Computation of the exponential function of matrices by a formula without oscillatory integrals on infinite intervals

作     者：Suzuki, Masato Tanaka, Kenichiro 

作者机构：Department of Mathematical Informatics Graduate School of Information Science and Technology University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo113-8656 Japan Department of Mathematical and Computing Science School of Computing Institute of Science Tokyo 2-12-1 Ookayama Tokyo Meguro-ku152-8550 Japan 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2024年

核心收录：

主　　题：Choquet integral 

摘      要：We propose a quadrature-based formula for computing the exponential function of matrices with a non-oscillatory integral on an infinite interval and an oscillatory integral on a finite interval. In the literature, existing quadrature-based formulas are based on the inverse Laplace transform or the Fourier transform. We show these expressions are essentially equivalent in terms of complex integrals and choose the former as a starting point to reduce computational cost. By choosing a simple integral path, we derive an integral expression mentioned above. Then, we can easily apply the double-exponential formula and the Gauss-Legendre formula, which have rigorous error bounds. As numerical experiments show, the proposed formula outperforms the existing formulas when the imaginary parts of the eigenvalues of matrices have large absolute *** Codes 65F60, 65D30 Copyright © 2024, The Authors. All rights reserved.