On preconditioned generalized shift-splitting iteration methods for saddle point problems

被引:23
作者
Cao, Yang [1 ]
Miao, Shu-Xin [2 ]
Ren, Zhi-Ru [3 ]
机构
[1] Nantong Univ, Sch Transportat, Nantong 226019, Peoples R China
[2] Northwest Normal Univ, Coll Math & Stat, Lanzhou 730070, Peoples R China
[3] Cent Univ Finance & Econ, Sch Stat & Math, Beijing 100081, Peoples R China
基金
中国博士后科学基金; 中国国家自然科学基金;
关键词
Saddle point problem; Shift-splitting; Iterative method; Convergence; Preconditioning; DEFINITE LINEAR-SYSTEMS; MESHLESS METHODS; MATRICES; INEXACT;
D O I
10.1016/j.camwa.2017.05.031
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We study a preconditioned generalized shift-splitting iteration method for solving saddle point problems. The unconditional convergence theory of the preconditioned generalized shift-splitting iteration method is established. When the splitting matrix is used as a preconditioner, we analyze eigenvalue distribution of the preconditioned saddle point matrix. It is proved that complex eigenvalues having nonzero imaginary parts of the preconditioned matrix are located in an intersection of two circles and the real parts of all eigenvalues of the preconditioned matrix are located in a positive interval. Numerical experiments are used to verify our theoretical results and illustrate effectiveness of the proposed iteration method and the corresponding splitting preconditioner. (C) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码:859 / 872
页数:14
相关论文
共 39 条
[1]  
[Anonymous], 1999, SPRINGER SCI
[2]  
[Anonymous], 2014, FINITE ELEMENTS FAST, DOI DOI 10.1093/ACPROF:OSO/9780199678792.003.0009
[3]  
[Anonymous], 2003, ITERATIVE METHODS SP, DOI DOI 10.1137/1.9780898718003
[4]   Unified analysis of preconditioning methods for saddle point matrices [J].
Axelsson, Owe .
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2015, 22 (02) :233-253
[5]  
Bai ZZ, 2007, IMA J NUMER ANAL, V27, P1, DOI [10.1093/imanum/dr1017, 10.1093/imanum/drl017]
[6]  
Bai ZZ, 2006, MATH COMPUT, V76, P287
[7]  
Bai ZZ, 2006, J COMPUT MATH, V24, P539
[8]   Optimization of extrapolated Cayley transform with non-Hermitian positive definite matrix [J].
Bai, Zhong-Zhi ;
Hadjidimos, Apostolos .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2014, 463 :322-339
[9]   Eigenvalue estimates for saddle point matrices of Hermitian and indefinite leading blocks [J].
Bai, Zhong-Zhi .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2013, 237 (01) :295-306
[10]   On generalized successive overrelaxation methods for augmented linear systems [J].
Bai, ZZ ;
Parlett, BN ;
Wang, ZQ .
NUMERISCHE MATHEMATIK, 2005, 102 (01) :1-38