Edit Profile (opens in new tab) Higham, Nicholas J. Compute Distance To: Compute 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 · Wikidata · Google Scholar · dblp · GND · IdRef · theses.fr Documents Indexed: 173 Publications since 1986, including 10 Books 3 Contributions as Editor · 2 Further Contributions Biographic References: 1 Publication Co-Authors: 89 Co-Authors with 123 Joint Publications 2,114 Co-Co-Authors all top 5 Co-Authors 53 single-authored 18 Tisseur, Françoise 10 Higham, Desmond J. 9 Al-Mohy, Awad H. 7 Mary, Theo A. 6 Mackey, D. Steven 6 Pranesh, Srikara 5 Cheng, Sheung Hun 5 Fasi, Massimiliano 5 Lin, Lijing 5 Relton, Samuel D. 4 Cox, Anthony J. 4 Davies, Philip I. 4 Guo, Chun-Hua 3 Blanchard, Pierre 3 Carson, Erin Claire 3 Demmel, James Weldon 3 Dongarra, Jack J. 3 Knight, Philip A. 3 Mackey, Niloufer 3 Strabić, Nataša 2 Aprahamian, Mary 2 Bojanczyk, Adam W. 2 Borsdorf, Rüdiger 2 Gautschi, Walter 2 Haidar, Azzam 2 Kim, Hyunmin 2 Lettington, Matthew C. 2 Nakatsukasa, Yuji 2 Papadimitriou, Pythagoras 2 Patel, Harikrishna 2 Schreiber, Robert S. 2 Stewart, Gilbert Wright 2 Tomov, Stanimire Z. 2 Zounon, Mawussi 1 Abdelfattah, Ahmad 1 Bai, Zhaojun 1 Bayraktar, Harun H. 1 Benzi, Michele 1 Betcke, Timo 1 Bini, Dario Andrea 1 Björk, Åke 1 Braconnier, Thierry 1 Brezinski, Claude 1 Chan, Raymond Hon-Fu 1 Connolly, Michael P. 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 Gates, Mark 1 Glendinning, Paul Alexander 1 Golub, Gene Howard 1 Grammont, Laurence 1 Greenbaum, Anne 1 Greif, Chen 1 Grigori, Laura 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 E. 1 Kurzak, Jakub 1 Laffey, Thomas J. 1 Laub, Alan J. 1 Li, Rencang 1 Lopez, Florent 1 Luszczek, Piotr 1 Martin, Paul Andrew 1 Mehl, Christian 1 Mehrman, Volker 1 Mehrmann, Volker 1 Meini, Beatrice 1 Mikaitis, Mantas 1 Nadukandi, Prashanth 1 Noferini, Vanni 1 O’Leary, Dianne P. 1 Pan, Jianxin 1 Pothen, Alex 1 Puerta, Ferran 1 Raydan, Marcos 1 Sameh, Ahmed H. 1 Santosa, Fadil N. 1 Schmidt, Karl Michael 1 Schröder, Christian 1 Šego, Vedran 1 Segura, Javier 1 Smith, Matthew I. 1 Spalević, Miodrag M. 1 Tanner, Jared W. 1 Trefethen, Lloyd Nicholas 1 Van Dooren, Paul M. all top 5 Serials 49 SIAM Journal on Matrix Analysis and Applications 25 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 2 Mathematics of Computation 2 Numerische Mathematik 2 SIAM Journal on Numerical Analysis 2 Other Titles in Applied Mathematics 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 Acta Numerica 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 1 London Mathematical Society. Newsletter all top 5 Fields 164 Numerical analysis (65-XX) 73 Linear and multilinear algebra; matrix theory (15-XX) 7 Statistics (62-XX) 7 Computer science (68-XX) 6 General and overarching topics; collections (00-XX) 6 Operations research, mathematical programming (90-XX) 3 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 164 Publications have been cited 4,913 times in 3,204 Documents Cited by ▼ Year ▼ Accuracy and stability of numerical algorithms. 2nd ed. Zbl 1011.65010Higham, Nicholas J. 685 2002 Functions of matrices. Theory and computation. Zbl 1167.15001Higham, Nicholas J. 586 2008 Accuracy and stability of numerical algorithms. Zbl 0847.65010Higham, Nicholas J. 302 1996 Computing the nearest correlation matrix – a problem from finance. Zbl 1006.65036Higham, Nicholas J. 148 2002 Computing a nearest symmetric positive semidefinite matrix. Zbl 0649.65026Higham, Nicholas J. 134 1988 Computing the action of the matrix exponential, with an application to exponential integrators. Zbl 1234.65028Al-Mohy, Awad H.; Higham, Nicholas J. 115 2011 The scaling and squaring method for the matrix exponential revisited. Zbl 1081.65037Higham, Nicholas J. 107 2005 NLEVP, a collection of nonlinear eigenvalue problems. Zbl 1295.65140Betcke, Timo; Higham, Nicholas J.; Mehrmann, Volker; Schröder, Christian; Tisseur, Françoise 101 2013 The numerical stability of barycentric Lagrange interpolation. Zbl 1067.65016Higham, Nicholas J. 88 2004 Computing the polar decomposition - with applications. Zbl 0607.65014Higham, Nicholas J. 79 1986 A new scaling and squaring algorithm for the matrix exponential. Zbl 1194.15021Al-Mohy, Awad H.; Higham, Nicholas J. 73 2010 Computing \(A^\alpha, \log(A)\), and related matrix functions by