M. Fasi and M. Mikaitis.
Algorithms for stochastically rounded elementary arithmetic operations in IEEE 754 floating-point arithmetic, MIMS EPrint 2020.9, 2020. (01 April 2020) M. Fasi and N. Higham.
Generating Extreme-Scale Matrices with Specified Singular Values or Condition Numbers, MIMS EPrint 2020.8, 2020. (27 March 2020) N. Higham and E. Hopkins.
A Catalogue of Software for Matrix Functions. Version 3.0, MIMS EPrint 2020.7, 2020. (27 March 2020) E.Carson, N. J. Higham and S. Pranesh.
Three-Precision GMRES-based Iterative Refinement for Least Squares Problems, MIMS EPrint 2020.5, 2020. (03 February 2020) N. J. Higham and T. Mary.
Sharper Probabilistic Backward Error Analysis for Basic Linear Algebra Kernels With Random Data, MIMS EPrint 2020.4, 2020. (21 January 2020) J. Dongarra, N. J. Higham and L. Grigori.
Numerical Algorithms for High-Performance Computational Science, Phil. Trans. R. Soc. A, 378(2166):1-18, 2020. (20 January 2020) F. Tisseur and M. Van Barel.
Min-Max Elementwise Backward Error for Roots of Polynomials and a Corresponding Backward Stable Root Finder, arXiv:2001.05281, 2020. (15 January 2020) M. Mikaitis.
Stochastic Rounding: Algorithms and Hardware Accelerator, arXiv:2001.01501, 2020. (06 January 2020) M. Mikaitis.
Issues with rounding in the GCC implementation of the ISO 18037:2008 standard fixed-point arithmetic, arXiv:2001.01496, 2020. (06 January 2020) 2019
N. J. Higham and S. Pranesh.
Exploiting Lower Precision Arithmetic in Solving Symmetric Positive Definite Linear Systems and Least Squares Problems, MIMS EPrint 2019.20, 2019. (06 November 2019) P. Blanchard, F. Lopez, N. J. Higham, T. May and S. Pranesh.
Mixed Precision Block Fused Multiply-Add: Error Analysis and Application to GPU Tensor Cores, MIMS EPrint 2019.18, 2019. (22 February 2020) N. J. Higham and T. Mary.
A New Approach to Probabilistic Rounding Error Analysis, SIAM J. Sci. Comput., 41(5):A2815-A2835, 2019. (12 September 2019) N. J. Higham and T. Mary.
Solving Block Low-Rank Linear Systems by LU Factorization is Numerically Stable, MIMS EPrint 2019.15, 2019. (09 September 2019) P. Blanchard, D. J. Higham and N. J. Higham.
Accurate Computation of the Log-Sum-Exp and Softmax Functions, MIMS EPrint 2019.16, 2019. (31 January 2020) S. Pranesh.
Backward error and condition number of a generalized Sylvester equation, with application to the stochastic Galerkin method, MIMS EPrint 2019.13, 2019. (19 June 2019) J. Dongarra, M. Gates, A. Haidar, J. Kurzak, P. Luszczek, P. Wu, I. Yamazaki, A. Yarkhan, M. Abalenkovs, N. Bagherpour, S. Hammarling, J. Šístek, D. Stevens, M. Zounon, and S. Relton.
PLASMA: Parallel Linear Algebra Software for Multicore Using OpenMP, ACM Transactions on Mathematical Software (TOMS), 45(2), 16, 2019. (06 June 2019) S. Elsworth and S. Güttel.
ABBA: Adaptive Brownian bridge-based symbolic aggregation of time series, MIMS 2019.11, 2019. (28 May 2019)
, Bridging the Gap between Flat and Hierarchical Low-rank Matrix Formats: the Multilevel Block Low-Rank Format SIAM J. Sci. Comput., 41 (3) :A1414-A1442, 2019. (02 May 2019) A. Erlich, G. W. Jones, F. Tisseur, D. E. Moulton and A. Goriely.
The role of network topology, growth laws and mechanics in the dynamics of cell assemblies, arXiv:1904.11161, 2019. (25 April 2019) P. Blanchard, N. J. Higham and T. Mary.
A Class of Fast and Accurate Summation Algorithms, MIMS EPrint 2019.6, 2019. To appear in SIAM J. Sci. Comput. (22 February 2020) M. Fasi.
Optimality of the Paterson-Stockmeyer methods for evaluating matrix polynomials and rational functions, Linear Algebra Appl., 574:182–200, 2019.
, Performance and Scalability of the Block Low-Rank Multifrontal Factorization on Multicore Architectures ACM Trans. Math. Software, 45 (1) :2:1-2:26, 2019. (28 March 2019) N. J. Higham and S. Pranesh.
Simulating Low Precision Floating-Point Arithmetic, MIMS EPrint 2019.4, 2019. (20 March 2019) L. Wang, F. Tisseur, G. Strang and B. K. P. Horn.
