On Parameterized PMHSS Iteration Method For A Class Of Complex Symmetric Linear Systems

Based on the ideas of the preconditioned modified Hermitian and skew-Hermitian splitting (PMHSS) iteration method and the alternating-directional PMHSS (ADP-MHSS) iteration method, a new iteration method is proposed in this work to solve a class of complex symmetric linear systems, i.e. parameterized PMHSS (P2MHSS)iteration method. In this work, from the view point of preconditioning matrix,the computational formulas of the iteration parameters involved in the P2MHSS method are proposed. Besides, the convergence properties of this method are anal-ysed, which show that the P2MHSS iteration method will convergent to the exact solution of this linear system for any initial vector under some conditions. Final-ly, we use some numerical results to verify the feasibility and the efficiency of the P2MHSS iteration method.