contour integrals. Zbl 1176.65053Hale, Nicholas; Higham, Nicholas J.; Trefethen, Lloyd N. 68 2008 Matrix nearness problems and applications. Zbl 0681.65029Higham, N. J. 61 1989 Computing real square roots of a real matrix. Zbl 0625.65032Higham, Nicholas J. 56 1987 Symmetric linearizations for matrix polynomials. Zbl 1137.15006Higham, Nicholas J.; Mackey, D. Steven; Mackey, Niloufer; Tisseur, Françoise 55 2006 The scaling and squaring method for the matrix exponential revisited. Zbl 1178.65040Higham, Nicholas J. 51 2009 Structured pseudospectra for polynomial eigenvalue problems, with applications. Zbl 0996.65042Tisseur, Françoise; Higham, Nicholas J. 50 2001 Structured backward error and condition of generalized eigenvalue problems. Zbl 0935.65032Higham, Desmond J.; Higham, Nicholas J. 49 1998 A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra. Zbl 0959.65061Higham, Nicholas J.; Tisseur, Françoise 46 2000 Bounds for eigenvalues of matrix polynomials. Zbl 1055.15030Higham, Nicholas J.; Tisseur, Françoise 46 2003 A Schur-Parlett algorithm for computing matrix functions. Zbl 1052.65031Davies, Philip I.; Higham, Nicholas J. 43 2003 Newton’s method for the matrix square root. Zbl 0614.65045Higham, Nicholas J. 42 1986 Backward error and condition of structured linear systems. Zbl 0747.65028Higham, Desmond J.; Higham, Nicholas J. 42 1992 The conditioning of linearizations of matrix polynomials. Zbl 1131.65034Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise 42 2006 Numerical analysis of a quadratic matrix equation. Zbl 0966.65040Higham, Nicholas J.; Kim, Hyun-Min 41 2000 Backward error of polynomial eigenproblems solved by linearization. Zbl 1159.65042Higham, Nicholas J.; Li, Ren-Cang; Tisseur, Françoise 41 2008 Iterative solution of a nonsymmetric algebraic Riccati equation. Zbl 1146.65035Guo, Chun-Hua; Higham, Nicholas J. 39 2008 \(J\)-orthogonal matrices: Properties and generation. Zbl 1034.65026Higham, Nicholas J. 37 2003 A survey of condition number estimation for triangular matrices. Zbl 0635.65049Higham, Nicholas J. 36 1987 Computing matrix functions. Zbl 1242.65090Higham, Nicholas J.; Al-Mohy, Awad H. 35 2010 A survey of componentwise perturbation theory in numerical linear algebra. Zbl 0815.65062Higham, Nicholas J. 34 1994 Error analysis of the Björck-Pereyra algorithms for solving Vandermonde systems. Zbl 0595.65029Higham, Nicholas J. 33 1987 FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimations. Zbl 0665.65043Higham, Nicholas J. 32 1988 Stable iterations for the matrix square root. Zbl 0884.65035Higham, Nicholas J. 32 1997 Detecting a definite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems. Zbl 1004.65045Higham, Nicholas J.; Tisseur, Françoise; Van Dooren, Paul M. 30 2002 The accuracy of floating point summation. Zbl 0788.65053Higham, Nicholas J. 30 1993 A Schur-Newton method for the matrix \(p\)th root and its inverse. Zbl 1128.65030Guo, Chun-Hua; Higham, Nicholas J. 29 2006 Solving a quadratic matrix equation by newton’s method with exact line searches. Zbl 1017.65038Higham, Nicholas J.; Kim, Hyun-Min 28 2001 The symmetric Procrustes problem. Zbl 0641.65034Higham, Nicholas J. 27 1988 More on pseudospectra for polynomial eigenvalue problems and applications in control theory. Zbl 1004.65046Higham, Nicholas J.; Tisseur, Françoise 27 2002 The matrix sign decomposition and its relation to the polar decomposition. Zbl 0816.15012Higham, Nicholas J. 26 1994 A Schur-Padé algorithm for fractional powers of a matrix. Zbl 1242.65091Higham, Nicholas J.; Lin, Lijing 26 2011 A preconditioned Newton algorithm for the nearest correlation matrix. Zbl 1188.65055Borsdorf, Rüdiger; Higham, Nicholas J. 26 2010 Algorithms for the matrix \(p\)th root. Zbl 1103.65046Bini, Dario A.; Higham, Nicholas; Meine, Beatrice 26 2005 Stability analysis of algorithms for solving confluent Vandermonde-like systems. Zbl 0724.65025Higham, Nicholas J. 25 1990 Perturbation theory and backward error for \(AX - XB = C\). Zbl 0781.65034Higham, Nicholas J. 25 1993 An improved Schur-Padé algorithm for fractional powers of a matrix and their Fréchet derivatives. Zbl 1279.65050Higham, Nicholas J.; Lin, Lijing 25 2013 Stability of block. Zbl 0834.65010Demmel, James W.; Higham, Nicholas J.; Schreiber, Robert S. 24 1995 Efficient algorithms for the