Preconditioned GSOR iterative method for a class of complex symmetric system of linear equations

TL;DR

This paper introduces a preconditioned GSOR iterative method for complex symmetric linear systems, demonstrating improved convergence through spectral radius reduction and optimal parameter selection, validated by numerical experiments.

Contribution

It develops a novel preconditioned GSOR method with theoretical analysis and numerical validation for complex symmetric linear systems.

Findings

Preconditioned GSOR reduces spectral radius compared to standard GSOR.

Optimal iteration parameters are identified for improved convergence.

Numerical experiments confirm theoretical advantages and effectiveness.

Abstract

In this paper, we present a preconditioned variant of the generalized successive overrelaxation (GSOR) iterative method for solving a broad class of complex symmetric linear systems. We study conditions under which the spectral radius of the iteration matrix of the preconditioned GSOR method is smaller than that of the GSOR method and determine the optimal values of iteration parameters. Numerical experiments are given to verify the validity of the presented theoretical results and the effectiveness of the preconditioned GSOR method.