A Flexible Global GCRO-DR Method for Shifted Linear Systems and General Coupled Matrix Equations

Author:

Meng Jing12,Gu Xian-Ming3ORCID,Luo Wei-Hua4,Fang Liang1

Affiliation:

1. School of Mathematics and Statistics, Taishan University, Taian 271021, Shandong, China

2. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100000, China

3. Institute of Mathematics, School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan 611130, China

4. School of Mathematics and Physics Science, Hunan University of Arts and Science, Changde, Hunan 415000, China

Abstract

In this paper, we mainly focus on the development and study of a new global GCRO-DR method that allows both the flexible preconditioning and the subspace recycling for sequences of shifted linear systems. The novel method presented here has two main advantages: firstly, it does not require the right-hand sides to be related, and, secondly, it can also be compatible with the general preconditioning. Meanwhile, we apply the new algorithm to solve the general coupled matrix equations. Moreover, by performing an error analysis, we deduce that a much looser tolerance can be applied to save computation by limiting the flexible preconditioned work without sacrificing the closeness of the computed and the true residuals. Finally, numerical experiments demonstrate that the proposed method illustrated can be more competitive than some other global GMRES-type methods.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

General Mathematics

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