Nicholas J. Higham

ORCID

Publication Activity (10 Years)

Years Active: 1988-2024
Publications (10 Years): 52

Top Venues

SIAM J. Sci. Comput.

SIAM J. Matrix Anal. Appl.

CoRR

ACM Trans. Math. Softw.

Publications

Patrick Amestoy, Alfredo Buttari, Nicholas J. Higham, Jean-Yves L'Excellent, Théo Mary, Bastien Vieuble
Five-Precision GMRES-Based Iterative Refinement. SIAM J. Matrix Anal. Appl. 45 (1) (2024)
Massimiliano Fasi, Nicholas J. Higham, Florent Lopez, Théo Mary, Mantas Mikaitis
Matrix Multiplication in Multiword Arithmetic: Error Analysis and Application to GPU Tensor Cores. SIAM J. Sci. Comput. 45 (1) (2023)
Patrick Amestoy, Alfredo Buttari, Nicholas J. Higham, Jean-Yves L'Excellent, Théo Mary, Bastien Vieuble
Combining Sparse Approximate Factorizations with Mixed-precision Iterative Refinement. ACM Trans. Math. Softw. 49 (1) (2023)
Massimiliano Fasi, Nicholas J. Higham, Xiaobo Liu
Computing the Square Root of a Low-Rank Perturbation of the Scaled Identity Matrix. SIAM J. Matrix Anal. Appl. 44 (1) (2023)
Nicholas J. Higham
The Power of Bidiagonal Matrices. CoRR (2023)
Michael P. Connolly, Nicholas J. Higham
Probabilistic Rounding Error Analysis of Householder QR Factorization. SIAM J. Matrix Anal. Appl. 44 (3) (2023)
Nicholas J. Higham, Mantas Mikaitis
Anymatrix: an extensible MATLAB matrix collection. Numer. Algorithms 90 (3) (2022)
Awad H. Al-Mohy, Nicholas J. Higham, Xiaobo Liu
Arbitrary Precision Algorithms for Computing the Matrix Cosine and its Fréchet Derivative. SIAM J. Matrix Anal. Appl. 43 (1) (2022)
Nicholas J. Higham, Théo Mary
Mixed precision algorithms in numerical linear algebra. Acta Numer. 31 (2022)
Mawussi Zounon, Nicholas J. Higham, Craig Lucas, Françoise Tisseur
Performance impact of precision reduction in sparse linear systems solvers. PeerJ Comput. Sci. 8 (2022)
Sven Hammarling, Nicholas J. Higham
The Influence and Contribution of Jack Dongarra to Numerical Linear Algebra. Comput. Sci. Eng. 24 (4) (2022)
Nicholas J. Higham, Matthew C. Lettington
Optimizing and Factorizing the Wilson Matrix. Am. Math. Mon. 129 (5) (2022)
Massimiliano Fasi, Nicholas J. Higham, Mantas Mikaitis, Srikara Pranesh
Numerical behavior of NVIDIA tensor cores. PeerJ Comput. Sci. 7 (2021)
Massimiliano Fasi, Nicholas J. Higham
Generating Extreme-Scale Matrices With Specified Singular Values or Condition Number. SIAM J. Sci. Comput. 43 (1) (2021)
Nicholas J. Higham, Xiaobo Liu
A Multiprecision Derivative-Free Schur-Parlett Algorithm for Computing Matrix Functions. SIAM J. Matrix Anal. Appl. 42 (3) (2021)
Ahmad Abdelfattah, Hartwig Anzt, Erik G. Boman, Erin C. Carson, Terry Cojean, Jack J. Dongarra, Alyson Fox, Mark Gates, Nicholas J. Higham, Xiaoye S. Li, Jennifer A. Loe, Piotr Luszczek, Srikara Pranesh, Siva Rajamanickam, Tobias Ribizel, Barry F. Smith, Kasia Swirydowicz, Stephen J. Thomas, Stanimire Tomov, Yaohung M. Tsai, Ulrike Meier Yang
A survey of numerical linear algebra methods utilizing mixed-precision arithmetic. Int. J. High Perform. Comput. Appl. 35 (4) (2021)
Michael P. Connolly, Nicholas J. Higham, Théo Mary
Stochastic Rounding and Its Probabilistic Backward Error Analysis. SIAM J. Sci. Comput. 43 (1) (2021)
Ahmad Abdelfattah, Timothy B. Costa, Jack J. Dongarra, Mark Gates, Azzam Haidar, Sven Hammarling, Nicholas J. Higham, Jakub Kurzak, Piotr Luszczek, Stanimire Tomov, Mawussi Zounon
