The Variants of the MGSS Methods for Complex Symmetric Linear System of Equations

Abstract

Recently, inspired by a modified generalized shift-splitting iteration method for complex symmetric linear systems, we propose two variants of the modified generalized shift-splitting iteration (MGSS) methods for solving complex symmetric linear systems. One is a parameterized MGSS iteration method and the other is a modified parameterized MGSS iteration method. We prove that the proposed methods are convergent under appropriate constraints on the parameters. In addition, we also give the eigenvalue distributions of different preconditioned matrices to verify the effectiveness of the preconditioners proposed in this paper.