TITLE:
Some Results on the Range-Restricted GMRES Method
AUTHORS:
Yiqin Lin
KEYWORDS:
Nonsymmetric Linear System, Krylov Subspace Method, Arnoldi Process, GMRES, RRGMRES
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.11 No.12,
December
25,
2023
ABSTRACT: 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.