Miscellaneous Papers

Anymatrix: An Extensible MATLAB Matrix Collection, (with M. Mikaitis), Numer. Algorithms, 90(3):1175–1196, 2021.
Anymatrix: An Extensible MATLAB Matrix Collection. Users’ Guide (with M. Mikaitis). MIMS EPrint 2021.15, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, October 2021. 31 pp.
Disseminating Research Through Articles and Blogs. Mathematics Today, 57(4):116–117, 2021. Also available as a page on the IMA website.
A Set of Batched Basic Linear Algebra Subprograms and LAPACK Routines (with A. Abdelfattah, T. Costa, J. Dongarra, M. Gates, A. Haidar, S. Hammarling, J. Kurzak, P. Luszczek, S. Tomov, and M. Zounon). ACM Trans. Math. Software, 47(3):21:1–21:23, 2021.
The Mathematics Of Floating-Point Arithmetic. LMS Newsletter, 493:35–41, 2021.
Integer Matrix Factorisations, Superalgebras and the Quadratic Form Obstruction (with M. C. Lettington and K. M. Schmidt). Linear Algebra Appl., 622:250–267, 2021.
Matrices with Tunable Infinity-Norm Condition Number and No Need for Pivoting in LU Factorization (with M. Fasi). SIAM J. Matrix Anal. Appl. 42(1):417–435, 2021. Blog post.
Advances in Mixed Precision Algorithms: 2021 Edition (with A. Abdelfattah et al.), Technical Report LLNL-TR-825909, Lawrence Livermore National Laboratory, Livermore, CA, USA, August 2021.
A Survey of Numerical Methods Utilizing Mixed Precision Arithmetic (with A. Abdelfattah et al.). Int. J. High Performance Computing Applications, 35(4):344–369, 2021.
Stochastic Rounding and Its Probabilistic Backward Error Analysis (with M. P. Connolly and and T. Mary), SIAM J. Sci. Comput., 43(1):A566–A585, 2021. Blog post.
Numerical Behavior of NVIDIA Tensor Cores (with M. Fasi), M. Mikaitis, and S. Pranesh), PeerJ Comput. Sci. 7:e330(1–19), 2021. Blog post.
Cover Image: Bohemian Matrices (with R. M. Corless, and S. E. Thornton). LMS Newsletter, 491:16, 2020.
Sharper Probabilistic Backward Error Analysis for Basic Linear Algebra Kernels With Random Data (with T. Mary). SIAM J. Sci. Comput., 42(5):A3427-A3446, 2020. Blog post.
Numerical Algorithms for High-Performance Computational Science (with J. Dongarra and L. Grigori). Phil. Trans. R. Soc. A, 378(2166):1-18, 2020.
Accurately Computing the Log-Sum-Exp and Softmax Functions (with P. Blanchard and D. J. Higham). IMA J. Numer. Anal. 41(4):2311–2330, 2020.
Mixed Precision Block Fused Multiply-Add: Error Analysis and Application to GPU Tensor Coress (with P. Blanchard, F. Lopez, T. Mary and S. Pranesh). SIAM J. Sci. Comput., 42(3):C124-C141, 2020.
A Class of Fast and Accurate Summation Algorithms (with P. Blanchard and T. Mary). SIAM J. Sci. Comput., 42(3):A1541-A1557, 2020. Blog post.
Simulating Low Precision Floating-Point Arithmetic (with S. Pranesh). SIAM J. Sci. Comput., 41(5):C585-C602, 2019. Blog post.
A New Approach to Probabilistic Rounding Error Analysis (with T. Mary). SIAM J. Sci. Comput., 41(5):A2815-A2835, 2019. Blog post.
Etymo: A New Discovery Engine for AI Research (with W. Zhang, J. Deakin and S. Wang), in Companion Proceedings of the Web Conference 2018, International World Wide Web Conferences Steering Committee, pp. 227-230, 2018.