Stability analysis of a chain of non-identical vehicles under bilateral cruise control, MIMS EPrint 2018.3, 2019. (17 March 2019) J. Hook, J. Pestana, F. Tisseur and J. Hogg.
Max-Balanced Hungarian Scalings, SIAM J. Matrix Anal. Appl., 40(1), 320–346, 2019. (26 February 2019) H. Anzt, J. Dongarra, G. Flegar, N. J. Higham and E. S. Quintana-Orti.
Adaptive Precision in Block-Jacobi Preconditioning for Iterative Sparse Linear System Solvers, Concurrency Computat.: Pract. Exper, 31(6), e4460, 2019 (18 February 2019) S. Elsworth and S. Güttel.
The block rational Arnoldi method, MIMS 2019.2, 2019. (17 February 2019) C. Jeannerod, T. Mary, C. Pernet and D. Roche.
Exploiting Fast Matrix Arithmetic in Block Low-Rank Factorizations, MIMS EPrint 2019.1, 2019. (03 February 2019) N. J. Higham and T. Mary.
A new preconditioner that exploits low-rank approximations to factorization error, SIAM J. Sci. Comput., 41(1), A59-A82, 2019. (02 January 2019) 2018
M. Fasi and N. J. Higham.
An Arbitrary Precision Scaling and Squaring Algorithm for the Matrix Exponential, MIMS EPrint 2018.36, 2018. (25 November 2018) A.Haidar, S. Tomov, J. Dongarra and N. J. Higham.
Harnessing GPU Tensor Cores for Fast FP16 Arithmetic to Speed up Mixed-Precision Iterative Refinement Solvers, In Proceedings of the International Conference for High Performance Computing, Networking, Storage, and Analysis (p. 47), IEEE Press, 2018. (11 November 2018) S. Elsworth and S. Güttel.
Conversions between barycentric, RKFUN, and Newton representations of rational interpolants, MIMS EPrint 2017.40, 2018. (4 October 2018) M. Fasi and B. Iannazzo.
Computing Primary Solutions of Equations Involving Primary Matrix Functions, Linear Algebra and its Applications, 560, 17-42, 2018. (18 September 2018) P. Lietaert, K. Meerbergen and F. Tisseur.
Compact Two-Sided Krylov Methods for Nonlinear Eigenvalue Problems, SIAM J. Sci. Comput., 40(5), A2801-A2829, 2018. (4 September 2018) C. Qiu, S. Güttel, X. Ren, C. Yin, U. Liu, B. Zhang and G.Egbert.
A block rational Krylov method for three-dimensional time-domain marine controlled-source electromagnetic modelinga Search A block rational Krylov method for three-dimensional time-domain marine controlled-source electromagnetic modeling, MIMS EPrint 2018.22, 2018. (19 August 2018) P. Nadukandi and N. J. Higham.
Computing the wave-kernel matrix functions,, SIAM J. Sci. Comput., 40(6), A4060–A4082, 2019. (6 December 2018) A. Haidar, A. Abdelfattah, M. Zounon, P. Wu, S. Pranesh, S. Tomov, and J. Dongarra.
The Design of Fast and Energy-Efficient Linear Solvers: On the Potential of Half-Precision Arithmetic and Iterative Refinement Techniques, In International Conference on Computational Science, pp. 586-600. Springer, Cham, 2018. (12 June 2048) M. Zemaite, F. Tisseur and R. Kannan.
Filtering Frequencies in a Shift-and-invert Lanczos Algorithm for the Dynamic Analysis of Structures, MIMS EPrint 2018.17, 2018. (25 May 2018) W. Zhang, J. Deakin N. J. Higham and S. Wang
Etymo: A New Discovery Engine for AI Research, in Companion Proceedings of the Web Conference 2018, International World Wide Web Conferences Steering Committee, pp. 227-230, 2018. (23 April 2018) T. Kinyanjui, J. Middleton, S. G
üttel, J. Cassell, J. Ross and T. House. Scabies in residential care homes: Modelling, inference and interventions for well-connected population sub-units , PLoS Computational Biology, 14(3):1–24,2018. (26 March 2018) M. Fasi and N. J. Higham.
Multiprecision Algorithms for Computing The Matrix Logarithm, SIAM J. Matrix Anal. Appl., 39(1):472-491, 2018. (17 March 2018) M. Fasi and N. J. Higham.
Multiprecision Algorithms for Computing the Matrix Logarithm, SIAM J. Matrix Anal. Appl., 39(1), 472–491, 2018. 15 March 2018) E. Carson and N, J. Higham,
Accelerating the Solution of Linear Systems by Iterative Refinement in Three Precisions, SIAM J. Sci. Comput., 40(2), A817–A847, 2018. (15 March 2018) D. I. Georgescu, G. W. Peter and N. J. Higham.
