简化全局GMRES算法的扩张及收缩  

Global simpler GMRES with augmentation and deflation

作　　者：贾子薇 刘巧华[1] JIA Ziwei;LIU Qiaohua(College of Sciences,Shanghai University,Shanghai 200444,China)

机构地区：[1]上海大学理学院,上海200444

出　　处：《应用数学与计算数学学报》2018年第3期486-496,共11页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11001167)

摘　　要：简化的全局GMRES算法作为求解多右端项线性方程组的方法之一,与标准的全局GMRES算法相比,需要较少的计算量,但对应的重启动方法由于矩阵Krylov子空间维数的限制,收敛会较慢.基于调和Ritz矩阵,提出了简化全局GMRES的扩张及收缩算法.数值实验结果表明,新提出的扩张及收缩算法比标准的全局GMRES算法更为快速高效.The global simpler GMRES method is one of the feasible methods for nonsymmetric systems with multiple right-hand sides.Compared with the standard global GMRES method,it requires less computational work.However,the restarted version sometimes converges more slowly due to the limited dimension of the matrix Krylov subspace.In this paper,based on the harmonic Ritz matrices,we present the restarted global simpler GMRES with augmentation and deflation techniques.According to the numerical tests,the augmented and deflated versions have better numerical stability and efficieny.

关 键 词：矩阵方程 简化全局GMRES 矩阵Krylov子空间 调和Ritz矩阵 重启动 

分 类 号：O241[理学—计算数学]