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On convergence rate of the randomized Kaczmarz method
Bai, Zhong-Zhi1,2; Wu, Wen-Ting1,2
2018-09-15
Source PublicationLINEAR ALGEBRA AND ITS APPLICATIONS
ISSN0024-3795
Volume553Pages:252-269
AbstractFor consistent system of linear equations with the coefficient matrix being flat, we conduct an exact closed-form formula for the mean squared error of the iterate generated by the randomized Kaczmarz method, which completes the existing closed-form formula derived only for the tall coefficient matrix. Based upon these formulas, we further estimate an upper bound for the convergence rate of the randomized Kaczmarz method. Both theoretical analysis and numerical experiments demonstrate that this bound can significantly improve the existing ones. (C) 2018 Elsevier Inc. All rights reserved.
KeywordSystem of linear equations Randomized Kaczmarz method Convergence rate
DOI10.1016/j.laa.2018.05.009
Language英语
Funding ProjectNational Natural Science Foundation, P.R. China[11671393] ; P.R. China
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000436050600014
PublisherELSEVIER SCIENCE INC
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/30600
Collection计算数学与科学工程计算研究所
Corresponding AuthorBai, Zhong-Zhi
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci Engn Comp, Inst Computat Math & 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 convergence rate of the randomized Kaczmarz method[J]. LINEAR ALGEBRA AND ITS APPLICATIONS,2018,553:252-269.
APA Bai, Zhong-Zhi,&Wu, Wen-Ting.(2018).On convergence rate of the randomized Kaczmarz method.LINEAR ALGEBRA AND ITS APPLICATIONS,553,252-269.
MLA Bai, Zhong-Zhi,et al."On convergence rate of the randomized Kaczmarz method".LINEAR ALGEBRA AND ITS APPLICATIONS 553(2018):252-269.
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