Modified accelerated parameterized inexact Uzawa method for singular and nonsingular saddle point problems

被引：22
作者：
Li, Xu [1 ]
Wu, Yu-Jiang [2 ,3 ]
Yang, Ai-Li [2 ,4 ]
Yuan, Jin-Yun [5 ]
机构：
[1] Lanzhou Univ Technol, Dept Appl Math, Lanzhou 730050, Peoples R China
[2] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China
[3] IMPA, Inst Ind Math, BR-81531980 Curitiba, PR, Brazil
[4] Key Lab Appl Math & Complex Syst, Lanzhou 730000, Gansu, Peoples R China
[5] Univ Fed Parana, Ctr Politecn, Dept Math, BR-81531980 Curitiba, PR, Brazil
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 244卷
基金：
中国国家自然科学基金;
关键词：
Saddle point problem; Parameterized inexact Uzawa method; Convergence; Semi-convergence; CONJUGATE-GRADIENT METHODS; HERMITIAN SPLITTING METHODS; SOR-LIKE METHOD; ITERATION METHOD; AOR METHOD; PRECONDITIONERS;
D O I：
10.1016/j.amc.2014.07.031
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Recently, Bai and Wang (2008) [9] presented an efficient accelerated parameterized inexact Uzawa (APIU) method for solving both symmetric and nonsymmetric nonsingular saddle point problems. In this work, we propose a modified APIU (MAPIU) method for solving saddle point problems, which is an extension of the APIU iteration method and covers a series of existing iterative methods. The MAPIU method can be applied not only to the nonsingular case but also to the singular case. The convergence properties for the nonsingular saddle point problems and the semi-convergence properties for the singular one are carefully discussed under suitable restrictions. We prove that the MAPIU method has a wider convergence (or semi-convergence) region than the APIU method. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：552 / 560
页数：9
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