Euler polynomials for the matrix exponential approximation

被引：8

作者：

Alonso, Jose M. ^{[1
]}

Ibanez, J. ^{[2
]}

Defez, E. ^{[2
]}

Alonso-Jorda, P. ^{[3
]}

机构：

[1] Univ Politecn Valencia, Inst Instrumentac Imagen Mol, Camino Vera S-N, Valencia 46022, Spain

[2] Univ Politecn Valencia, Inst Matemat Multidisciplinar, Camino Vera S-N, Valencia 46022, Spain

[3] Univ Politecn Valencia, Dept Comp Syst & Computat, Camino Vera S-N, Valencia 46022, Spain

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2023年 / 425卷

关键词：

Matrix functions; Matrix exponential; Euler polynomials; SQUARING ALGORITHM; PADE-APPROXIMATION; BERNOULLI; COMPUTE;

D O I：

10.1016/j.cam.2023.115074

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, a new method to compute the matrix exponential function by using an approximation based on Euler polynomials is proposed. These polynomials are used in combination with the scaling and squaring technique, considering an absolute forward-type theoretical error. Its numerical and computational properties have been evaluated and compared with the most current and competitive codes dedicated to the computation of the matrix exponential. Under a heterogeneous test battery and a set of exhaustive experiments, it has been demonstrated that the new method offers performance in terms of accuracy and stability which is as good as or even better than those of the considered methods, with an intermediate computational cost among all of them. All of the above makes this a very competitive alternative that should be considered in the growing list of available numerical methods and implementations dedicated to the approximation of the matrix exponential.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

引用

页数：15

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