Nicholas Higham, FRS, FIET, FIMA, CEng, CMath

Search results

• 2022

  ARBITRARY PRECISION ALGORITHMS FOR COMPUTING THE MATRIX COSINE AND ITS FRECHET DERIVATIVE

  Al-Mohy, A., Higham, N. & Liu, X., 17 Feb 2022, In: SIAM Journal on Matrix Analysis and Applications.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Precision 100%
  • Algorithms 87%
  • Computing 75%
  • Matrix 50%
  • Accuracy 25%
  44 Downloads (Pure)

• Combining sparse approximate factorizations with mixed precision iterative refinement

  Amestoy, P., Buttari, A., Higham, N., L’EXCELLENT, JEAN-YVES., Mary, T. & VIEUBLÉ, BASTIEN., 7 Nov 2022, (Accepted/In press) In: ACM Transactions on Mathematical Software.

  Research output: Contribution to journal › Article › peer-review

  • Iterative Refinement 100%
  • Precision 60%
  • Approximates 60%
  • Factorization 40%
  • Memory Consumption 40%

• COMPUTING THE SQUARE ROOT OF A LOW-RANK PERTURBATION OF THE SCALED IDENTITY MATRIX∗

  Fasi, M., Higham, N. N. & Liu, X., 18 Aug 2022, (Accepted/In press) In: SIAM Journal on Matrix Analysis and Applications.

  Research output: Contribution to journal › Article › peer-review

  • Square Root 100%
  • Matrix 80%
  • Low-Rank 80%
  • Roots 60%
  • Computing 60%

• MATRIX MULTIPLICATION IN MULTIWORD ARITHMETIC: ERROR ANALYSIS AND APPLICATION TO GPU TENSOR CORES∗

  Fasi, M., Higham, N., Lopez, F., Mary, T. & Mikaitis, M., 24 Aug 2022, (Accepted/In press) In: SIAM Journal on Scientific Computing.

  Research output: Contribution to journal › Article › peer-review

  • Error 100%
  • Matrix Multiplication 80%
  • Core 60%
  • Precision 60%
  • Algorithms 60%

• Stochastic Rounding: Implementation, Error Analysis, and Applications

  Croci, M., Fasi, M., Higham, N., Mary, T. & Mikaitis, M., 4 Feb 2022, (Accepted/In press) In: Royal Society Open Science.

  Research output: Contribution to journal › Article › peer-review

  • Computer Arithmetic 100%
• 2021

  A MULTIPRECISION DERIVATIVE-FREE SCHUR{PARLETT ALGORITHM FOR COMPUTING MATRIX FUNCTIONS

  Higham, N. & Liu, X., 18 Jun 2021, (Accepted/In press) In: SIAM Journal on Matrix Analysis and Applications.

  Research output: Contribution to journal › Article › peer-review

• Anymatrix: An Extensible MATLAB Matrix Collection

  Higham, N. & Mikaitis, M., 2021, In: Numerical Algorithms.

  Research output: Contribution to journal › Article › peer-review

  • Collection 100%
  • Group 66%
  • User 33%
  • Tool 16%
  • Ability 16%

• Integer matrix factorisations, superalgebras and the quadratic form obstruction

  Higham, N. J., Lettington, M. C. & Schmidt, K. M., 1 Aug 2021, In: Linear Algebra and its Applications. 622, p. 250-267

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Matrix 100%
  • Integer 100%
  • Quadratic Form 66%
  • Matrix Decomposition 66%
  • Factorization 66%
  14 Downloads (Pure)

• Mixed Precision Algorithms in Numerical Linear Algebra

  Higham, N. & Mary, T., 29 Dec 2021, (Accepted/In press) In: Acta Numerica.

