Abstract: How to efficiently solve non-Hermitian positive definite linear systems is discussed, and an extrapolated and generalized Hermitian and skew-Hermitian splitting iteration method (EGHSS) is proposed. Firstly, the method constructs a new asymmetric two-step iterative scheme based on the generalized Hermitian and skew-Hermitian splitting iteration. Secondly, the convergence of the new method is theoretically analyzed, and the necessary and sufficient conditions for the convergence are given. Finally, numerical experiments show that the EGHSS iteration method is more effective than the GHSS iteration method and the EHSS iteration method in dealing with some problems.

Key words: non-Hermitian positive definite linear systems；GHSS iteration method；EHSS iteration method；convergence ,