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ON GREEDY RANDOMIZED KACZMARZ METHOD FOR SOLVING LARGE SPARSE LINEAR SYSTEMS
Bai, Zhong-Zhi; Wu, Wen-Ting
2018
Source PublicationSIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN1064-8275
Volume40Issue:1Pages:A592-A606
AbstractFor solving large-scale systems of linear equations by iteration methods, we introduce an effective probability criterion for selecting the working rows from the coefficient matrix and construct a greedy randomized Kaczmarz method. It is proved that this method converges to the unique least-norm solution of the linear system when it is consistent. Theoretical analysis demonstrates that the convergence rate of the greedy randomized Kaczmarz method is much faster than the randomized Kaczmarz method, and numerical results also show that the greedy randomized Kaczmarz method is more efficient than the randomized Kaczmarz method.
Keywordsystem of linear equations Kaczmarz method randomized iteration convergence property
DOI10.1137/17M1137747
Language英语
Funding ProjectNational Natural Science Foundation[11671393]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000426743500025
PublisherSIAM PUBLICATIONS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29905
Collection计算数学与科学工程计算研究所
AffiliationChinese Acad Sci, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, POB 2719, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Bai, Zhong-Zhi,Wu, Wen-Ting. ON GREEDY RANDOMIZED KACZMARZ METHOD FOR SOLVING LARGE SPARSE LINEAR SYSTEMS[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2018,40(1):A592-A606.
APA Bai, Zhong-Zhi,&Wu, Wen-Ting.(2018).ON GREEDY RANDOMIZED KACZMARZ METHOD FOR SOLVING LARGE SPARSE LINEAR SYSTEMS.SIAM JOURNAL ON SCIENTIFIC COMPUTING,40(1),A592-A606.
MLA Bai, Zhong-Zhi,et al."ON GREEDY RANDOMIZED KACZMARZ METHOD FOR SOLVING LARGE SPARSE LINEAR SYSTEMS".SIAM JOURNAL ON SCIENTIFIC COMPUTING 40.1(2018):A592-A606.
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