A Variant Modified Skew-Normal Splitting Iterative Method for Non-Hermitian Positive Definite Linear Systems

Abstract

We propose a variant modified skew-normal splitting iterative method to solve a class of large sparse non-Hermitian positive definite linear systems. Applying the preconditioning technique we also construct the preconditioned version of the proposed method. Theoretical analysis shows that the proposed method is unconditionally convergent even when the real part and the imaginary part of the coefficient matrix are non-symmetric. Meanwhile, when the real part and the imaginary part of the coefficient matrix are symmetric positive definite, we prove that the preconditioned variant modified skew-normal splitting iterative method will also unconditionally converge. Numerical experiments are presented to illustrate the efficiency of the proposed method and show better performance of it when compared with some other methods.