Improved PMHSS Iteration Methods for Complex Symmetric Linear Systems (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 iterativemethods, namely, the modified PMHSS (MPMHSS) method and the double modifiedPMHSS (DMPMHSS) method, are proposed in this paper. The spectral radii of theiteration matrices of two methods are given. We show that by choosing an appropriateparameter, MPMHSS could speed up the convergence on PMHSS. The DMPMHSSmethod is a four-step alternating iteration that is developed upon the two-step alternatingiteration of MPMHSS. We discuss the choice of the parameters and establish the convergenceof DMPMHSS. In particular, we give an analysis of the spectral radius of PMHSSand DMPMHSS at the parameter free situation, and we show that DMPMHSS convergesfaster than PMHSS in most cases. Our numerical experiments show these points.
Keywords: Complex symmetric linear system; PMHSS.