On the m-step two-parameter generalized Hermitian and skew-Hermitian splitting preconditioning method

Abstract

In this paper, the non-Hermitian positive definite linear systems are solved via preconditioned Krylov subspace methods such as the generalized minimal residual (GMRES) method. To do so, the two-parameter generalized Hermitian and skew-Hermitian splitting (TGHSS) iteration method is applied to establish an m-step polynomial preconditioner. Some theoretical results are also given to investigate the convergence properties of the preconditioned method. Three numerical examples are presented to demonstrate the performance of the new method and to compare it with a recently proposed method.