(untitled) (Journal of Computational Mathematics, 2018)
Based on the preconditioned modified Hermitian and skew-Hermitian splitting (PMHSS) iteration method for the complex symmetric linear system, two improved iterative methods, namely, the modified PMHSS (MPMHSS) method and the double modified PMHSS (DMPMHSS) method, are proposed in this paper. The spectral radii of the iteration matrices of two methods are given. We show that by choosing an appropriate parameter, MPMHSS could speed up the convergence on PMHSS. The DMPMHSS method is a four-step alternating iteration that is developed upon the two-step alternating iteration of MPMHSS. We discuss the choice of the parameters and establish the convergence of DMPMHSS. In particular, we give an analysis of the spectral radius of PMHSS and DMPMHSS at the parameter free situation, and we show that DMPMHSS converges faster than PMHSS in most cases. Our numerical experiments show these points.