Optimized Batched Linear Algebra for Modern Architectures. (with J. Dongarra, S. Hammarling, S. D. Relton, and M. Zounon). In Euro-Par 2017: Parallel Processing, F. F. Rivera, T. F. Pena, and J. C. Cabaleiro, editors, volume 10417 of Lecture Notes in Computer Science, Springer-Verlag, Cham, 2017, pages 511-522.
The Design and Performance of Batched BLAS on Modern High-Performance Computing Systems (with Jack Dongarra, Sven Hammarling, Samuel D. Relton, Pedro Valero-Lara and Mawussi Zounon). Procedia Computer Science, 108:495-504, 2017.
Creating a Standardised Set of Batched BLAS Routines (with J. Dongarra, S. Hammarling, S. D. Relton, P. Valero-Lara, and M. Zounon). In Proceedings of the Fourth Workshop on Sustainable Software for Science: Practice and Experiences (WSSSPE4), G. Allen, J. Carver, S.-C. T. Choi, et al., editors, volume 1686, CEUR Workshop Proceedings, 2016.
A proposed API for Batched Basic Linear Algebra Subprograms (with Jack Dongarra, Iain Duff, Mark Gates, Azzam Haidar, Sven Hammarling, Jonathon Hogg, Pedro Valero-Lara, Samuel D. Relton, Stanimire Tomov, and Mawussi Zounon), MIMS EPrint 2016.25, April 2016.
UManSysProp V1.0: An Online and Open-Source Facility for Molecular Property Prediction and Atmospheric Aerosol Calculations (with David Topping, Mark Barley, Michael J. Bane, Bernard Aumont, Nicholas Dingle, and Gordon McFiggans), Geoscientific Model Development, 9(2):899-914, 2016.
Matrix Depot: An Extensible Test Matrix Collection for Julia (with Weijian Zhang ), PeerJ Computer Science, 2:e58, 2016. Usage statistics.
Making the Princeton Companion to Applied Mathematics, Mathematics Today, 51(5):212-214, 2015.
Numerical Linear Algebra and Matrix Analysis, in N. J. Higham, M. R. Dennis, P. Glendinning, P. A. Martin, F. Santosa, and J. Tanner, editors, The Princeton Companion to Applied Mathematics, pages 263-281. Princeton University Press, Princeton, NJ, USA, 2015.
The Singular Value Decomposition, in N. J. Higham, M. R. Dennis, P. Glendinning, P. A. Martin, F. Santosa, and J. Tanner, edit ors, The Princeton Companion to Applied Mathematics, pages 126-127. Princeton University Press, Princeton, NJ, USA, 2015.
Color Spaces and Digital Imaging, in N. J. Higham, M. R. Dennis, P. Glendinning, P. A. Martin, F. Santosa, and J. Tanner, editors, The Princeton Companion to Applied Mathematics, pages 808-813. Princeton University Press, Princeton, NJ, USA, 2015.
How to Read and Understand a Paper, in N. J. Higham, M. R. Dennis, P. Glendinning, P. A. Martin, F. Santosa, and J. Tanner, editors, The Princeton Companion to Applied Mathematics, pages 903-906. Princeton University Press, Princeton, NJ, USA, 2015.
Workflow, in N. J. Higham, M. R. Dennis, P. Glendinning, P. A. Martin, F. Santosa, and J. Tanner, editors, The Princeton Companion to Applied Mathematics, pages 912-916. Princeton University Press, Princeton, NJ, USA, 2015.
Sylvester’s Influence on Applied Mathematics, Mathematics Today, 50(4):202-206, 2014. (This version contains additional historical references. The version published in Mathematics Today is available on request.)
Matrix Computations in Basic on a Microcomputer. MIMS EPrint 2013.51, October 2013. This is a reissue of a 1985 technical report. The original report was published, without the appendices, as Matrix Computations in Basic on a Microcomputer, IMA Bulletin, 22:13-20, 1986.
