Generalized SOR iterative method for a class of complex symmetric linear system of equations

TL;DR

This paper introduces a generalized SOR iterative method for complex symmetric linear systems, analyzing its convergence, optimizing parameters, and demonstrating improved performance over existing methods through numerical experiments.

Contribution

It develops a new GSOR iterative method for complex symmetric systems, analyzes its convergence, and integrates it as a preconditioner for Krylov subspace methods.

Findings

Optimal iteration parameter and convergence factor derived

GSOR method outperforms MHSS in numerical tests

Effective preconditioning for Krylov methods demonstrated

Abstract

In this paper, to solve a broad class of complex symmetric linear systems, we recast the complex system in a real formulation and apply the generalized successive overrelaxation (GSOR) iterative method to the equivalent real system. We then investigate its convergence properties and determine its optimal iteration parameter as well as its corresponding optimal convergence factor. In addition, the resulting GSOR preconditioner is used to preconditioned Krylov subspace methods such as GMRES for solving the real equivalent formulation of the system. Finally, we give some numerical experiments to validate the theoretical results and compare the performance of the GSOR method with the modified Hermitian and skew-Hermitian splitting (MHSS) iteration.