奇异鞍点问题中广义位移分裂迭代方法的半收敛性分析  

The Semi-Convergence Properties of the Generalized Shift-Splitting Methods for Singular Saddle Point Problems

作　　者：黄卓红 HUANG Zhuo-hong(College of Mathematics and Physics,Center for Applied Mathematics of Guangxi,Guangxi Minzu University,Nanning 530006,China)

机构地区：[1]College of Mathematics and Physics,Center for Applied Mathematics of Guangxi,Guangxi Minzu University,Nanning 530006,China

出　　处：《Chinese Quarterly Journal of Mathematics》2023年第2期145-156,共12页数学季刊（英文版）

基　　金：Supported by Guangxi Science and Technology Department Specific Research Project of Guangxi for Research Bases and Talents(Grant No.GHIKE-AD23023001);Natural Science Foundation of Guangxi Minzu University(Grant No.2021KJQD01);Xiangsi Lake Young Scholars Innovation Team of Guangxi University for Nationalities(Grant No.2021RSCXSHQN05)。

摘　　要：Recently,some authors(Shen and Shi,2016)studied the generalized shiftsplitting(GSS)iteration method for singular saddle point problem with nonsymmetric positive definite(1,1)-block and symmetric positive semidefinite(2,2)-block.In this paper,we further apply the GSS iteration method to solve singular saddle point problem with nonsymmetric positive semidefinite(1,1)-block and symmetric positive semidefinite(2,2)-block,prove the semi-convergence of the GSS iteration method and analyze the spectral properties of the corresponding preconditioned matrix.Numerical experiment is given to indicate that the GSS iteration method with appropriate iteration parameters is effective and competitive for practical use.

关 键 词：Generalized shift-splitting Semi-convergence Positive definite matrix Generalized saddle point problems Krylov subspace methods 

分 类 号：O241.6[理学—计算数学]