On short recurrence Krylov type method's for linear systems with many right-hand sides

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:300

Article

Rashedi, Somaiyeh¹  Ebadi, Ghodrat¹  Birk, Sebastian²  Frommer, Andreas² 

[1] Univ Tabriz, Dept Math Sci, Tabriz 5166614766, Iran

[2] Berg Univ Wuppertal, Fachbereich Math & Nat Wissensch, Fachbereich 9, D-42097 Wuppertal, Germany

关键词: Sparse linear systems;    Multiple right-hand sides;    Block methods;    Krylov subspace;    Non-Hermitian matrices;   

DOI  :  10.1016/j.cam.2015.11.040

来源: Elsevier

【 摘 要 】

Block and global Krylov subspace methods have been proposed as methods adapted to the situation where one iteratively solves systems with the same matrix and several right hand sides. These methods are advantageous, since they allow to cast the major part of the arithmetic in terms of matrix-block vector products, and since, in the block case, they take their iterates from a potentially richer subspace. In this paper we consider the most established Krylov subspace methods which rely on short recurrences, i.e. BiCG, QMR and BiCGStab. We propose modifications of their block variants which increase numerical stability, thus at least partly curing a problem previously observed by several authors. Moreover, we develop modifications of the global variants which almost halve the number of matrix vector multiplications. We present a discussion as well as numerical evidence which both indicate that the additional work present in the block methods can be substantial, and that the new economic versions of the global BiCG and QMR method can be considered as good alternatives to the BiCGStab variants. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free