matrix cosine and sine. Zbl 1084.65039Hargreaves, Gareth I.; Higham, Nicholas J. 24 2005 Solving the indefinite least squares problem by hyperbolic QR factorization. Zbl 1036.65035Bojanczyk, Adam; Higham, Nicholas J.; Patel, Harikrishna 24 2003 Fast solution of Vandermonde-like systems involving orthogonal polynomials. Zbl 0666.65025Higham, Nicholas J. 23 1988 Functions preserving matrix groups and iterations for the matrix square root. Zbl 1079.65053Higham, Nicholas J.; Mackey, D. Steven; Mackey, Niloufer; Tisseur, Françoise 23 2005 Approximating the logarithm of a matrix to specified accuracy. Zbl 0989.65057Cheng, Sheung Hun; Higham, Nicholas J.; Kenney, Charles S.; Laub, Alan J. 23 2001 Computing the Fréchet derivative of the matrix exponential, with an application to condition number estimation. Zbl 1180.65049Al-Mohy, Awad H.; Higham, Nicholas J. 22 2009 Computing the Fréchet derivative of the matrix logarithm and estimating the condition number. Zbl 1362.65051Al-Mohy, Awad H.; Higham, Nicholas J.; Relton, Samuel D. 22 2013 Factorizing complex symmetric matrices with positive definite real and imaginary parts. Zbl 0909.65016Higham, Nicholas J. 21 1998 Accelerating the solution of linear systems by iterative refinement in three precisions. Zbl 1453.65067Carson, Erin; Higham, Nicholas J. 21 2018 Numerically stable generation of correlation matrices and their factors. Zbl 0969.65036Davies, Philip I.; Higham, Nicholas J. 20 2000 Computing the field of values and pseudospectra using the Lanczos method with continuation. Zbl 0861.65033Braconnier, Thierry; Higham, Nicholas J. 19 1996 A modified Cholesky algorithm based on a symmetric indefinite factorization. Zbl 0949.65022Cheng, Sheung Hun; Higham, Nicholas J. 19 1998 New algorithms for computing the matrix sine and cosine separately or simultaneously. Zbl 1315.65045Al-Mohy, Awad H.; Higham, Nicholas J.; Relton, Samuel D. 18 2015 Exploiting fast matrix multiplication within the level 3 BLAS. Zbl 0900.65118Higham, Nicholas J. 18 1990 Algorithm 694: A collection of test matrices in MATLAB. Zbl 0900.65120Higham, Nicholas J. 18 1991 Detecting and solving hyperbolic quadratic eigenvalue problems. Zbl 1180.65042Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Françoise 17 2009 Computing the polar decomposition and the matrix sign decomposition in matrix groups. Zbl 1066.65033Higham, Nicholas J.; Mackey, D. Steven; Mackey, Niloufer; Tisseur, Françoise 17 2004 Large growth factors in Gaussian elimination with pivoting. Zbl 0681.65012Higham, Nicholas J.; Higham, Desmond J. 17 1989 An improved arc algorithm for detecting definite Hermitian pairs. Zbl 1202.65054Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Françoise 17 2010 A new analysis of iterative refinement and its application to accurate solution of ill-conditioned sparse linear systems. Zbl 1379.65019Carson, Erin; Higham, Nicholas J. 17 2017 Estimating the matrix \(p\)-norm. Zbl 0741.65040Higham, Nicholas J. 16 1992 A framework for analyzing nonlinear eigenproblems and parametrized linear systems. Zbl 1288.65049Grammont, Laurence; Higham, Nicholas J.; Tisseur, Françoise 16 2011 Componentwise perturbation theory for linear systems with multiple right- hand sides. Zbl 0801.65043Higham, Desmond J.; Higham, Nicholas J. 16 1992 Improved inverse scaling and squaring algorithms for the matrix logarithm. Zbl 1252.15027Al-Mohy, Awad H.; Higham, Nicholas J. 16 2012 A new approach to probabilistic rounding error analysis. Zbl 07123205Higham, Nicholas J.; Mary, Theo 16 2019 Anderson acceleration of the alternating projections method for computing the nearest correlation matrix. Zbl 1347.65074Higham, Nicholas J.; Strabić, Nataša 15 2016 The complex step approximation to the Fréchet derivative of a matrix function. Zbl 1188.65054Al-Mohy, Awad H.; Higham, Nicholas J. 15 2010 Bounding the error in Gaussian elimination for tridiagonal systems. Zbl 0716.65025Higham, Nicholas J. 15 1990 Analysis of the Cholesky decomposition of a semi-definite matrix. Zbl 0721.65014Higham, Nicholas J. 15 1990 Scaling, sensitivity and stability in the numerical solution of quadratic eigenvalue problems. Zbl 1166.74009Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise; Garvey, Seamus D. 15 2008 Accuracy and stability of the null space method for solving the equality constrained least squares problem. Zbl 0924.65033Cox, Anthony J.; Higham, Nicholas J. 15 1999 Matlab guide. 