A Generalized Preconditioned MHSS Method for a Class of Complex Symmetric Linear Systems

Abstract

Based on the MHSS (Modified Hermitian and skew-Hermitian splitting) and preconditioned MHSS methods, we will present a generalized preconditioned MHSS method for solving a class of complex symmetric linear systems. The new method (GPMHSS) is essentially a two-parameter iteration method where the iterative sequence is unconditionally convergent to the unique solution of the linear system. A parameter region of the convergence for our method is provided. An efficient preconditioner is presented for the actual implementation of the new method. Some numerical results are given to show its effectiveness.

Keywords:

• complex symmetric matrix
• Hermitian and skew-Hermitian splitting
• preconditioner
• inexact generalized preconditioned modified Hermitian and skew-Hermitian splitting (IGPMHSS) method

AMS Subject Classification:

• 65F10
• 65F50