文献类型：期刊文献

英文题名：Residual-Based Simpler Block GMRES for Nonsymmetric Linear Systems with Multiple Right-Hand Sides

作者：Wu, Qinghua[1,2];Bao, Liang[3];Lin, Yiqin[2]

机构：[1]Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Peoples R China;[2]Hunan Univ Sci & Engn, Coll Sci, Yongzhou 425100, Peoples R China;[3]East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2018

卷号：2018

外文期刊名：ADVANCES IN MATHEMATICAL PHYSICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000431335400001)】；

基金：This work is supported by the National Natural Science Foundation of China under Grants 11701170 and 11501193, the Natural Science Foundation of Hunan Province under Grants 2017JJ3092 and 2017JJ2102, the Key Program of the Scientific Research Foundation from Education Bureau of Hunan Province under Grant 09A033, the Scientific Research Foundation of Education Bureau of Hunan Province for Outstanding Young Scholars in University under Grant 10B038, and the Young Core Teacher Foundation of Hunan Province in University.

语种：英文

摘要：We propose in this paper a residual-based simpler block GMRES method for solving a system of linear algebraic equations with multiple right-hand sides. We show that this method is mathematically equivalent to the block GMRES method and thus equivalent to the simpler block GMRES method. Moreover, it is shown that the residual-based method is numerically more stable than the simpler block GMRES method. Based on the deflation strategy proposed by Calandra et al. (2013), we derive a deflation strategy to detect the possible linear dependence of the residuals and a near rank deficiency occurring in the block Arnoldi procedure. Numerical experiments are conducted to illustrate the performance of the new method.