Convergence of Relaxed Hermitian and Skew-hermitian Splitting Method

Abstract

In this paper, based on the method first considered by Bai, Golub and Ng [Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems, SIAM J.Matrix Anal. Appl.}, 24(2003): 603-626], the relaxed Hermitian and skew-Hermitian (RHSS) splitting method is presented and then we prove the convergence of the method for solving positive definite, non-Hermitian linear systems. Moreover, we find that the new scheme can outperform the standard HSS method and can be used as an effective preconditioner for certain linear systems, which is shown through numerical experiments.