The semi-convergence properties of MHSS method for a class of complex nonsymmetric singular linear systems

We use the modified Hermitian and skew-Hermitian splitting (MHSS) iteration method to solve a class of complex nonsymmetric singular linear systems. The semi-convergence properties of the MHSS method are studied by analyzing the spectrum of the iteration matrix. Moreover, after investigating the semi-convergence factor and estimating its upper bound for the MHSS iteration method, an optimal iteration parameter that minimizes the upper bound of the semi-convergence factor is obtained. Numerical experiments are used to illustrate the theoretical results and examine the effectiveness of the MHSS method served both as a preconditioner for GMRES method and as a solver.