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On parameterized inexact Uzawa methods for generalized saddle point problems

文献类型：期刊论文

作者Bai, Zhong-Zhi; Wang, Zeng-Qi
刊名LINEAR ALGEBRA AND ITS APPLICATIONS
出版日期2008-06-01
卷号428期号:11-12页码:2900-2932
关键词generalized saddle point problem parameterized inexact Uzawa method acceleration technique convergence quasi-optimal relaxation parameter quasi-optimal convergence factor
ISSN号0024-3795
DOI10.1016/j.laa.2008.01.018
英文摘要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.
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000256392900040
出版者ELSEVIER SCIENCE INC
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/5666]  
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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