On partially randomized extended Kaczmarz method for solving large sparse overdetermined inconsistent linear systems

doi:10.1016/j.laa.2019.05.005

	On partially randomized extended Kaczmarz method for solving large sparse overdetermined inconsistent linear systems
	Bai, Zhong-Zhi1,2 ; Wu, Wen-Ting 1,2
	2019-10-01
发表期刊	LINEAR ALGEBRA AND ITS APPLICATIONS
ISSN	0024-3795
卷号	578 页码:225-250
摘要	For solving large sparse, overdetermined, and inconsistent system of linear equations by iteration methods, by further reconstructing the randomized extended Kaczmarz method proposed by Zouzias and Freris in 2013 (SIAM J. Matrix Anal. Appl. 34 (2013), 773-793), we propose a partially randomized extended Kaczmarz method. When the coefficient matrix is assumed to be of full column rank, we prove the convergence and derive an upper bound for the expected convergence rate of the partially randomized extended Kaczmarz method. This bound could be smaller than that of the randomized extended Kaczmarz method under certain conditions. Moreover, with numerical results we show that the partially randomized extended Kaczmarz method can be much more effective than the randomized extended Kaczmarz method. (C) 2019 Elsevier Inc. All rights reserved.
关键词	System of linear equations Inconsistency Kaczmarz method Randomized iteration Convergence property
DOI	10.1016/j.laa.2019.05.005
语种	英语
资助项目	National Natural Science Foundation, P.R. China[11671393] ; National Natural Science Foundation, P.R. China[11911530082]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000478705400012
出版者	ELSEVIER SCIENCE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/35252
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	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.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Bai, Zhong-Zhi,Wu, Wen-Ting. On partially randomized extended Kaczmarz method for solving large sparse overdetermined inconsistent linear systems[J]. LINEAR ALGEBRA AND ITS APPLICATIONS,2019,578:225-250.
APA	Bai, Zhong-Zhi,&Wu, Wen-Ting.(2019).On partially randomized extended Kaczmarz method for solving large sparse overdetermined inconsistent linear systems.LINEAR ALGEBRA AND ITS APPLICATIONS,578,225-250.
MLA	Bai, Zhong-Zhi,et al."On partially randomized extended Kaczmarz method for solving large sparse overdetermined inconsistent linear systems".LINEAR ALGEBRA AND ITS APPLICATIONS 578(2019):225-250.