Explicit Solutions to Correlation Matrix Completion Problems, with an Application to Risk Management and Insurance, Roy. Soc. Open Sci., 5(3):1-11, 2018. (1 March 2018) I. Yamazaki, J. Kurzak, P. Wu, M. Zounon, and J. Dongarra.
Symmetric Indefinite Linear Solver Using OpenMP Task on Multicore Architectures, IEEE Trans. Parallel Distrib. Syst. 29(8): 1879-1892, 2018. (23 February 2018) M. Fasi and B. Iannazzo.
Computing the weighted geometric mean of two large-scale matrices and its inverse times a vector (with B. Iannazzo). SIAM J. Matrix Anal. Appl., 39(1):178-203, 2018. (01 February 2018) Y. Makatsukasa, L. Taslaman, F. Tisseur and I. Zaballa.
Reduction of Matrix Polynomials to Simpler Forms, SIAM. J. Matrix Anal. & Appl., 39(1), 148-177, 2018. (30 January 2018) 2017
E. Carson and N. 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):A2834-A2856, 2017. (6 December 2017) B. Arslan, V. Noferini and F. Tisseur.
The Structured Condition Number of a Differentiable Map Between Matrix Manifolds, with Applications, MIMS EPrint 2017.36, 2017. (8 November 2017) M. Berljafa and S. Güttel.
Parallelization of the rational Arnoldi algorithm, SIAM J. Sci. Comput., 39(5):S197–S221, 2017. (8 November 2017) J. Hogg, J. Hook, J. Scott and F. Tisseur.
A max-plus approach to incomplete Cholesky factorization preconditioners, MIMS EPrint 2016.59, 2016. (8 November 2017) S. Güttel and F. Tisseur.
The Nonlinear Eigenvalue Problem, MIMS EPrint 2017.7, 2017. (20 October 2017) S. Hammarling.
Second Workshop on Batched, Reproducible, and Reduced Precision BLAS, MIMS 2017.14, 2017. J. Hook and F. Tisseur.
Incomplete LU Preconditioner Based on Max-Plus Approximation of LU Factorization, SIAM. J. Matrix Anal. & Appl., 38(4), 1160-1189, 2017. (19 October 2017) S. Güttel and J. W. Pearson.
A rational deferred correction approach to parabolic optimal control problems, IMA Journal of Numerical Analysis, 38(4), 1861-1892, 2017. (8 November 2017) M.J Gander, S. Güttel and M. Petcu.
A nonlinear ParaExp algorithm, MIMS EPrint 2017.17. (21 January 2018). M. Berljafa and S. Güttel.
The RKFIT algorithm for nonlinear rational approximation, SIAM J. Sci. Comput., 39(5):A2049–A2071, 2017. (8 November 2017) H. Chen, Y. Maeda, A. Imakura, T. Sakurai and F. Tisseur.
Improving the numerical stability of the Sakurai-Sugiura method for quadratic eigenvalue problems, JSIAM Letters Vol.9 (2017) pp.17-20, 2017. (24 March 2017) 2016
M. Van Barel and F. Tisseur.
Polynomial eigenvalue solver based on tropically scaled Lagrange linearization, MIMS EPrint 2016.61, 2016. (8 November 2017) V. Druskin, S. Güttel and L. Knizhnerman.
Compressing variable-coefficient exterior Helmholtz problems via RKFIT, MIMS EPrint 2016.53, 2016. V. Mehrmann, V. Noferini, F. Tisseur and H. Xu.
On the sign characteristics of Hermitian matrix polynomials, Linear Algebra Appl., 511: 328-364, 2016. (14 September 2016) V. Druskin, S. Güttel and L. Knizhnerman.
Near-optimal perfectly matched layers for indefinite Helmholtz problems, SIAM Rev., 58(1):90–116, 2016. (20 October 2017) S. Güttel and Y. Nakatsukasa.
Scaled and squared subdiagonal Padé approximation for the matrix exponential, SIAM J. Matrix Anal. Appl., 37(1):145–170, 2016. S. Hammarling.
Workshop on batched, reproducible, and reduced precision BLAS. MIMS EPrint 2016.41, 2016. (20 October 2017) J. Dongarra, I Duff, M. Gates, A. Haidar, S. Hammarling, N. J. Higham, J. Hogg, P. ValeroLara, S. Relton, S. Tomov, and M. Zounon.
A proposed API for batched basic linear algebra subprograms. MIMS EPrint 2016.25, 2016. (08 November 2017) J.Pestana, R. Muddle, M. Heil, F. Tisseur and M. Mihajlovic.
Efficient block preconditioning for a C1 finite element discretisation of the Dirichlet biharmonic problem, SIAM J. Sci. Comput., 38(1), A325-A345, 2016. (08 November 2017)