A SHSS–SS iteration method for non-Hermitian positive definite linear systems

Abstract

In this paper, based on the single-step HSS (SHSS) method and shift-splitting (SS) method, we propose a SHSS–SS iteration method to solve the non-Hermitian positive definite linear systems by coupling the SHSS method with the SS method. Theoretical analysis shows that the SHSS–SS method is convergent under suitable conditions. Numerical experiments are reported to verify the efficiency of the SHSS–SS method; numerical comparisons show that the proposed SHSS–SS method is superior to the SHSS method and the SS method.

Keywords

• Non-Hermitian matrix
• Matrix splitting
• SS method
• SHSS method
• Convergence