Lopsided PMQHSS and double lopsided PMQHSS iteration methods for solving complex symmetric linear equations

Abstract

By applying the lopsided technology to the preconditioned modified quasi-Hermitian and skew-Hermitian splitting (PMQHSS) iteration method, we construct a lopsided PMQHSS (LPMQHSS) iteration method for solving complex symmetric linear equations. We discuss the convergence properties of the LPMQHSS method. Specially, the convergence properties of the LPMQHSS method with \(V=T\) are established. In addition, we also give another new iteration method, referred to as double lopsided PMQHSS (DLPMQHSS) iteration method. The convergence conditions of the DLPMQHSS iteration method are analyzed. The proposed LPMQHSS and DLPMQHSS methods have faster convergence rates than the PMQHSS one. Numerical experiments are reported to illustrate the feasibility and effectiveness of the proposed methods.