On Relaxed Greedy Randomized Augmented Kaczmarz Methods for Solving Large Sparse Inconsistent Linear Systems

doi:10.4208/eajam.100821.251121

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	On Relaxed Greedy Randomized Augmented Kaczmarz Methods for Solving Large Sparse Inconsistent Linear Systems
	Bai, Zhong-Zhi 1,2; Wang, Lu 1,2; Muratova, Galina, V 3
	2021-12-27
发表期刊	EAST ASIAN JOURNAL ON APPLIED MATHEMATICS
ISSN	2079-7362
页码	10
摘要	For solving large-scale sparse inconsistent linear systems by iteration me-thods, we introduce a relaxation parameter in the probability criterion of the greedy randomized augmented Kaczmarz method, obtaining a class of relaxed greedy rando-mized augmented Kaczmarz methods. We prove the convergence of these methods and estimate upper bounds for their convergence rates. Theoretical analysis and numerical experiments show that these methods can perform better than the greedy randomized augmented Kaczmarz method if the relaxation parameter is chosen appropriately.
关键词	System of linear equations relaxation augmented linear system randomized Kaczmarz method convergence property
DOI	10.4208/eajam.100821.251121
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation, China[12071472] ; Grant of the Government of the Russian Federation, Russia[075-15-2019-1928]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000736922900001
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59749
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Lu
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 3.Southern Fed Univ, II Vorovich Inst Math Mech & Comp Sci, Lab Computat Mech, Rostov Na Donu 344090, Russia
推荐引用方式 GB/T 7714	Bai, Zhong-Zhi,Wang, Lu,Muratova, Galina, V. On Relaxed Greedy Randomized Augmented Kaczmarz Methods for Solving Large Sparse Inconsistent Linear Systems[J]. EAST ASIAN JOURNAL ON APPLIED MATHEMATICS,2021:10.
APA	Bai, Zhong-Zhi,Wang, Lu,&Muratova, Galina, V.(2021).On Relaxed Greedy Randomized Augmented Kaczmarz Methods for Solving Large Sparse Inconsistent Linear Systems.EAST ASIAN JOURNAL ON APPLIED MATHEMATICS,10.
MLA	Bai, Zhong-Zhi,et al."On Relaxed Greedy Randomized Augmented Kaczmarz Methods for Solving Large Sparse Inconsistent Linear Systems".EAST ASIAN JOURNAL ON APPLIED MATHEMATICS (2021):10.