奇异鞍点问题中广义位移分裂迭代方法的半收敛性分析

黄卓红

doi:10.13371/j.cnki.chin.q.j.m.2023.02.004

数学季刊 >

2023 , Vol. 38 >Issue 2: 145 - 156

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2023.02.004

奇异鞍点问题中广义位移分裂迭代方法的半收敛性分析

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College of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Minzu
University

Huang Zhuo-Hong (1977-), male, native of Shaoyang, Hunan, associate professor of Guangxi Minzu University, master supervisor, Ph.D, engages in numerical algebra.

收稿日期: 2022-04-25

网络出版日期: 2023-06-30

基金资助

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).

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

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College of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Minzu
University

Huang Zhuo-Hong (1977-), male, native of Shaoyang, Hunan, associate professor of Guangxi Minzu University, master supervisor, Ph.D, engages in numerical algebra.

Received date: 2022-04-25

Online published: 2023-06-30

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摘要

Recently, some authors (Shen and Shi, 2016) studied the generalized shift- splitting (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; Gen- eralized saddle point problems; Krylov subspace methods

本文引用格式

黄卓红 . 奇异鞍点问题中广义位移分裂迭代方法的半收敛性分析[J]. 数学季刊, 2023 , 38(2) : 145 -156 . DOI: 10.13371/j.cnki.chin.q.j.m.2023.02.004

Abstract

Key words： Generalized shift-splitting; Semi-convergence; Positive definite matrix; Gen- eralized saddle point problems; Krylov subspace methods

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