2nd ed. Zbl 1067.68180Higham, Desmond J; Higham, Nicholas J. 14 2005 Definite matrix polynomials and their linearization by definite pencils. Zbl 1232.65059Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise 14 2009 Improved error bounds for undetermined system solvers. Zbl 0770.65025Demmel, James W.; Higham, Nicholas J. 14 1993 Experience with a matrix norm estimator. Zbl 0752.65036Higham, Nicholas J. 14 1990 Computing the matrix cosine. Zbl 1033.65027Higham, Nicholas J.; Smith, Matthew I. 14 2003 Stable and efficient spectral divide and conquer algorithms for the symmetric eigenvalue decomposition and the SVD. Zbl 1326.65049Nakatsukasa, Yuji; Higham, Nicholas J. 13 2013 Stability of methods for matrix inversion. Zbl 0748.65021Du Croz, Jeremy J.; Higham, Nicholas J. 13 1992 Efficient algorithms for computing the condition number of a tridiagonal matrix. Zbl 0599.65026Higham, Nicholas J. 13 1986 Stability of block algorithms with fast level-3 BLAS. Zbl 0892.65016Demmel, James W.; Higham, Nicholas J. 13 1992 On \(p\)th roots of stochastic matrices. Zbl 1223.15042Higham, Nicholas J.; Lin, Lijing 12 2011 Stability of the diagonal pivoting method with partial pivoting. Zbl 0884.65024Higham, Nicholas J. 12 1997 Iterative refinement enhances the stability of \(QR\) factorization methods for solving linear equations. Zbl 0736.65016Higham, Nicholas J. 12 1991 Computing a nearest correlation matrix with factor structure. Zbl 1213.65022Borsdorf, Rüdiger; Higham, Nicholas J.; Raydan, Marcos 12 2010 Matlab guide. Zbl 0953.68642Higham, Desmond J.; Higham, Nicholas J. 11 2000 Computing \(f(A)b\) for matrix functions \(f\). Zbl 1117.65319Davies, Philip I.; Higham, Nicholas J. 11 2005 Fast polar decomposition of an arbitrary matrix. Zbl 0711.65024Higham, Nicholas J.; Schreiber, Robert S. 11 1990 The canonical generalized polar decomposition. Zbl 1222.15018Higham, Nicholas J.; Mehl, Christian; Tisseur, Françoise 11 2010 Finite precision behavior of stationary iteration for solving singular systems. Zbl 0787.65021Higham, Nicholas J.; Knight, Philip A. 11 1993 Iterative refinement for linear systems and LAPACK. Zbl 0887.65034Higham, Nicholas J. 11 1997 Stability of Householder QR factorization for weighted least squares problems. Zbl 0903.65036Cox, A. J.; Higham, N. J. 11 1998 The equality constrained indefinite least squares problem: Theory and algorithms. Zbl 1050.65035Bojanczyk, Adam; Higham, Nicholas J.; Patel, Harikrishna 11 2003 Arbitrary precision algorithms for computing the matrix cosine and its Fréchet derivative. Zbl 07487115Al-Mohy, Awad H.; Higham, Nicholas J.; Liu, Xiaobo 1 2022 Optimizing and factorizing the Wilson matrix. Zbl 07525560Higham, Nicholas J.; Lettington, Matthew C. 1 2022 Exploiting lower precision arithmetic in solving symmetric positive definite linear systems and least squares problems. Zbl 1467.65023Higham, Nicholas J.; Pranesh, Srikara 4 2021 A multiprecision derivative-free Schur-Parlett algorithm for computing matrix functions. Zbl 1476.65067Higham, Nicholas J.; Liu, Xiaobo 4 2021 Integer matrix factorisations, superalgebras and the quadratic form obstruction. Zbl 1467.15009Higham, Nicholas J.; Lettington, Matthew C.; Schmidt, Karl Michael 2 2021 Random matrices generating large growth in LU factorization with pivoting. Zbl 1459.65036Higham, Desmond J.; Higham, Nicholas J.; Pranesh, Srikara 1 2021 Stochastic rounding and its probabilistic backward error analysis. Zbl 1462.65050Connolly, Michael P.; Higham, Nicholas J.; Mary, Theo 1 2021 Generating extreme-scale matrices with specified singular values or condition number. Zbl 1462.65041Fasi, Massimiliano; Higham, Nicholas J. 1 2021 Matrices with tunable infinity-norm condition number and no need for pivoting in LU factorization. Zbl 1467.65035Fasi, Massimiliano; Higham, Nicholas J. 1 2021 Accurately computing the log-sum-exp and softmax functions. Zbl 07528305Blanchard, Pierre; Higham, Desmond J.; Higham, Nicholas J. 1 2021 Mixed precision block fused multiply-add: error analysis and application to GPU tensor cores. Zbl 1452.65425Blanchard, Pierre; Higham, Nicholas J.; Lopez, Florent; Mary, Theo; Pranesh, Srikara 6 2020 Three-precision GMRES-based iterative refinement