A Set of Batched Basic Linear Algebra Subprograms and LAPACK Routines. ACM Trans. Math. Softw. 47 (3) (2021)
Desmond J. Higham, Nicholas J. Higham, Srikara Pranesh
Random Matrices Generating Large Growth in LU Factorization with Pivoting. SIAM J. Matrix Anal. Appl. 42 (1) (2021)
Nicholas J. Higham, Srikara Pranesh
Exploiting Lower Precision Arithmetic in Solving Symmetric Positive Definite Linear Systems and Least Squares Problems. SIAM J. Sci. Comput. 43 (1) (2021)
Massimiliano Fasi, Nicholas J. Higham
Matrices with Tunable Infinity-Norm Condition Number and No Need for Pivoting in LU Factorization. SIAM J. Matrix Anal. Appl. 42 (1) (2021)
Erin C. Carson, Nicholas J. Higham, Srikara Pranesh
Three-Precision GMRES-Based Iterative Refinement for Least Squares Problems. SIAM J. Sci. Comput. 42 (6) (2020)
Pierre Blanchard, Nicholas J. Higham, Théo Mary
A Class of Fast and Accurate Summation Algorithms. SIAM J. Sci. Comput. 42 (3) (2020)
Ahmad Abdelfattah, Hartwig Anzt, Erik G. Boman, Erin C. Carson, Terry Cojean, Jack J. Dongarra, Mark Gates, Thomas Grützmacher, Nicholas J. Higham, Xiaoye Sherry Li, Neil Lindquist, Yang Liu, Jennifer A. Loe, Piotr Luszczek, Pratik Nayak, Srikara Pranesh, Sivasankaran Rajamanickam, Tobias Ribizel, Barry Smith, Kasia Swirydowicz, Stephen J. Thomas, Stanimire Tomov, Yaohung M. Tsai, Ichitaro Yamazaki, Ulrike Meier Yang
A Survey of Numerical Methods Utilizing Mixed Precision Arithmetic. CoRR (2020)
Nicholas J. Higham, Théo Mary
Sharper Probabilistic Backward Error Analysis for Basic Linear Algebra Kernels with Random Data. SIAM J. Sci. Comput. 42 (5) (2020)
Pierre Blanchard, Nicholas J. Higham, Florent Lopez, Théo Mary, Srikara Pranesh
Mixed Precision Block Fused Multiply-Add: Error Analysis and Application to GPU Tensor Cores. SIAM J. Sci. Comput. 42 (3) (2020)
Nicholas J. Higham, Théo Mary
A New Preconditioner that Exploits Low-Rank Approximations to Factorization Error. SIAM J. Sci. Comput. 41 (1) (2019)
Hartwig Anzt, Jack J. Dongarra, Goran Flegar, Nicholas J. Higham, Enrique S. Quintana-Ortí
Adaptive precision in block-Jacobi preconditioning for iterative sparse linear system solvers. Concurr. Comput. Pract. Exp. 31 (6) (2019)
Nicholas J. Higham, Théo Mary
A New Approach to Probabilistic Rounding Error Analysis. SIAM J. Sci. Comput. 41 (5) (2019)
Pierre Blanchard, Desmond J. Higham, Nicholas J. Higham
Accurate Computation of the Log-Sum-Exp and Softmax Functions. CoRR (2019)
Massimiliano Fasi, Nicholas J. Higham
An Arbitrary Precision Scaling and Squaring Algorithm for the Matrix Exponential. SIAM J. Matrix Anal. Appl. 40 (4) (2019)
Nicholas J. Higham, Srikara Pranesh
Simulating Low Precision Floating-Point Arithmetic. SIAM J. Sci. Comput. 41 (5) (2019)
Nicholas J. Higham, Srikara Pranesh, Mawussi Zounon
Squeezing a Matrix into Half Precision, with an Application to Solving Linear Systems. SIAM J. Sci. Comput. 41 (4) (2019)
Prashanth Nadukandi, Nicholas J. Higham
Computing the Wave-Kernel Matrix Functions. SIAM J. Sci. Comput. 40 (6) (2018)
Weijian Zhang, Jonathan Deakin, Nicholas J. Higham, Shuaiqiang Wang
Etymo: A New Discovery Engine for AI Research. CoRR (2018)
Azzam Haidar, Stanimire Tomov, Jack J. Dongarra, Nicholas J. Higham