  Research output: Contribution to journal › Article › peer-review

  • Precision 100%
  • Algorithms 61%
  • Algorithm 61%
  • Accuracy 23%
  • Numerical Linear Algebra 23%

• Numerical Behavior of NVIDIA Tensor Cores

  Fasi, M., Higham, N., Mikaitis, M. & Pranesh, S., 10 Feb 2021, In: PeerJ Computer Science. 7, p. e330 19 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Hardware 100%
  • Matrix Multiplication 100%
  • Floating Point 100%
  • Arithmetic Operation 50%
  • Microarchitecture 50%

• Numerical Stability of Algorithms at Extreme Scale and Low Precisions*

  Higham, N. J., 29 Dec 2021, (Accepted/In press) Proceedings of International Congress of Mathematicians 202 .

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

  • Accuracy 100%
  • Constant 50%
  • Rounding Error 50%
  • Precision 37%
  • Algorithm 37%

• Optimizing and Factorizing the Wilson Matrix

  Higham, N. & Lettington, M., 2021, In: The American Mathematical Monthly.

  Research output: Contribution to journal › Article › peer-review

  • Matrix 100%
  • Bounds 33%
  • Condition Number 33%
  • Classes 16%
  • Number 16%

• Performance Impact of Precision Reduction In Sparse Linear Systems Solvers

  Zounon, M., Higham, N., Lucas, C. & Tisseur, F., 19 Oct 2021, (Accepted/In press) In: PeerJ Computer Science.

  Research output: Contribution to journal › Article › peer-review

  • Single Precision 100%
  • Linear System 83%
  • Double Precision 83%
  • Factorization 66%
  • Kernel 33%

• Solving Block Low-Rank Linear Systems by LU Factorization is Numerically Stable

  Higham, N. & Mary, T., 1 Mar 2021, (Accepted/In press) In: IMA Journal of Numerical Analysis.

  Research output: Contribution to journal › Article › peer-review

  • Low-Rank 100%
  • Matrix 30%
  • Factorization 20%
  • Linear System 20%
  • Rank Approximation 20%
• 2020

  Accurately Computing the Log-Sum-Exp and Softmax Functions

  Blanchard, P., Higham, D. J. & Higham, N., 26 May 2020, (Accepted/In press) In: IMA Journal of Numerical Analysis.

  Research output: Contribution to journal › Article › peer-review

  • Functions 100%
  • Evaluation 66%
  • Algorithms 66%
  • Accuracy 66%
  • Softmax Function 66%

• A Class of Fast and Accurate Summation Algorithms

  Blanchard, P., Higham, N. & Mary, T., 7 May 2020, In: S I A M Journal on Scientific Computing. 42, 3, p. A1541-A1557

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Algorithms 100%
  • Classes 50%
  • Backward Error 50%
  • Application 25%
  • Computing 25%

• A Set of Batched Basic Linear Algebra Subprograms and LAPACK Routines

  Abdelfattah, A., Costa, T., Dongarra, J., Gates, M., Haidar, A., Hammarling, S., Higham, N., Kurzak, J., Luszczek, P., Tomov, S. & Zounon, M., 26 Oct 2020, (Accepted/In press) In: ACM Transactions on Mathematical Software.

  Research output: Contribution to journal › Article › peer-review

  • Standards 100%
  • Standard 100%
  • Matrix 100%
  • Many-Core 66%
  • Set 66%

• EXPLOITING LOWER PRECISION ARITHMETIC IN SOLVING SYMMETRIC POSITIVE DEFINITE LINEAR SYSTEMS AND LEAST SQUARES PROBLEMS

  Higham, N. & Pranesh, S., 26 Oct 2020, (Accepted/In press) In: SIAM Journal on Scientific Computing.

  Research output: Contribution to journal › Article › peer-review

  • Accuracy 100%
  • Precision 80%
  • Algorithm 40%
  • Arithmetic 30%
  • Cholesky Factorization 20%

• GENERATING EXTREME-SCALE MATRICES WITH SPECIFIED SINGULAR VALUES OR CONDITION NUMBERS

  Fasi, M. & Higham, N., 26 Oct 2020, (Accepted/In press) In: SIAM Journal on Scientific Computing.

  Research output: Contribution to journal › Article › peer-review

  • Matrix 100%
  • Algorithm 60%
  • Singular Value 60%
  • Algorithms 60%
  • Communication 40%

• MATRICES WITH TUNABLE INFINITY-NORM CONDITION NUMBER AND NO NEED FOR PIVOTING IN LU FACTORIZATION

  Fasi, M. & Higham, N., 29 Dec 2020, (Accepted/In press) In: SIAM Journal on Matrix Analysis and Applications.

