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On convergence rate of the randomized Gauss-Seidel method

文献类型：期刊论文

作者Bai, Zhong-Zhi1,2; Wang, Lu1,2; Wu, Wen-Ting3
刊名LINEAR ALGEBRA AND ITS APPLICATIONS
出版日期2021-02-15
卷号611页码:237-252
关键词System of linear equations Randomized Gauss-Seidel method Randomized Kaczmarz method Convergence rate
ISSN号0024-3795
DOI10.1016/j.laa.2020.10.028
英文摘要The Gauss-Seidel and Kaczmarz methods are two classic iteration methods for solving systems of linear equations, which operate in column and row spaces, respectively. Utilizing the connections between these two methods and imitating the exact analysis of the mean-squared error for the randomized Kaczmarz method, we conduct an exact closed-form formula for the mean-squared residual of the iterate generated by the randomized Gauss-Seidel method. Based on this new formula, we further estimate an upper bound for the convergence rate of the randomized Gauss-Seidel method. Theoretical analysis and numerical experiments show that this bound measurably improves the existing ones. Moreover, these theoretical results are also extended to the more general extrapolated randomized Gauss-Seidel method. (C) 2020 Elsevier Inc. All rights reserved.
资助项目National Natural Science Foundation, P.R. China[12071472] ; National Natural Science Foundation, P.R. China[11671393] ; National Natural Science Foundation, P.R. China[12001043] ; Grant of the Government of the Russian Federation, Russia[075-15-2019-1928] ; China-Russia (NSFC-RFBR) International Cooperative Research Project[11911530082] ; China-Russia (NSFC-RFBR) International Cooperative Research Project[19-51-53013] ; Beijing Institute of Technology Research Fund Program for Young Scholars ; Science and Technology Commission of Shanghai Municipality, P.R. China[18dz2271000]
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000600065400013
出版者ELSEVIER SCIENCE INC
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/57846]  
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.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
3.Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China
推荐引用方式
GB/T 7714		 Bai, Zhong-Zhi,Wang, Lu,Wu, Wen-Ting. On convergence rate of the randomized Gauss-Seidel method[J]. LINEAR ALGEBRA AND ITS APPLICATIONS,2021,611:237-252.
APA Bai, Zhong-Zhi,Wang, Lu,&Wu, Wen-Ting.(2021).On convergence rate of the randomized Gauss-Seidel method.LINEAR ALGEBRA AND ITS APPLICATIONS,611,237-252.
MLA Bai, Zhong-Zhi,et al."On convergence rate of the randomized Gauss-Seidel method".LINEAR ALGEBRA AND ITS APPLICATIONS 611(2021):237-252.

入库方式： OAI收割

来源：数学与系统科学研究院

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