Reducing the Influence of Tiny Normwise Relative Errors on Performance Profiles (with Nicholas J. Dingle), ACM Trans. Math. Soft. 39 (4): 24:1-24:11, 2013. Published version.
Applications/Algorithms Roadmapping Activity. First Stage Final Report (with Anne Trefethen, Iain Duff and Peter Coveney), MIMS EPrint 2009.85, June 2009.
Developing a High-Performance Computing/Numerical Analysis Roadmap (with Anne Trefethen, Iain Duff and Peter Coveney), Int. J. High Performance Computing Applications, 23(4):423-426, 2009.
Cayley, Sylvester, and Early Matrix Theory, Linear Algebra Appl., 428:39-43, 2008. Published version. Commentary on Matrix Factorizations and Applications, in R. H. Chan, C. Greif, and D. P. O’Leary, editors, Milestones in Matrix Computation: The Selected Works of Gene H. Golub, with Commentaries, pages 227-235, Oxford University Press, 2007.
The Numerical Stability of Barycentric Lagrange Interpolation IMA J. Numer. Anal., 24:547-556, 2004.
The Sensitivity of Computational Control Problems (with Mihail Konstantinov, Volker Mehrmann and Petko Petkov), IEEE Control Systems Magazine, 24(1):28-43, Feb. 2004. Original technical report (longer version).
The Matrix Computation Toolbox for MATLAB (Version 1.0), NA Report 410, August 2002.
Notes on Accuracy and Stability of Algorithms in Numerical Linear Algebra, in M. Ainsworth, J. Levesley, and M. Marletta, eds, The Graduate Student’s Guide to Numerical Analysis ’98, pages 48-82. Springer-Verlag, Berlin, 1999.
Testing Linear Algebra Software , in R. F. Boisvert, editor, Quality of Numerical Software: Assessment and Enhancement, pages 109-122. Chapman and Hall, London, 1997.
Recent Developments in Dense Numerical Linear Algebra, in I. S. Duff and G. A. Watson, editors, The State of the Art in Numerical Analysis, pages 1-26. Oxford University Press, 1997.
Matrix Powers in Finite Precision Arithmetic (with Philip A. Knight), SIAM J. Matrix Anal. Appl., 16(2):343-358, Apr. 1995
The Test Matrix Toolbox for Matlab (Version 3.0) , NA Report 276, September 1995. Test Matrix Toolbox (zip file of the MATLAB toolbox).
A Survey of Componentwise Perturbation Theory in Numerical Linear Algebra, In W. Gautschi, editor, Mathematics of Computation 1943-1993: A Half Century of Computational Mathematics, volume 48 of Proceedings of Symposia in Applied Mathematics, pages 49-77, American Mathematical Society, Providence, RI, USA, 1994.
The Accuracy of Floating Point Summation, SIAM J. Sci. Comput., 14(4):783-799, July 1993.
Optimization by Direct Search in Matrix Computations, SIAM J. Matrix Anal. Appl., 14(2):317-333, April 1993.
Stability of a Method for Multiplying Complex Matrices with Three Real Matrix Multiplications, SIAM J. Matrix Anal. Appl., 13(3):681-687, July 1992.
Algorithm 694: A collection of test matrices in MATLAB, ACM Trans. Math. Soft., 17(3):289-305, Sept. 1991.
Matrix Nearness Problems and Applications, In M. J. C. Gover and S. Barnett, editors, Applications of Matrix Theory, pages 1-27, Oxford University Press, 1989.
Computing a Nearest Symmetric Positive Semidefinite Matrix, Linear Algebra and Appl., 103:103-118, 1988.
Numerical Linear Algebra in Statistical Computing (with G. W. Stewart), in A. Iserles and M. J. D. Powell, editors, The State of the Art in Numerical Analysis, pages 41-57. Oxford University Press, 1987.
Nearness Problems in Numerical Linear Algebra, Ph.D. Thesis, University of Manchester, July 1985.
Matrix Condition Numbers, M.Sc. Thesis, University of Manchester, October 1983.

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