  Research output: Contribution to journal › Article › peer-review

• Mixed precision block fused multiply-add: error analysis and application to GPU tensor cores

  Blanchard, P., Higham, N., Lopez, F., Mary, T. & Pranesh, S., 25 Feb 2020, (Accepted/In press) In: S I A M Journal on Scientific Computing.

  Research output: Contribution to journal › Article › peer-review

  • Precision 100%
  • Block 100%
  • Core 74%
  • Utilization 50%
  • Kernel 50%

• Mixed-Precision Iterative Refinement using Tensor Cores on GPUs to Accelerate Solution of Linear Systems

  Haidar, A., Bayraktar, H., Tomov, S., Dongarra, J. & Higham, N., 24 Sep 2020, (Accepted/In press) In: Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

  Research output: Contribution to journal › Article › peer-review

  • Precision 100%
  • Core 40%
  • Linear Systems 40%
  • Numerical Stability 40%
  • Floating Point Arithmetic 40%

• Numerical Algorithms for High-Performance Computational Science

  Dongarra, J., Grigori, L. & Higham, N., Mar 2020, In: Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences. 378, 2166

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Algorithms 100%
  • Computational Science 100%
  • Generation 66%
  • Accuracy 33%
  • Energy Consumption 33%
  458 Downloads (Pure)

• Random Matrices Generating Large Growth in Lu Factorization with Pivoting

  Higham, D. J., Higham, N. & Pranesh, S., 17 Nov 2020, (Accepted/In press) In: SIAM Journal on Matrix Analysis and Applications.

  Research output: Contribution to journal › Article › peer-review

  • Matrix 100%
  • Orthogonal Matrix 75%
  • Random Matrix 50%
  • Iterative Refinement 50%
  • Atom 50%

• Sharper Probabilistic Backward Error Analysis for Basic Linear Algebra Kernels with Random Data

  Higham, N. & Mary, T., 17 Aug 2020, (Accepted/In press) In: S I A M Journal on Scientific Computing.

  Research output: Contribution to journal › Article › peer-review

  • Bounds 100%
  • Order 50%
  • Zeros 50%
  • Matrix 50%
  • Algorithm 50%

• STOCHASTIC ROUNDING AND ITS PROBABILISTIC BACKWARD ERROR ANALYSIS

  Connolly, M., Higham, N. & Mary, T., 16 Nov 2020, (Accepted/In press) In: S I A M Journal on Scientific Computing.

  Research output: Contribution to journal › Article › peer-review

• Three-Precision GMRES-Based Iterative Refinement for Least Squares Problems

  Carson, E., Higham, N. & Pranesh, S., 18 Sep 2020, (Accepted/In press) In: SIAM Journal on Scientific Computing.

  Research output: Contribution to journal › Article › peer-review
• 2019

  An Arbitrary Precision Scaling and Squaring Algorithm for the Matrix Exponential

  Fasi, M. & Higham, N., 2019, In: S I A M Journal on Matrix Analysis and Applications. 40, 4

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Algorithm 100%
  • Precision 33%
  • Parameters 33%
  • Arithmetic 33%
  • Approximant 33%

• A New Approach to Probabilistic Rounding Error Analysis

  Higham, N. & Mary, T., 12 Sep 2019, In: S I A M Journal on Scientific Computing. 41, 5, p. A2815–A2835

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Rounding Error 100%
  • Constant 80%
  • Bounds 80%
  • Error Analysis 60%
  • Computation 40%

• A New Preconditioner that Exploits Low-Rank Approximations to Factorization Error

  Higham, N. & Mary, T., 2019, In: SIAM Journal on Matrix Analysis and Applications. 41, 1, p. A59-A82 24 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Preconditioner 100%
  • Low-Rank 100%
  • LU Factorization 80%
  • Precision 40%
  • Matrix 40%

