KMS Of Academy of mathematics and systems sciences, CAS
ON GREEDY RANDOMIZED KACZMARZ METHOD FOR SOLVING LARGE SPARSE LINEAR SYSTEMS | |
Bai, Zhong-Zhi; Wu, Wen-Ting | |
2018 | |
发表期刊 | SIAM JOURNAL ON SCIENTIFIC COMPUTING |
ISSN | 1064-8275 |
卷号 | 40期号:1页码:A592-A606 |
摘要 | For 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. |
关键词 | system of linear equations Kaczmarz method randomized iteration convergence property |
DOI | 10.1137/17M1137747 |
语种 | 英语 |
资助项目 | National Natural Science Foundation[11671393] |
WOS研究方向 | Mathematics |
WOS类目 | Mathematics, Applied |
WOS记录号 | WOS:000426743500025 |
出版者 | SIAM PUBLICATIONS |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/29905 |
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, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, POB 2719, Beijing 100190, Peoples R China |
推荐引用方式 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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