inverse. Zbl 1128.65030 Guo, Chun-Hua; Higham, Nicholas J. 30 2006 The scaling and squaring method for the matrix exponential revisited. Zbl 1081.65037 Higham, Nicholas J. 129 2005 Algorithms for the matrix \(p\)th root. Zbl 1103.65046 Bini, Dario A.; Higham, Nicholas; Meini, Beatrice 34 2005 Functions preserving matrix groups and iterations for the matrix square root. Zbl 1079.65053 Higham, Nicholas J.; Mackey, D. Steven; Mackey, Niloufer; Tisseur, Françoise 28 2005 Efficient algorithms for the matrix cosine and sine. Zbl 1084.65039 Hargreaves, Gareth I.; Higham, Nicholas J. 27 2005 Matlab guide. 2nd ed. Zbl 1067.68180 Higham, Desmond J; Higham, Nicholas J. 21 2005 Computing \(f(A)b\) for matrix functions \(f\). Zbl 1117.65319 Davies, Philip I.; Higham, Nicholas J. 11 2005 The numerical stability of barycentric Lagrange interpolation. Zbl 1067.65016 Higham, Nicholas J. 111 2004 Computing the polar decomposition and the matrix sign decomposition in matrix groups. Zbl 1066.65033 Higham, Nicholas J.; Mackey, D. Steven; Mackey, Niloufer; Tisseur, Françoise 18 2004 Bounds for eigenvalues of matrix polynomials. Zbl 1055.15030 Higham, Nicholas J.; Tisseur, Françoise 56 2003 A Schur-Parlett algorithm for computing matrix functions. Zbl 1052.65031 Davies, Philip I.; Higham, Nicholas J. 54 2003 \(J\)-orthogonal matrices: Properties and generation. Zbl 1034.65026 Higham, Nicholas J. 45 2003 Solving the indefinite least squares problem by hyperbolic QR factorization. Zbl 1036.65035 Bojanczyk, Adam; Higham, Nicholas J.; Patel, Harikrishna 29 2003 Computing the matrix cosine. Zbl 1033.65027 Higham, Nicholas J.; Smith, Matthew I. 17 2003 The equality constrained indefinite least squares problem: Theory and algorithms. Zbl 1050.65035 Bojanczyk, Adam; Higham, Nicholas J.; Patel, Harikrishna 14 2003 Accuracy and stability of numerical algorithms. 2nd ed. Zbl 1011.65010 Higham, Nicholas J. 844 2002 Computing the nearest correlation matrix – a problem from finance. Zbl 1006.65036 Higham, Nicholas J. 172 2002 Detecting a definite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems. Zbl 1004.65045 Higham, Nicholas J.; Tisseur, Françoise; Van Dooren, Paul M. 32 2002 More on pseudospectra for polynomial eigenvalue problems and applications in control theory. Zbl 1004.65046 Higham, Nicholas J.; Tisseur, Françoise 29 2002 Structured pseudospectra for polynomial eigenvalue problems, with applications. Zbl 0996.65042 Tisseur, Françoise; Higham, Nicholas J. 53 2001 ...and 71 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 4,989 Authors 63 Higham, Nicholas J. 59 Wei, Yimin 39 Peña, Juan Manuel 37 Kressner, Daniel 36 Dopico, Froilán M. 29 Rump, Siegfried Michael 28 Nakatsukasa, Yuji 28 Reichel, Lothar 26 Miyajima, Shinya 26 Tisseur, Françoise 24 Li, Rencang 24 Mehrmann, Volker 24 Noferini, Vanni 24 Van Dooren, Paul M. 23 Bini, Dario Andrea 23 Diao, Huaian 22 Ibáñez González, Jacinto Javier 22 Li, Hanyu 21 Benner, Peter 21 Ogita, Takeshi 19 Defez, Emilio 19 Soleymani, Fazlollah 18 Benzi, Michele 18 Sastre, Jorge 17 Melman, Aaron 17 Simoncini, Valeria 16 Corless, Robert Malcolm 15 Graillat, Stef 15 Iannazzo, Bruno 15 Jarlebring, Elias 15 Meini, Beatrice 15 Poloni, Federico Giovanni 15 Rozložník, Miroslav 15 Vabishchevich, Pëtr Nikolaevich 14 Alonso, Pedro 14 Cardoso, João R. 14 Delgado, Jorge F. M. 14 Liu, Qiaohua 14 Mackey, D. Steven 14 Robol, Leonardo 14 Wu, Xinyuan 13 Faßbender, Heike 13 Li, Wen 13 Marco García, Ana 13 Oishi, Shin’ichi 12 Fasi, Massimiliano 12 Guo, Chun-Hua 12 Güttel, Stefan 12 Hu, Xiyan 12 Kulikov, Gennady Yur’evich 12 Martínez, José-Javier 12 Mary, Theo A. 12 Noschese, Silvia 12 Pérez, Javier J. 12 Schweitzer, Marcel 11 Caliari, Marco 11 Frommer, Andreas 11 Gemignani, Luca 11 Gratton, Serge 11 Kim, Hyunmin 11 Massei, Stefano 11 Mitrouli, Marilena 11 Ostermann, Alexander 11 Ozaki, Katsuhisa 11 Psarrakos, Panayiotis J. 11 Sadkane, Miloud 11 Smoktunowicz, Alicja 11 Szyld, Daniel B. 11 Wang, Shaoxin 10 Barrio, Roberto 10 Bochev, M. A. 10 Cucker, Felipe 10 de Terán, Fernando 10 Estrada, Ernesto 10 Lin, Wen-Wei 10 Liu, Xinguo 10 Neff, Patrizio 10 Olshevsky, Vadim 10 Raydan, Marcos 10 Vandebril, Raf 10 Wei, Musheng 10 Yang, Hu 10 Ziętak, Krystyna 