Harnessing GPU tensor cores for fast FP16 arithmetic to speed up mixed-precision iterative refinement solvers. SC (2018)
Weijian Zhang, Jonathan Deakin, Nicholas J. Higham, Shuaiqiang Wang
Etymo: A New Discovery Engine for AI Research. WWW (Companion Volume) (2018)
Massimiliano Fasi, Nicholas J. Higham
Multiprecision Algorithms for Computing the Matrix Logarithm. SIAM J. Matrix Anal. Appl. 39 (1) (2018)
Erin C. Carson, Nicholas J. Higham
Accelerating the Solution of Linear Systems by Iterative Refinement in Three Precisions. SIAM J. Sci. Comput. 40 (2) (2018)
Nicholas J. Higham, Peter Kandolf
Computing the Action of Trigonometric and Hyperbolic Matrix Functions. SIAM J. Sci. Comput. 39 (2) (2017)
Jack J. Dongarra, Sven Hammarling, Nicholas J. Higham, Samuel D. Relton, Mawussi Zounon
Optimized Batched Linear Algebra for Modern Architectures. Euro-Par (2017)
Jack J. Dongarra, Sven Hammarling, Nicholas J. Higham, Samuel D. Relton, Pedro Valero-Lara, Mawussi Zounon
The Design and Performance of Batched BLAS on Modern High-Performance Computing Systems. ICCS (2017)
Erin C. Carson, Nicholas J. Higham
A New Analysis of Iterative Refinement and Its Application to Accurate Solution of Ill-Conditioned Sparse Linear Systems. SIAM J. Sci. Comput. 39 (6) (2017)
Nicholas J. Higham, Natasa Strabic, Vedran Sego
Restoring Definiteness via Shrinking, with an Application to Correlation Matrices with a Fixed Block. SIAM Rev. 58 (2) (2016)
Mary Aprahamian, Nicholas J. Higham
Matrix Inverse Trigonometric and Inverse Hyperbolic Functions: Theory and Algorithms. SIAM J. Matrix Anal. Appl. 37 (4) (2016)
Nicholas J. Higham, Natasa Strabic
Anderson acceleration of the alternating projections method for computing the nearest correlation matrix. Numer. Algorithms 72 (4) (2016)
Weijian Zhang, Nicholas J. Higham
Matrix Depot: an extensible test matrix collection for Julia. PeerJ Comput. Sci. 2 (2016)
Mary Aprahamian, Desmond J. Higham, Nicholas J. Higham
Matching exponential-based and resolvent-based centrality measures. J. Complex Networks 4 (2) (2016)
Nicholas J. Higham, Vanni Noferini
An algorithm to compute the polar decomposition of a 3 × 3 matrix. Numer. Algorithms 73 (2) (2016)
Nicholas J. Higham, Samuel D. Relton
Estimating the Largest Elements of a Matrix. SIAM J. Sci. Comput. 38 (5) (2016)
Nicholas J. Higham, Natasa Strabic
Bounds for the Distance to the Nearest Correlation Matrix. SIAM J. Matrix Anal. Appl. 37 (3) (2016)
Edvin Deadman, Nicholas J. Higham
Testing Matrix Function Algorithms Using Identities. ACM Trans. Math. Softw. 42 (1) (2016)
Awad H. Al-Mohy, Nicholas J. Higham, Samuel D. Relton
New Algorithms for Computing the Matrix Sine and Cosine Separately or Simultaneously. SIAM J. Sci. Comput. 37 (1) (2015)
Massimiliano Fasi, Nicholas J. Higham, Bruno Iannazzo
An Algorithm for the Matrix Lambert W Function. SIAM J. Matrix Anal. Appl. 36 (2) (2015)
Lijing Lin, Nicholas J. Higham, Jianxin Pan
Covariance structure regularization via entropy loss function. Comput. Stat. Data Anal. 72 (2014)
Mary Aprahamian, Nicholas J. Higham
The Matrix Unwinding Function, with an Application to Computing the Matrix Exponential. SIAM J. Matrix Anal. Appl. 35 (1) (2014)
Iain Bethune, J. Mark Bull, Nicholas J. Dingle, Nicholas J. Higham
