On parameterized inexact Uzawa methods for generalized saddle point problems | |
Bai, Zhong-Zhi; Wang, Zeng-Qi | |
刊名 | LINEAR ALGEBRA AND ITS APPLICATIONS |
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 |
DOI | 10.1016/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 |
出版者 | ELSEVIER SCIENCE INC |
WOS记录号 | WOS:000256392900040 |
内容类型 | 期刊论文 |
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. |
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