Some Results on the Range-Restricted GMRES Method  

作　　者：Yiqin Lin Yiqin Lin(School of Science, Hunan University of Science and Engineering, Yongzhou, China)

机构地区：[1]School of Science, Hunan University of Science and Engineering, Yongzhou, China

出　　处：《Journal of Applied Mathematics and Physics》2023年第12期3902-3908,共7页应用数学与应用物理（英文）

摘　　要：In this paper we reconsider the range-restricted GMRES (RRGMRES) method for solving nonsymmetric linear systems. We first review an important result for the usual GMRES method. Then we give an example to show that the range-restricted GMRES method does not admit such a result. Finally, we give a modified result for the range-restricted GMRES method. We point out that the modified version can be used to show that the range-restricted GMRES method is also a regularization method for solving linear ill-posed problems.In this paper we reconsider the range-restricted GMRES (RRGMRES) method for solving nonsymmetric linear systems. We first review an important result for the usual GMRES method. Then we give an example to show that the range-restricted GMRES method does not admit such a result. Finally, we give a modified result for the range-restricted GMRES method. We point out that the modified version can be used to show that the range-restricted GMRES method is also a regularization method for solving linear ill-posed problems.

关 键 词：Nonsymmetric Linear System Krylov Subspace Method Arnoldi Process GMRES RRGMRES 

分 类 号：O24[理学—计算数学]