Performance analysis of asynchronous Jacobi's method implemented in MPI, SHMEM and OpenMP. Int. J. High Perform. Comput. Appl. 28 (1) (2014)
Nicholas J. Higham, Samuel D. Relton
Estimating the Condition Number of the Fréchet Derivative of a Matrix Function. SIAM J. Sci. Comput. 36 (6) (2014)
Nicholas J. Higham, Samuel D. Relton
Higher Order Fréchet Derivatives of Matrix Functions and the Level-2 Condition Number. SIAM J. Matrix Anal. Appl. 35 (3) (2014)
Nicholas J. Higham, Lijing Lin
An Improved Schur-Padé Algorithm for Fractional Powers of a Matrix and Their Fréchet Derivatives. SIAM J. Matrix Anal. Appl. 34 (3) (2013)
Timo Betcke, Nicholas J. Higham, Volker Mehrmann, Christian Schröder, Françoise Tisseur
NLEVP: A Collection of Nonlinear Eigenvalue Problems. ACM Trans. Math. Softw. 39 (2) (2013)
Nicholas J. Dingle, Nicholas J. Higham
Reducing the influence of tiny normwise relative errors on performance profiles. ACM Trans. Math. Softw. 39 (4) (2013)
Awad H. Al-Mohy, Nicholas J. Higham, Samuel D. Relton
Computing the Fréchet Derivative of the Matrix Logarithm and Estimating the Condition Number. SIAM J. Sci. Comput. 35 (4) (2013)
Yuji Nakatsukasa, Nicholas J. Higham
Stable and Efficient Spectral Divide and Conquer Algorithms for the Symmetric Eigenvalue Decomposition and the SVD. SIAM J. Sci. Comput. 35 (3) (2013)
Yuji Nakatsukasa, Nicholas J. Higham
Backward Stability of Iterations for Computing the Polar Decomposition. SIAM J. Matrix Anal. Appl. 33 (2) (2012)
Edvin Deadman, Nicholas J. Higham, Rui Ralha
Blocked Schur Algorithms for Computing the Matrix Square Root. PARA (2012)
Awad H. Al-Mohy, Nicholas J. Higham
Improved Inverse Scaling and Squaring Algorithms for the Matrix Logarithm. SIAM J. Sci. Comput. 34 (4) (2012)
Nicholas J. Higham, Lijing Lin
A Schur-Padé Algorithm for Fractional Powers of a Matrix. SIAM J. Matrix Anal. Appl. 32 (3) (2011)
Awad H. Al-Mohy, Nicholas J. Higham
Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators. SIAM J. Sci. Comput. 33 (2) (2011)
Nicholas J. Higham, Awad H. Al-Mohy
Computing matrix functions. Acta Numer. 19 (2010)
Awad H. Al-Mohy, Nicholas J. Higham
The complex step approximation to the Fréchet derivative of a matrix function. Numer. Algorithms 53 (1) (2010)
Nicholas J. Higham, Christian Mehl, Françoise Tisseur
The Canonical Generalized Polar Decomposition. SIAM J. Matrix Anal. Appl. 31 (4) (2010)
Rüdiger Borsdorf, Nicholas J. Higham, Marcos Raydan
Computing a Nearest Correlation Matrix with Factor Structure. SIAM J. Matrix Anal. Appl. 31 (5) (2010)
Anne E. Trefethen, Nicholas J. Higham, Iain S. Duff, Peter V. Coveney
Developing a High-Performance Computing/Numerical Analysis Roadmap. Int. J. High Perform. Comput. Appl. 23 (4) (2009)
Awad H. Al-Mohy, Nicholas J. Higham
A New Scaling and Squaring Algorithm for the Matrix Exponential. SIAM J. Matrix Anal. Appl. 31 (3) (2009)
Nicholas J. Higham, D. Steven Mackey, Françoise Tisseur
Definite Matrix Polynomials and their Linearization by Definite Pencils. SIAM J. Matrix Anal. Appl. 31 (2) (2009)
Chun-Hua Guo, Nicholas J. Higham, Françoise Tisseur
An Improved Arc Algorithm for Detecting Definite Hermitian Pairs. SIAM J. Matrix Anal. Appl. 31 (3) (2009)
Nicholas J. Higham
The Scaling and Squaring Method for the Matrix Exponential Revisited. SIAM Rev. 51 (4) (2009)
Awad H. Al-Mohy, Nicholas J. Higham
