On parameterized inexact Uzawa methods for generalized saddle point problems

doi:10.1016/j.laa.2008.01.018

	On parameterized inexact Uzawa methods for generalized saddle point problems
	Bai, Zhong-Zhi; Wang, Zeng-Qi
	2008-06-01
发表期刊	LINEAR ALGEBRA AND ITS APPLICATIONS
ISSN	0024-3795
卷号	428 期号:11-12 页码:2900-2932
摘要	For the large sparse saddle point problems, Bai et al. recently studied a class of parameterized inexact Uzawa (PIU) methods [Z.-Z. Bai, B.N. Parlett, Z.-Q. Wang. On generalized successive overrelaxation methods for augmented linear systems, Numer. Math. 102 (2005) 1-38]. For a special case that the (1, 1)-block is solved exactly, they determined the convergence domain and computed the optimal iteration parameters and the corresponding optimal convergence factor for the induced method. In this paper, we develop these methods to the large sparse generalized saddle point problems. For the obtained parameterized inexact Uzawa method, we prove its convergence under suitable restrictions on the iteration parameters. In particular, we determine its quasi-optimal iteration parameters and the corresponding quasi-optimal convergence factor for the saddle point problems. Furthermore, this PIU method is generalized to obtain a framework of accelerated variants of the parameterized inexact Uzawa methods for solving both symmetric and nonsymmetric generalized saddle point problems by using the techniques of vector extrapolation, matrix relaxation and inexact iteration. (C) 2008 Elsevier Inc. All rights reserved.
关键词	generalized saddle point problem parameterized inexact Uzawa method acceleration technique convergence quasi-optimal relaxation parameter quasi-optimal convergence factor
DOI	10.1016/j.laa.2008.01.018
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000256392900040
出版者	ELSEVIER SCIENCE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/5667
专题	计算数学与科学工程计算研究所
通讯作者	Bai, Zhong-Zhi
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Bai, Zhong-Zhi,Wang, Zeng-Qi. On parameterized inexact Uzawa methods for generalized saddle point problems[J]. LINEAR ALGEBRA AND ITS APPLICATIONS,2008,428(11-12):2900-2932.
APA	Bai, Zhong-Zhi,&Wang, Zeng-Qi.(2008).On parameterized inexact Uzawa methods for generalized saddle point problems.LINEAR ALGEBRA AND ITS APPLICATIONS,428(11-12),2900-2932.
MLA	Bai, Zhong-Zhi,et al."On parameterized inexact Uzawa methods for generalized saddle point problems".LINEAR ALGEBRA AND ITS APPLICATIONS 428.11-12(2008):2900-2932.