for least squares problems. Zbl 1461.65032Carson, Erin; Higham, Nicholas J.; Pranesh, Srikara 3 2020 A class of fast and accurate summation algorithms. Zbl 1471.65035Blanchard, Pierre; Higham, Nicholas J.; Mary, Theo 2 2020 Sharper probabilistic backward error analysis for basic linear algebra kernels with random data. Zbl 1452.65090Higham, Nicholas J.; Mary, Theo 2 2020 Numerical algorithms for high-performance computational science. Zbl 1462.65231Dongarra, Jack; Grigori, Laura; Higham, Nicholas J. 2 2020 Mixed-precision iterative refinement using tensor cores on GPUs to accelerate solution of linear systems. Zbl 1472.65174Haidar, Azzam; Bayraktar, Harun; Tomov, Stanimire; Dongarra, Jack; Higham, Nicholas J. 1 2020 A new approach to probabilistic rounding error analysis. Zbl 07123205Higham, Nicholas J.; Mary, Theo 16 2019 Squeezing a matrix into half precision, with an application to solving Linear systems. Zbl 1420.65017Higham, Nicholas J.; Pranesh, Srikara; Zounon, Mawussi 11 2019 Simulating low precision floating-point arithmetic. Zbl 07124603Higham, Nicholas J.; Pranesh, Srikara 9 2019 A new preconditioner that exploits low-rank approximations to factorization error. Zbl 1408.65013Higham, Nicholas J.; Mary, Theo 6 2019 An arbitrary precision scaling and squaring algorithm for the matrix exponential. Zbl 1437.65033Fasi, Massimiliano; Higham, Nicholas J. 2 2019 Accelerating the solution of linear systems by iterative refinement in three precisions. Zbl 1453.65067Carson, Erin; Higham, Nicholas J. 21 2018 Multiprecision algorithms for computing the matrix logarithm. Zbl 1390.15073Fasi, Massimiliano; Higham, Nicholas J. 5 2018 Computing the wave-kernel matrix functions. Zbl 1403.65020Nadukandi, Prashanth; Higham, Nicholas J. 3 2018 A new analysis of iterative refinement and its application to accurate solution of ill-conditioned sparse linear systems. Zbl 1379.65019Carson, Erin; Higham, Nicholas J. 17 2017 Matlab guide. 3rd revised and updated edition. Zbl 1357.68001Higham, Desmond J; Higham, Nicholas J. 7 2017 Computing the action of trigonometric and hyperbolic matrix functions. Zbl 1365.65135Higham, Nicholas J.; Kandolf, Peter 7 2017 Anderson acceleration of the alternating projections method for computing the nearest correlation matrix. Zbl 1347.65074Higham, Nicholas J.; Strabić, Nataša 15 2016 Matrix inverse trigonometric and inverse hyperbolic functions: theory and algorithms. Zbl 1388.15012Aprahamian, Mary; Higham, Nicholas J. 9 2016 Restoring definiteness via shrinking, with an application to correlation matrices with a fixed block. Zbl 1386.15062Higham, Nicholas J.; Strabić, Nataša; Šego, Vedran 7 2016 Estimating the largest elements of a matrix. Zbl 1352.65132Higham, Nicholas J.; Relton, Samuel D. 3 2016 Bounds for the distance to the nearest correlation matrix. Zbl 1347.65075Higham, Nicholas J.; Strabić, Nataša 2 2016 Testing matrix function algorithms using identities. Zbl 1347.65087Deadman, Edvin; Higham, Nicholas J. 2 2016 An algorithm to compute the polar decomposition of a \(3 \times 3\) matrix. Zbl 1353.65020Higham, Nicholas J.; Noferini, Vanni 2 2016 New algorithms for computing the matrix sine and cosine separately or simultaneously. Zbl 1315.65045Al-Mohy, Awad H.; Higham, Nicholas J.; Relton, Samuel D. 18 2015 An algorithm for the matrix Lambert \(W\) function. Zbl 1317.65116Fasi, Massimiliano; Higham, Nicholas J.; Iannazzo, Bruno 10 2015 The Princeton companion to applied mathematics. Zbl 1327.00002 4 2015 Matrix functions: a short course. Zbl 1332.15021Higham, Nicholas J.; Lin, Lijing 1 2015 Higher order Fréchet derivatives of matrix functions and the level-2 condition number. Zbl 1308.65066Higham, Nicholas J.; Relton, Samuel D. 7 2014 The matrix unwinding function, with an application to computing the matrix exponential. Zbl 1300.65024Aprahamian, Mary; Higham, Nicholas J. 6 2014 Covariance structure regularization via entropy loss function. Zbl 06983908Lin, Lijing; Higham, Nicholas J.; Pan, Jianxin 5 2014 Estimating the condition number of the Fréchet derivative of a matrix function. Zbl 1377.65054Higham, Nicholas J.; Relton, Samuel D. 3 2014 NLEVP, a collection of nonlinear eigenvalue problems. Zbl 1295.65140Betcke, Timo; Higham, Nicholas J.; Mehrmann, Volker; Schröder, Christian; Tisseur, Françoise 101 2013 An