• Simulating low precision floating-point arithmetic

  Higham, N. & Pranesh, S., 2019, In: S I A M Journal on Scientific Computing. 41, 5

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Precision 100%
  • Accuracy 100%
  • Arithmetic 66%
  • Simulation 33%
  • Format 22%

• Squeezing a Matrix into Half Precision, with an Application to Solving Linear Systems

  Higham, N., Pranesh, S. & Zounon, M., 1 Aug 2019, (E-pub ahead of print) In: S I A M Journal on Scientific Computing.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Matrix 100%
  • Single Precision 83%
  • Double Precision 83%
  • Algorithms 83%
  • Iterative Refinement 66%
• 2018

  ACCELERATING THE SOLUTION OF LINEAR SYSTEMS BY ITERATIVE REFINEMENT IN THREE PRECISIONS

  Carson, E. & Higham, N., 2018, In: SIAM Journal on Scientific Computing. 40, 2, p. A817-A847

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Precision 100%
  • Iterative Refinement 33%
  • Linear System 33%
  • Single Precision 33%
  • Linear Systems 33%

• Adaptive Precision in Block-Jacobi Preconditioning for Iterative Sparse Linear System Solvers

  Anzt, H., Dongarra, J., Flegar, G., Higham, N. & Quintana-Orti, E. S., 2018, In: Concurrency and Computation: Practice and Experience.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Preconditioner 100%
  • Linear System 66%
  • Potential Benefit 33%
  • Energy Consumption 33%
  • Communication Overhead 33%
  103 Downloads (Pure)

• COMPUTING THE WAVE-KERNEL MATRIX FUNCTIONS

  Nadukandi, P. & Higham, N., 2018, In: SIAM Journal on Scientific Computing.

  Research output: Contribution to journal › Article › peer-review

  Open Access

• Explicit solutions to correlation matrix completion problems, with an application to risk management and insurance

  Georgescu, D. I., Higham, N. J. & Peters, G. W., 2018, In: Royal Society Open Science. 5, 3, 172348.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Correlation Matrix 100%
  • Application 50%
  • Risk Management 50%
  • Explicit Solution 50%
  • Testing 25%

• Harnessing GPU Tensor Cores for Fast FP16 Arithmetic to Speed up Mixed-Precision Iterative Refinement Solvers

  Haidar, A., Tomov, S., Dongarra, J. & Higham, N., 11 Nov 2018, SC '18: Proceedings of the International Conference for High Performance Computing, Networking, Storage, and Analysis. IEEE, Vol. 0. p. 1-11 47

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

  Open Access

  File

  • Accuracy 100%
  • Iterative Refinement 100%
  • Application 50%
  • Computing 50%
  • High-Performance Computing 50%
  467 Downloads (Pure)

• Multiprecision Algorithms for Computing the Matrix Logarithm

  Fasi, M. & Higham, N., 2018, In: SIAM Journal on Matrix Analysis and Applications. 39, 1, p. 472-491 20 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Algorithms 100%
  • Matrix 42%
  • Computing 42%
  • Floating Point 28%
  • Environment 14%
• 2017

  A NEW ANALYSIS OF ITERATIVE REFINEMENT AND ITS APPLICATION TO ACCURATE SOLUTION OF ILL-CONDITIONED SPARSE LINEAR SYSTEMS

  Carson, E. & Higham, N., 6 Dec 2017, In: SIAM Journal on Scientific Computing. 39, 6, p. A2834

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Order 100%
  • Relative Error 75%
  • Condition Number 75%
  • Precision 50%
  • Matrix 50%

• COMPUTING THE ACTION OF TRIGONOMETRIC AND HYPERBOLIC MATRIX FUNCTIONS

  Higham, N. & Kandolf, P., 2017, In: SIAM Journal on Scientific Computing. 39, 2, p. A613–A627 15 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Algorithms 100%
  • Algorithm 100%
  • Matrix 60%
  • Computing 60%
  • Alternative 20%
  92 Downloads (Pure)

• Optimized Batched Linear Algebra for Modern Architectures

  Dongarra, J., Hammarling, S., Higham, N., Relton, S. & Zounon, M., 2017, Euro-Par 2017: Parallel Processing : 23rd International Conference on Parallel and Distributed Computing, Santiago de Compostela, Spain, August 28-September 1, 2017, Proceedings . Rivera, F. F., Pena, T. F. & Cabaleiro, J. C. (eds.). Springer Nature, p. 511-522 12 p. (Lecture notes in computer science; vol. 10417).

