ON GREEDY RANDOMIZED AUGMENTED KACZMARZ METHOD FOR SOLVING LARGE SPARSE INCONSISTENT LINEAR SYSTEMS
文献类型：期刊论文
| 作者 | Bai, Zhong-Zhi1; Wu, Wen-Ting2 |
| 刊名 | SIAM JOURNAL ON SCIENTIFIC COMPUTING
 |
| 出版日期 | 2021 |
| 卷号 | 43期号:6页码:A3892-A3911 |
| 关键词 | system of linear equations inconsistency augmented linear system Kaczmarz method randomized iteration convergence property |
| ISSN号 | 1064-8275 |
| DOI | 10.1137/20M1352235 |
| 英文摘要 | For solving large-scale inconsistent systems of linear equations by iteration methods, with the application of the greedy randomized Kaczmarz method to a consistent augmented linear system, we find an appropriate balance between the updates of the two iteration vectors in the randomized extended Kaczmarz method, and, based on this balance, we propose a greedy randomized augmented Kaczmarz method. We prove the convergence of the greedy randomized augmented Kaczmarz method and derive an upper bound for its expected convergence rate. Numerical results show that the greedy randomized augmented Kaczmarz method can be much more effective than the randomized extended Kaczmarz method as well as the partially randomized extended Kaczmarz method. |
| 资助项目 | National Natural Science Foundation, People's Republic of China[12071472] ; National Natural Science Foundation, People's Republic of China[12001043] ; Beijing Institute of Technology Research Fund Program for Young Scholars, People's Republic of China |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000736742800006 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/59754]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Bai, Zhong-Zhi |
| 作者单位 | 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.Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China |
| 推荐引用方式 GB/T 7714 | Bai, Zhong-Zhi,Wu, Wen-Ting. ON GREEDY RANDOMIZED AUGMENTED KACZMARZ METHOD FOR SOLVING LARGE SPARSE INCONSISTENT LINEAR SYSTEMS[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2021,43(6):A3892-A3911. |
| APA | Bai, Zhong-Zhi,&Wu, Wen-Ting.(2021).ON GREEDY RANDOMIZED AUGMENTED KACZMARZ METHOD FOR SOLVING LARGE SPARSE INCONSISTENT LINEAR SYSTEMS.SIAM JOURNAL ON SCIENTIFIC COMPUTING,43(6),A3892-A3911. |
| MLA | Bai, Zhong-Zhi,et al."ON GREEDY RANDOMIZED AUGMENTED KACZMARZ METHOD FOR SOLVING LARGE SPARSE INCONSISTENT LINEAR SYSTEMS".SIAM JOURNAL ON SCIENTIFIC COMPUTING 43.6(2021):A3892-A3911. |
入库方式： OAI收割
来源：数学与系统科学研究院
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