improved Schur-Padé algorithm for fractional powers of a matrix and their Fréchet derivatives. Zbl 1279.65050Higham, Nicholas J.; Lin, Lijing 25 2013 Computing the Fréchet derivative of the matrix logarithm and estimating the condition number. Zbl 1362.65051Al-Mohy, Awad H.; Higham, Nicholas J.; Relton, Samuel D. 22 2013 Stable and efficient spectral divide and conquer algorithms for the symmetric eigenvalue decomposition and the SVD. Zbl 1326.65049Nakatsukasa, Yuji; Higham, Nicholas J. 13 2013 Reducing the influence of tiny normwise relative errors on performance profiles. Zbl 1298.65086Dingle, Nicholas J.; Higham, Nicholas J. 6 2013 Improved inverse scaling and squaring algorithms for the matrix logarithm. Zbl 1252.15027Al-Mohy, Awad H.; Higham, Nicholas J. 16 2012 Backward stability of iterations for computing the polar decomposition. Zbl 1252.65083Nakatsukasa, Yuji; Higham, Nicholas J. 7 2012 Computing the action of the matrix exponential, with an application to exponential integrators. Zbl 1234.65028Al-Mohy, Awad H.; Higham, Nicholas J. 115 2011 A Schur-Padé algorithm for fractional powers of a matrix. Zbl 1242.65091Higham, Nicholas J.; Lin, Lijing 26 2011 A framework for analyzing nonlinear eigenproblems and parametrized linear systems. Zbl 1288.65049Grammont, Laurence; Higham, Nicholas J.; Tisseur, Françoise 16 2011 On \(p\)th roots of stochastic matrices. Zbl 1223.15042Higham, Nicholas J.; Lin, Lijing 12 2011 A new scaling and squaring algorithm for the matrix exponential. Zbl 1194.15021Al-Mohy, Awad H.; Higham, Nicholas J. 73 2010 Computing matrix functions. Zbl 1242.65090Higham, Nicholas J.; Al-Mohy, Awad H. 35 2010 A preconditioned Newton algorithm for the nearest correlation matrix. Zbl 1188.65055Borsdorf, Rüdiger; Higham, Nicholas J. 26 2010 An improved arc algorithm for detecting definite Hermitian pairs. Zbl 1202.65054Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Françoise 17 2010 The complex step approximation to the Fréchet derivative of a matrix function. Zbl 1188.65054Al-Mohy, Awad H.; Higham, Nicholas J. 15 2010 Computing a nearest correlation matrix with factor structure. Zbl 1213.65022Borsdorf, Rüdiger; Higham, Nicholas J.; Raydan, Marcos 12 2010 The canonical generalized polar decomposition. Zbl 1222.15018Higham, Nicholas J.; Mehl, Christian; Tisseur, Françoise 11 2010 The scaling and squaring method for the matrix exponential revisited. Zbl 1178.65040Higham, Nicholas J. 51 2009 Computing the Fréchet derivative of the matrix exponential, with an application to condition number estimation. Zbl 1180.65049Al-Mohy, Awad H.; Higham, Nicholas J. 22 2009 Detecting and solving hyperbolic quadratic eigenvalue problems. Zbl 1180.65042Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Françoise 17 2009 Definite matrix polynomials and their linearization by definite pencils. Zbl 1232.65059Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise 14 2009 Functions of matrices. Theory and computation. Zbl 1167.15001Higham, Nicholas J. 586 2008 Computing \(A^\alpha, \log(A)\), and related matrix functions by contour integrals. Zbl 1176.65053Hale, Nicholas; Higham, Nicholas J.; Trefethen, Lloyd N. 68 2008 Backward error of polynomial eigenproblems solved by linearization. Zbl 1159.65042Higham, Nicholas J.; Li, Ren-Cang; Tisseur, Françoise 41 2008 Iterative solution of a nonsymmetric algebraic Riccati equation. Zbl 1146.65035Guo, Chun-Hua; Higham, Nicholas J. 39 2008 Scaling, sensitivity and stability in the numerical solution of quadratic eigenvalue problems. Zbl 1166.74009Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise; Garvey, Seamus D. 15 2008 The solution of \(s\exp(s)=a\) is not always the Lambert \(w\) function of \(a\). Zbl 1190.34072Corless, 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 1121.65031Golub, Gene H. 1 2007 Symmetric linearizations for matrix polynomials. Zbl 1137.15006Higham, Nicholas J.; Mackey, D. Steven; Mackey, Niloufer; Tisseur, Françoise 55 2006 The conditioning of linearizations of matrix polynomials. Zbl 1131.65034Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise 42 2006 A Schur-Newton method for the matrix \(p\)th root and its inverse. Zbl 1128.65030Guo, Chun-Hua; Higham, Nicholas J. 29 2006 The scaling and squaring method for the matrix exponential revisited. Zbl 1081.65037Higham, Nicholas J. 107 2005 Algorithms for the matrix \(p\)th root. Zbl 1103.65046Bini, Dario A.; Higham, Nicholas; Meine, Beatrice 26 2005 Efficient algorithms for the matrix cosine and sine. Zbl 1084.65039Hargreaves, Gareth I.; Higham, Nicholas J. 24 2005 Functions preserving matrix groups and iterations for the matrix square root. Zbl 1079.65053Higham, Nicholas J.; Mackey, D. Steven; Mackey, Niloufer; Tisseur, Françoise 23 2005 Matlab guide. 