求解奇异线性系统的右预处理GMRES方法  

Right Preconditioned GMRES Method for Solving Singular Linear Systems

作　　者：王帅丽 WANG Shuaili(College of Mathematics and Physics,Wenzhou University,Wenzhou,China 325035)

机构地区：[1]温州大学数理学院,浙江温州325035

出　　处：《温州大学学报（自然科学版）》2021年第1期20-26,共7页Journal of Wenzhou University(Natural Science Edition)

基　　金：国家自然科学基金项目(61572018)。

摘　　要：本文讨论了用右预处理的广义极小残量(GMRES)法解决奇异线性系统.发现:若预处理子是通过对系数矩阵的恰当分裂得到的,则用GMRES求解预处理系统一定会得到Moore-Penrose广义逆解.进一步讨论了恰当分裂的特征,并推广了定常迭代法中的某些经典结果.In this paper,the generalized minimal residuals(GMRES)method with right preconditioning is discussed for solving singular linear systems.It is found that if the perconditioner is obtained by proper splitting of the coefficient matrix,the Moore-Prose generalized inverse solution will be obtained by solving the preconditioned system through GMRES.In addition,this paper discusses the characteristics of proper splitting and generalizes some classical results in stationary iterative method.

关 键 词：奇异线性系统 值域对称 恰当分裂 奇异右预处理子 

分 类 号：O241.6[理学—计算数学]