Methods For Large-scale Linear Systems Based On PS Splitting

Large-scale linear systems often appear in many fields such as engineering practice and scientific calculations.It is a significant task to study efficient and accurate numerical methods.For the solving method of large-scale linear systems,the direct method has low efficiency and large error.The traditional Jacobian iterative method has a simple format,but it requires higher quality of the matrix.In recent years,the HSS iteration method and PSS iteration method have been proposed.These methods have a simple format and good convergence properties,and have become the mainstream method for solving large-scale linear systems.Based on the PS(positive-definite and skew-Hermitian)Splitting,this paper proposes a generalized LHSS iteration method for large-scale positive definite linear systems.This method is simple in form and is superior to the HSS iterative method when dealing with certain large-scale linear systems.At the same time,for the solution of the saddle point problem,an SOR-Like iteration method based on PS Splitting and a GPSS method which is also based on PS Splitting are proposed.The effectiveness of these methods is verified by numerical experiments.At the end of the article,the methods proposed in this paper are summarized,and the directions for improvement in the future are analyzed.