On Bernoulli Matrix Polynomials and Matrix Exponential Approximation

[EN] We present in this paper a new method based on Bernoulli matrix polynomials to approximate the exponential of a matrix. The developed method has given rise to two new algorithms whose efficiency and precision are compared to the most efficient implementations that currently exist. For that, a state-of-the-art test matrix battery, that allows deeply exploring the highlights and downsides of each method, has been used. Since the new algorithms proposed here do make an intensive use of matrix products, we also provide a GPUs-based implementation that allows to achieve a high performance thanks to the optimal implementation of matrix multiplication available on these devices. (c) 2020 Elsevier B.V. All rights reserved This work has been partially supported by Spanish Ministerio de Economia y Competitividad and European Regional Development Fund (ERDF) grants TIN2017-89314-P and by the Programa de Apoyo a la Investigacion y Desarrollo 2018 of the Universitat Politecnica de Valencia (PAID-06-18) grants SP20180016. Defez Candel, E.; Ibáñez González, JJ.; Alonso-Jordá, P.; Alonso Abalos, JM.; Peinado Pinilla, J. (2022). On Bernoulli Matrix Polynomials and Matrix Exponential Approximation. Journal of Computational and Applied Mathematics. 404:1-16. https://doi.org/10.1016/j.cam.2020.113207