A Modified HSS Iteration Method for Solving the Complex Linear Matrix Equation $AXB = C$

Abstract

In this paper, a modified Hermitian and skew-Hermitian splitting (MHSS) iteration method for solving the complex linear matrix equation $AXB = C$ has been presented. As the theoretical analysis shows, the MHSS iteration method will converge under certain conditions. Each iteration in this method requires the solution of four linear matrix equations with real symmetric positive definite coefficient matrices, although the original coefficient matrices are complex and non-Hermitian. In addition, the optimal parameter of the new iteration method is proposed. Numerical results show that MHSS iteration method is efficient and robust.