The alternating-direction iterative method for saddle point problems

被引：9
作者：
Peng, Xiao-Fei [2 ,3 ]
Li, Wen [1 ]
机构：
[1] S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China
[2] Cent S Univ, Sch Math, Changsha 410083, Peoples R China
[3] S China Normal Univ, Nanhai Coll, Foshan 528225, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2010年 / 216卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Saddle point problem; Matrix splitting; The alternating-direction iterative method; The optimal parameter; Convergence; HERMITIAN SPLITTING METHODS; DEFINITE LINEAR-SYSTEMS; NUMERICAL-SOLUTION; INEXACT;
D O I：
10.1016/j.amc.2009.12.020
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the paper, a new alternating-direction iterative method is proposed based on matrix splittings for solving saddle point problems. The convergence analysis for the new method is given. When the better values of parameters are employed, the proposed method has faster convergence rate and less time cost than the Uzawa algorithm with the optimal parameter and the Hermitian and skew-Hermitian splitting iterative method. Numerical examples further show the effectiveness of the method. (C) 2009 Elsevier Inc. All rights reserved.
引用
收藏
页码：1845 / 1858
页数：14
相关论文
共 15 条
[1]  
[Anonymous], 1962, Matrix Iterative Analysis
[2]   On inexact Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems [J].
Bai, Zhong-Zhi ;
Golub, Gene H. ;
Ng, Michael K. .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 428 (2-3) :413-440
[3]  
Bai ZZ, 2007, IMA J NUMER ANAL, V27, P1, DOI [10.1093/imanum/dr1017, 10.1093/imanum/drl017]
[4]   Optimal parameters in the HSS-like methods for saddle-point problems [J].
Bai, Zhong-Zhi .
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2009, 16 (06) :447-479
[5]   On generalized successive overrelaxation methods for augmented linear systems [J].
Bai, ZZ ;
Parlett, BN ;
Wang, ZQ .
NUMERISCHE MATHEMATIK, 2005, 102 (01) :1-38
[6]   Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems [J].
Bai, ZZ ;
Golub, GH ;
Pan, JY .
NUMERISCHE MATHEMATIK, 2004, 98 (01) :1-32
[7]   Hermitian and skew-Hermitian splitting methods for non-hermitian positive definite linear systems [J].
Bai, ZZ ;
Golub, GH ;
Ng, MK .
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2003, 24 (03) :603-626
[8]  
Benzi M, 2005, ACTA NUMER, V14, P1, DOI 10.1017/S0962492904000212
[9]   A preconditioner for generalized saddle point problems [J].
Benzi, M ;
Golub, GH .
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2004, 26 (01) :20-41
[10]   Optimization of the hermitian and skew-Hermitian splitting iteration for saddle-point problems [J].
Benzi, M ;
Gander, MJ ;
Golub, GH .
BIT, 2003, 43 (05) :881-900
12