ART: Adaptive residual-time restarting for Krylov subspace matrix exponential evaluations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:364

Article

Botchev, M. A.¹  Knizhnerman, L. A.² 

[1] Russian Acad Sci, Keldysh Inst Appl Math, Miusskaya Sq 4, Moscow 125047, Russia

[2] Cent Geophys Expedit, Math Modelling Dept, Narodnogo Opolcheniya St,38,Bldg 3, Moscow 123298, Russia

关键词: Krylov subspace methods;    Exponential time integration;    Arnoldi method;    Krylov subspace restarting;    Shift-and-invert Krylov subspace methods;   

DOI  :  10.1016/j.cam.2019.06.027

来源: Elsevier

【 摘 要 】

In this paper a new restarting method for Krylov subspace matrix exponential evaluations is proposed. Since our restarting technique essentially employs the residual, some convergence results for the residual are given. We also discuss how the restart length can be adjusted after each restart cycle, which leads to an adaptive restarting procedure. Numerical tests are presented to compare our restarting with three other restarting methods. Some of the algorithms described in this paper are a part of the Octave/Matlab package expmARPACK available at http://team.kiam.ru/botchev/expm/. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free