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

  Open Access

  File

  • Design 100%
  • Matrix Multiplication 100%
  • Vectors 50%
  • Multicore 50%
  • Application Area 50%
  159 Downloads (Pure)

• Ranking the importance of nuclear reactions for activation and transmutation events

  Arter, W., Morgan, J. G., Relton, S. & Higham, N., 2017, In: Nuclear Science and Engineering. 184, 4, p. 561-574 14 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Inventory 100%
  • Activation 100%
  • Transmutation 100%
  • Analysis 100%
  • Order 50%
  86 Downloads (Pure)

• The Design and Performance of Batched BLAS on Modern High-Performance Computing Systems

  Dongarra, J., Hammarling, S., Higham, N., Relton, S., Valero-Lara, P. & Zounon, M., 2017, Procedia Computer Science. Vol. 108. p. 495-504 10 p.

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

  Open Access

  File

  • High-Performance Computing 100%
  • Matrix Multiplication 100%
  • Hardware 50%
  • Design 50%
  • Standards 50%
  78 Downloads (Pure)
• 2016

  Bounds for the distance to the nearest correlation matrix

  Higham, N. & Strabic, N., 2016, In: SIAM Journal on Matrix Analysis and Applications. 37, 3, p. 1188-1102 15 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Bounds 100%
  • Correlation Matrix 100%
  • Eigensystem 42%
  • Order 28%
  • Classes 28%

• ESTIMATING THE LARGEST ELEMENTS OF A MATRIX

  Higham, N. J. & Relton, S., 2016, In: SIAM Journal on Scientific Computing. 38, 5

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Algorithm 100%
  • Matrix 75%
  • Largest Element 25%
  • Matrix Vector Product 25%
  • Classes 12%

• Matching Exponential-Based and Resolvent-Based Centrality Measures

  Aprahamian, M., Higham, D. J. & Higham, N., 2016, In: Journal of Complex Networks.

  Research output: Contribution to journal › Article › peer-review

  • Functions 100%
  • Networks 100%
  • Centrality Measure 66%
  • Ranking 66%
  • Free Parameter 33%

• Matrix Depot: an extensible test matrix collection for Julia

  Zhang, W. & Higham, N., 18 Mar 2016, (Accepted/In press) In: PeerJ. 2, e58, p. 1-25

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Matrix 100%
  • Languages 10%
  • User 10%
  • Access 10%
  • Universities 5%
  113 Downloads (Pure)

• Matrix Inverse Trigonometric and Inverse Hyperbolic Functions: Theory and Algorithms

  Aprahamian, M. & Higham, N., 8 Nov 2016, In: SIAM Journal on Matrix Analysis and Applications. 37, 4, p. 1453-1477 25 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Matrix 100%
  • Functions 60%
  • Algorithm 60%
  • Algorithms 60%
  • Trigonometric 40%

• Restoring definiteness via shrinking, with an application to correlation matrices with a fixed block

  Higham, N. J., Strabic, N. & Sego, V., 2016, In: S I A M Review. p. 245-263 19 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Correlation Matrix 100%
  • Matrix 75%
  • Positive Semidefinite 75%
  • Approximation 50%
  • Eigenvalue Problems 25%
  88 Downloads (Pure)

• UManSysProp v1.0: an online and open-source facility for molecular property prediction and atmospheric aerosol calculations

  Topping, D., Mcfiggans, G., Barley, M., Bane, M. K., Higham, N., Aumont, B. & Dingle, N., 1 Mar 2016, In: Geoscientific Model Development.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Facilities 100%
  • Aerosol 80%
  • Calculation 60%
  • Prediction 60%
  • User 60%
  179 Downloads (Pure)