9 Alam, Rafikul 9 Dongarra, Jack J. 9 Drmač, Zlatko 9 Duan, Xuefeng 9 Higham, Desmond J. 9 Jeannerod, Claude-Pierre 9 Liao, Anping 9 Mehl, Christian 9 Pan, Victor Yakovlevich 9 Shen, Chungen 9 Stanimirović, Predrag S. 9 Wang, Weiguo 9 Zhang, Lei 8 Arrigo, Francesca 8 Bueno, María Isabel 8 Carson, Erin Claire 8 Chu, Moody T. ...and 4,889 more Authors all top 5 Cited in 497 Serials 434 Linear Algebra and its Applications 265 Journal of Computational and Applied Mathematics 161 SIAM Journal on Matrix Analysis and Applications 147 Numerical Algorithms 138 Applied Mathematics and Computation 129 SIAM Journal on Scientific Computing 119 BIT 89 Journal of Computational Physics 76 Numerical Linear Algebra with Applications 74 Computers & Mathematics with Applications 73 Applied Numerical Mathematics 68 Numerische Mathematik 67 Mathematics of Computation 58 Linear and Multilinear Algebra 44 Journal of Scientific Computing 40 Calcolo 38 Computer Methods in Applied Mechanics and Engineering 34 International Journal of Computer Mathematics 33 Computer Physics Communications 32 ELA. 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Zeitschrift für Angewandte Mathematik und Mechanik 6 Methodology and Computing in Applied Probability 6 Stochastic Models 6 Mediterranean Journal of Mathematics 6 Optimization Letters 6 Mathematical Programming Computation 5 Mathematical Methods in the Applied Sciences 5 Kybernetika 5 Numerical Functional Analysis and Optimization 5 Proceedings of the American Mathematical Society 5 Results in Mathematics 5 Annals of Operations Research 5 Computational Mathematics and Mathematical Physics ...and 397 more Serials all top 5 Cited in 61 Fields 2,641 Numerical analysis (65-XX) 1,337 Linear and multilinear algebra; matrix theory (15-XX) 313 Operations research, mathematical programming (90-XX) 237 Statistics (62-XX) 217 Partial differential equations (35-XX) 191 Systems theory; control (93-XX) 185 Computer science (68-XX) 172 Ordinary differential equations (34-XX) 159 Operator theory (47-XX) 143 Approximations and expansions (41-XX) 139 Probability theory and stochastic processes (60-XX) 86 Fluid mechanics (76-XX) 85 Calculus of variations and optimal control; optimization (49-XX) 84 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 83 Mechanics of deformable solids (74-XX) 81 Combinatorics (05-XX) 75 Quantum theory (81-XX) 69 Biology and other natural sciences (92-XX) 64 Real functions (26-XX) 61 Special functions (33-XX) 59 Dynamical systems and ergodic theory (37-XX) 52 Information and communication theory, circuits (94-XX) 51 Functions of a complex variable (30-XX) 43 Harmonic analysis on Euclidean spaces (42-XX) 39 Mechanics of particles and systems (70-XX) 38 Number theory (11-XX) 37 Differential geometry (53-XX) 36 Statistical mechanics, structure of matter (82-XX) 28 Field theory and polynomials (12-XX) 27 Integral equations (45-XX) 26 Optics, electromagnetic theory (78-XX) 23 Functional analysis (46-XX) 23 Geophysics (86-XX) 21 Integral transforms, operational calculus (44-XX) 18 Commutative algebra (13-XX) 17 Algebraic geometry (14-XX) 15 Difference and functional equations (39-XX) 15 Global analysis, analysis on manifolds (58-XX) 15 Relativity and gravitational theory (83-XX) 10 Associative rings and algebras (16-XX) 9 Topological groups, Lie groups (22-XX) 9 Convex and discrete geometry (52-XX) 8 History and biography (01-XX) 8 Classical thermodynamics, heat transfer (80-XX) 7 Several complex variables and analytic spaces (32-XX) 7 Geometry (51-XX) 6 General and overarching topics; collections (00-XX) 5 Mathematical logic and foundations (03-XX) 5 Measure and integration (28-XX) 5 Astronomy and astrophysics (85-XX) 4 Nonassociative rings and algebras (17-XX) 4 Potential theory (31-XX) 4 Manifolds and cell complexes (57-XX) 3 Group theory and generalizations (20-XX) 3 Sequences, series, summability (40-XX) 3 Algebraic topology (55-XX) 3 Mathematics education (97-XX) 2 General algebraic systems (08-XX) 2 General topology (54-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 \(K\)-theory (19-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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