On Bernoulli matrix polynomials and matrix exponential approximation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:404

Article

Defez, E.¹  Ibanez, J.²  Alonso-Jorda, P.³  Alonso, Jose M.²  Peinado, J.³ 

[1] Univ Politecn Valencia, Inst Matemat Multidisciplinar, Camino Vera s-n, Valencia 46022, Spain

[2] Univ Politecn Valencia, Inst Instrumentac Imagen Mol, Camino Vera s-n, Valencia 46022, Spain

[3] Univ Politecn Valencia, Dept Informat Syst & Computat, Camino Vera s-n, Valencia 46022, Spain

关键词: Bernoulli matrix approximation;    Matrix exponential function;    GPU computing;   

DOI  :  10.1016/j.cam.2020.113207

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free