ON GREEDY RANDOMIZED AUGMENTED KACZMARZ METHOD FOR SOLVING LARGE SPARSE INCONSISTENT LINEAR SYSTEMS

doi:10.1137/20M1352235

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	ON GREEDY RANDOMIZED AUGMENTED KACZMARZ METHOD FOR SOLVING LARGE SPARSE INCONSISTENT LINEAR SYSTEMS
	Bai, Zhong-Zhi 1; Wu, Wen-Ting 2
	2021
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	43 期号:6 页码:A3892-A3911
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.
关键词	system of linear equations inconsistency augmented linear system Kaczmarz method randomized iteration convergence property
DOI	10.1137/20M1352235
收录类别	SCI
语种	英语
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
WOS类目	Mathematics, Applied
WOS记录号	WOS:000736742800006
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/59755
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.