Computing the Fréchet Derivative of the Matrix Exponential, with an Application to Condition Number Estimation. SIAM J. Matrix Anal. Appl. 30 (4) (2008)
Chun-Hua Guo, Nicholas J. Higham, Françoise Tisseur
Detecting and Solving Hyperbolic Quadratic Eigenvalue Problems. SIAM J. Matrix Anal. Appl. 30 (4) (2008)
Nicholas Hale, Nicholas J. Higham, Lloyd N. Trefethen
log(A), and Related Matrix Functions by Contour Integrals. SIAM J. Numer. Anal. 46 (5) (2008)
Chun-Hua Guo, Nicholas J. Higham
Iterative Solution of a Nonsymmetric Algebraic Riccati Equation. SIAM J. Matrix Anal. Appl. 29 (2) (2007)
Nicholas J. Higham, Ren-Cang Li, Françoise Tisseur
Backward Error of Polynomial Eigenproblems Solved by Linearization. SIAM J. Matrix Anal. Appl. 29 (4) (2007)
Nicholas J. Higham, D. Steven Mackey, Françoise Tisseur
The Conditioning of Linearizations of Matrix Polynomials. SIAM J. Matrix Anal. Appl. 28 (4) (2006)
Nicholas J. Higham, D. Steven Mackey, Niloufer Mackey, Françoise Tisseur
Symmetric Linearizations for Matrix Polynomials. SIAM J. Matrix Anal. Appl. 29 (1) (2006)
Chun-Hua Guo, Nicholas J. Higham
A Schur-Newton Method for the Matrix \lowercase{\boldmathp}th Root and its Inverse. SIAM J. Matrix Anal. Appl. 28 (3) (2006)
Sven Hammarling, Nicholas J. Higham, Craig Lucas
Updating. PARA (2006)
Nicholas J. Higham, D. Steven Mackey, Niloufer Mackey, Françoise Tisseur
Functions Preserving Matrix Groups and Iterations for the Matrix Square Root. SIAM J. Matrix Anal. Appl. 26 (3) (2005)
Nicholas J. Higham
The Scaling and Squaring Method for the Matrix Exponential Revisited. SIAM J. Matrix Anal. Appl. 26 (4) (2005)
Gareth I. Hargreaves, Nicholas J. Higham
Efficient algorithms for the matrix cosine and sine. Numer. Algorithms 40 (4) (2005)
Dario Andrea Bini, Nicholas J. Higham, Beatrice Meini
th root. Numer. Algorithms 39 (4) (2005)
Nicholas J. Higham, D. Steven Mackey, Niloufer Mackey, Françoise Tisseur
Computing the Polar Decomposition and the Matrix Sign Decomposition in Matrix Groups. SIAM J. Matrix Anal. Appl. 25 (4) (2004)
Nicholas J. Higham
-Orthogonal Matrices: Properties and Generation. SIAM Rev. 45 (3) (2003)
Nicholas J. Higham, Matthew I. Smith
Computing the Matrix Cosine. Numer. Algorithms 34 (1) (2003)
Adam W. Bojanczyk, Nicholas J. Higham, Harikrishna Patel
Solving the Indefinite Least Squares Problem by Hyperbolic QR Factorization. SIAM J. Matrix Anal. Appl. 24 (4) (2003)
Philip I. Davies, Nicholas J. Higham
A Schur-Parlett Algorithm for Computing Matrix Functions. SIAM J. Matrix Anal. Appl. 25 (2) (2003)
Philip I. Davies, Nicholas J. Higham, Françoise Tisseur
Analysis of the Cholesky Method with Iterative Refinement for Solving the Symmetric Definite Generalized Eigenproblem. SIAM J. Matrix Anal. Appl. 23 (2) (2001)
Nicholas J. Higham
Evaluating Padé Approximants of the Matrix Logarithm. SIAM J. Matrix Anal. Appl. 22 (4) (2001)
Sheung Hun Cheng, Nicholas J. Higham
Parallel Implementation of a Block Algorithm for Matrix 1-Norm Estimation. Euro-Par (2001)
Nicholas J. Higham, Hyun-Min Kim
Solving a Quadratic Matrix Equation by Newton's Method with Exact Line Searches. SIAM J. Matrix Anal. Appl. 23 (2) (2001)

Nicholas J. Higham.css-eqlu8i{font-size:small;padding-left:4px;}

Publication Activity (10 Years)

Top Topics

Top Venues

Nicholas J. Higham