2nd ed. Zbl 1067.68180Higham, Desmond J; Higham, Nicholas J. 14 2005 Computing \(f(A)b\) for matrix functions \(f\). Zbl 1117.65319Davies, Philip I.; Higham, Nicholas J. 11 2005 The numerical stability of barycentric Lagrange interpolation. Zbl 1067.65016Higham, Nicholas J. 88 2004 Computing the polar decomposition and the matrix sign decomposition in matrix groups. Zbl 1066.65033Higham, Nicholas J.; Mackey, D. Steven; Mackey, Niloufer; Tisseur, Françoise 17 2004 Bounds for eigenvalues of matrix polynomials. Zbl 1055.15030Higham, Nicholas J.; Tisseur, Françoise 46 2003 A Schur-Parlett algorithm for computing matrix functions. Zbl 1052.65031Davies, Philip I.; Higham, Nicholas J. 43 2003 \(J\)-orthogonal matrices: Properties and generation. Zbl 1034.65026Higham, Nicholas J. 37 2003 Solving the indefinite least squares problem by hyperbolic QR factorization. Zbl 1036.65035Bojanczyk, Adam; Higham, Nicholas J.; Patel, Harikrishna 24 2003 Computing the matrix cosine. Zbl 1033.65027Higham, Nicholas J.; Smith, Matthew I. 14 2003 The equality constrained indefinite least squares problem: Theory and algorithms. Zbl 1050.65035Bojanczyk, Adam; Higham, Nicholas J.; Patel, Harikrishna 11 2003 Accuracy and stability of numerical algorithms. 2nd ed. Zbl 1011.65010Higham, Nicholas J. 685 2002 Computing the nearest correlation matrix – a problem from finance. Zbl 1006.65036Higham, Nicholas J. 148 2002 Detecting a definite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems. Zbl 1004.65045Higham, Nicholas J.; Tisseur, Françoise; Van Dooren, Paul M. 30 2002 More on pseudospectra for polynomial eigenvalue problems and applications in control theory. Zbl 1004.65046Higham, Nicholas J.; Tisseur, Françoise 27 2002 Structured pseudospectra for polynomial eigenvalue problems, with applications. Zbl 0996.65042Tisseur, Françoise; Higham, Nicholas J. 50 2001 Solving a quadratic matrix equation by newton’s method with exact line searches. Zbl 1017.65038Higham, Nicholas J.; Kim, Hyun-Min 28 2001 Approximating the logarithm of a matrix to specified accuracy. Zbl 0989.65057Cheng, Sheung Hun; Higham, Nicholas J.; Kenney, Charles S.; Laub, Alan J. 23 2001 Evaluating Padé approximants of the matrix logarithm. Zbl 0989.65054Higham, Nicholas J. 9 2001 Analysis of the Cholesky method with iterative refinement for solving the symmetric definite generalized eigenproblem. Zbl 1002.65044Davies, Philip I.; Higham, Nicholas J.; Tisseur, Françoise 4 2001 A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra. Zbl 0959.65061Higham, Nicholas J.; Tisseur, Françoise 46 2000 Numerical analysis of a quadratic matrix equation. Zbl 0966.65040Higham, Nicholas J.; Kim, Hyun-Min 41 2000 Numerically stable generation of correlation matrices and their factors. Zbl 0969.65036Davies, Philip I.; Higham, Nicholas J. 20 2000 ...and 64 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 4,040 Authors 57 Higham, Nicholas J. 57 Wei, Yimin 35 Peña, Juan Manuel 33 Dopico, Froilán M. 28 Kressner, Daniel 28 Rump, Siegfried Michael 26 Reichel, Lothar 24 Li, Rencang 24 Miyajima, Shinya 24 Tisseur, Françoise 23 Diao, Huaian 23 Nakatsukasa, Yuji 21 Bini, Dario Andrea 21 Li, Hanyu 21 Mehrmann, Volker 20 Ogita, Takeshi 19 Ibáñez González, Jacinto Javier 19 Noferini, Vanni 18 Van Dooren, Paul M. 17 Benner, Peter 17 Defez, Emilio 17 Sastre, Jorge 17 Soleymani, Fazlollah 16 Benzi, Michele 16 Rozlozník, Miroslav 15 Melman, Aaron 15 Simoncini, Valeria 14 Alonso, Pedro 14 Iannazzo, Bruno 14 Meini, Beatrice 14 Poloni, Federico G. 13 Graillat, Stef 13 Huang, Rong 13 Mackey, D. Steven 13 Oishi, Shin’ichi 13 Robol, Leonardo 13 Wu, Xinyuan 12 Cardoso, João R. 12 Corless, Robert Malcolm 12 Delgado, Jorge F. M. 12 Faßbender, Heike 12 Guo, Chun-Hua 12 Hu, Xiyan 12 Vabishchevich, Pëtr Nikolaevich 11 Jarlebring, Elias 11 Kim, Hyunmin 11 Marco García, Ana 11 Noschese, Silvia 11 