A generalized modified Hermitian and skew-Hermitian splitting (GMHSS) method for solving complex Sylvester matrix equation

Abstract

In this study, based on the MHSS (Modified Hermitian and skew-Hermitian splitting) method, we will present a generalized MHSS approach for solving large sparse Sylvester equation with non-Hermitian and complex symmetric positive definite/semi-definite matrices. The new method (GMHSS) is a four-parameter iteration procedure where the iterative sequence is unconditionally convergent to the unique solution of the Sylvester equation. Then to improve the GMHSS method, the inexact version of the GMHSS iterative method (IGMHSS) will be described and will be analyzed. Also, by using a new idea, we try to minimize the upper bound of the spectral radius of iteration matrix. Two test problems are given to illustrate the efficiency of the new approach.