ON GREEDY RANDOMIZED KACZMARZ METHOD FOR SOLVING LARGE SPARSE LINEAR SYSTEMS

doi:10.1137/17M1137747

	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.