求解鞍点问题的广义HSS移位分裂方法  

A Generalized HSS Shift-splitting Method for Solving Saddle Point Problem

作　　者：卜凡 马昌凤 BU Fan;MA Chang-feng(College of Mathematics and Informatics,Fujian Normal University,Fuzhou 350117,China)

机构地区：[1]福建师范大学数学与信息学院,福建福州350117

出　　处：《福建师范大学学报（自然科学版）》2019年第3期8-16,共9页Journal of Fujian Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11071041);福建省自然科学基金资助项目(2016J01005)

摘　　要：提出一种新的矩阵分裂方法,即广义HSS移位分裂方法,用于求解大型稀疏线性方程组(即鞍点问题),其中系数矩阵具有非Hermite正定(1,1)块子矩阵.同时,通过理论分析证明了在一定条件下该方法收敛到方程组的唯一解.此外,也讨论了预处理矩阵的谱性质.This paper presents a new matrix splitting method,i.e.a generalized HSS shiftsplitting method.We use it for solving linear system of equations (i.e.saddle point problem) whose coefficient matrix has the non-Hermitian positive definite (1,1)-block submatrix.Meanwhile,it proves this method converges to the unique solution of saddle point problem under certain conditions through theoretical analyses.Moreover,this paper also discusses the spectral properties of preconditioner.

关 键 词：鞍点问题 广义HSS移位分裂方法 收敛性分析 预处理子 特征值 

分 类 号：O241.6[理学—计算数学]