KMS Of Academy of mathematics and systems sciences, CAS
| On partially randomized extended Kaczmarz method for solving large sparse overdetermined inconsistent linear systems | |
Bai, Zhong-Zhi1,2 ; Wu, Wen-Ting1,2
| |
| 2019-10-01 | |
| Source Publication | LINEAR ALGEBRA AND ITS APPLICATIONS
 |
| ISSN | 0024-3795 |
| Volume | 578Pages:225-250 |
| Abstract | For solving large sparse, overdetermined, and inconsistent system of linear equations by iteration methods, by further reconstructing the randomized extended Kaczmarz method proposed by Zouzias and Freris in 2013 (SIAM J. Matrix Anal. Appl. 34 (2013), 773-793), we propose a partially randomized extended Kaczmarz method. When the coefficient matrix is assumed to be of full column rank, we prove the convergence and derive an upper bound for the expected convergence rate of the partially randomized extended Kaczmarz method. This bound could be smaller than that of the randomized extended Kaczmarz method under certain conditions. Moreover, with numerical results we show that the partially randomized extended Kaczmarz method can be much more effective than the randomized extended Kaczmarz method. (C) 2019 Elsevier Inc. All rights reserved. |
| Keyword | System of linear equations Inconsistency Kaczmarz method Randomized iteration Convergence property |
| DOI | 10.1016/j.laa.2019.05.005 |
| Language | 英语 |
| Funding Project | National Natural Science Foundation, P.R. China[11671393] ; National Natural Science Foundation, P.R. China[11911530082] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied ; Mathematics |
| WOS ID | WOS:000478705400012 |
| Publisher | ELSEVIER SCIENCE INC |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/35252 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Bai, Zhong-Zhi |
| Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, POB 2719, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
| Recommended Citation GB/T 7714 | Bai, Zhong-Zhi,Wu, Wen-Ting. On partially randomized extended Kaczmarz method for solving large sparse overdetermined inconsistent linear systems[J]. LINEAR ALGEBRA AND ITS APPLICATIONS,2019,578:225-250. |
| APA | Bai, Zhong-Zhi,&Wu, Wen-Ting.(2019).On partially randomized extended Kaczmarz method for solving large sparse overdetermined inconsistent linear systems.LINEAR ALGEBRA AND ITS APPLICATIONS,578,225-250. |
| MLA | Bai, Zhong-Zhi,et al."On partially randomized extended Kaczmarz method for solving large sparse overdetermined inconsistent linear systems".LINEAR ALGEBRA AND ITS APPLICATIONS 578(2019):225-250. |
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