Pérez, Javier J. 11 Smoktunowicz, Alicja 10 Cucker, Felipe 10 de Terán, Fernando 10 Gemignani, Luca 10 Gratton, Serge 10 Li, Wen 10 Lin, Wen-Wei 10 Liu, Qiaohua 10 Liu, Xinguo 10 Martínez, José-Javier 10 Mitrouli, Marilena 10 Ostermann, Alexander 10 Ozaki, Katsuhisa 10 Psarrakos, Panayiotis J. 10 Raydan, Marcos 10 Szyld, Daniel B. 10 Wang, Shaoxin 10 Wei, Musheng 10 Yang, Hu 10 Ziętak, Krystyna 9 Alam, Rafikul 9 Dongarra, Jack J. 9 Estrada, Ernesto 9 Fasi, Massimiliano 9 Frommer, Andreas 9 Liao, Anping 9 Massei, Stefano 9 Olshevsky, Vadim 9 Stanimirović, Predrag S. 9 Vandebril, Raf 9 Wang, Weiguo 9 Zhang, Lei 8 Bueno, María Isabel 8 Caliari, Marco 8 Dehghan Takht Fooladi, Mehdi 8 Duan, Xuefeng 8 Güttel, Stefan 8 Higham, Desmond J. 8 Huang, Ting-Zhu 8 Jeannerod, Claude-Pierre 8 Lin, Yiqin 8 Lu, Linzhang 8 Mehl, Christian 8 Neff, Patrizio 8 Novati, Paolo 8 Pan, Victor Yakovlevich 8 Peinado, Jesús 8 Ruiz, Pedro A. 8 Sadkane, Miloud 8 Sun, Defeng 8 Sun, Jiguang ...and 3,940 more Authors all top 5 Cited in 431 Serials 408 Linear Algebra and its Applications 243 Journal of Computational and Applied Mathematics 128 Applied Mathematics and Computation 127 SIAM Journal on Matrix Analysis and Applications 121 Numerical Algorithms 111 BIT 97 SIAM Journal on Scientific Computing 76 Numerical Linear Algebra with Applications 72 Journal of Computational Physics 70 Computers & Mathematics with Applications 68 Applied Numerical Mathematics 64 Mathematics of Computation 63 Numerische Mathematik 36 Linear and Multilinear Algebra 32 Journal of Scientific Computing 31 Calcolo 31 International Journal of Computer Mathematics 28 Applied Mathematics Letters 26 Computer Methods in Applied Mechanics and Engineering 26 ELA. 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Zeitschrift für angewandte Mathematik und Physik ...and 331 more Serials all top 5 Cited in 60 Fields 2,273 Numerical analysis (65-XX) 1,133 Linear and multilinear algebra; matrix theory (15-XX) 264 Operations research, mathematical programming (90-XX) 174 Statistics (62-XX) 172 Partial differential equations (35-XX) 155 Systems theory; control (93-XX) 148 Ordinary differential equations (34-XX) 134 Computer science (68-XX) 126 Operator theory (47-XX) 120 Approximations and expansions (41-XX) 103 Probability theory and stochastic processes (60-XX) 75 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 74 Calculus of variations and optimal control; optimization (49-XX) 69 Fluid mechanics (76-XX) 68 Combinatorics (05-XX) 61 Mechanics of deformable solids (74-XX) 53 Real functions (26-XX) 53 Biology and other natural sciences (92-XX) 50 Dynamical systems and ergodic theory (37-XX) 48 Special functions (33-XX) 46 Quantum theory (81-XX) 45 Functions of a complex variable (30-XX) 40 Information and communication theory, circuits (94-XX) 36 Mechanics of particles and systems (70-XX) 32 Number theory (11-XX) 31 Harmonic analysis on Euclidean spaces (42-XX) 29 Field theory and polynomials (12-XX) 27 Differential geometry (53-XX) 24 Statistical mechanics, structure of matter (82-XX) 22 Geophysics (86-XX) 21 Integral equations (45-XX) 21 Optics, electromagnetic theory (78-XX) 19 Functional analysis (46-XX) 18 Commutative algebra (13-XX) 17 Algebraic geometry (14-XX) 15 Difference and functional equations (39-XX) 15 Integral transforms, operational calculus (44-XX) 12 Global analysis, analysis on manifolds (58-XX) 10 Relativity and gravitational theory (83-XX) 9 Associative rings and algebras (16-XX) 8 History and biography (01-XX) 8 Convex and discrete geometry (52-XX) 6 Geometry (51-XX) 5 General and overarching topics; collections (00-XX) 5 Mathematics education (97-XX) 4 Mathematical logic and foundations (03-XX) 4 Topological groups, Lie groups (22-XX) 4 Potential theory (31-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Classical thermodynamics, heat transfer (80-XX) 4 Astronomy and astrophysics (85-XX) 3 Group theory and generalizations (20-XX) 3 Sequences, series, summability (40-XX) 2 General algebraic systems (08-XX) 2 Nonassociative rings and algebras (17-XX) 2 Measure and integration (28-XX) 2 General topology (54-XX) 2 Algebraic topology (55-XX) 2 Manifolds and cell complexes (57-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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