Parallel approximation of the exponential of Hermitian matrices
Distributed, Parallel, and Cluster Computing
2023-06-30 v1 Numerical Analysis
Numerical Analysis
Abstract
In this work, we consider a rational approximation of the exponential function to design an algorithm for computing matrix exponential in the Hermitian case. Using partial fraction decomposition, we obtain a parallelizable method, where the computation reduces to independent resolutions of linear systems. We analyze the effects of rounding errors on the accuracy of our algorithm. We complete this work with numerical tests showing the efficiency of our method and a comparison of its performances with Krylov algorithms.
Keywords
Cite
@article{arxiv.2306.16778,
title = {Parallel approximation of the exponential of Hermitian matrices},
author = {Frédéric Hecht and Sidi-Mahmoud Kaber and Lucas Perrin and Alain Plagne and Julien Salomon},
journal= {arXiv preprint arXiv:2306.16778},
year = {2023}
}