\daggerCorresponding author. (xuxuefeng@lsec.cc.ac.cn). \ddagger, and (zhangcs@lsec.cc.ac.cn). 512

doi:10.1137/21M140448X

CSpace

	\daggerCorresponding author. (xuxuefeng@lsec.cc.ac.cn). \ddagger, and (zhangcs@lsec.cc.ac.cn). 512
	Xu, Xuefeng 1; Zhang, Chen-Song 2,3,4
	2022
发表期刊	SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
ISSN	0895-4798
卷号	43 期号:1 页码:512-533
摘要	Two-grid methods with exact solution of the Galerkin coarse-grid system have been well studied by the multigrid community: an elegant identity has been established to characterize the convergence factor of exact two-grid methods. In practice, however, it is often too costly to solve the Galerkin coarse-grid system exactly, especially when its size is large. Instead, without essential loss of convergence speed, one may solve the coarse-grid system approximately. In this paper, we develop a new framework for analyzing the convergence of inexact two-grid methods: two-sided bounds for the energy norm of the error propagation matrix of inexact two-grid methods are presented. In the framework, a restricted smoother involved in the identity for exact two-grid convergence is used to measure how far the actual coarse-grid matrix deviates from the Galerkin one. As an application, we establish a new and unified convergence theory for multigrid methods.
关键词	multigrid inexact two-grid methods convergence factor two-sided bounds
DOI	10.1137/21M140448X
收录类别	SCI
语种	英语
资助项目	National Key R\&D Program of China ; National Science Foundation of China ; Key Research Program of Frontier Sciences of CAS ; [2020YFA0711900] ; [2020YFA0711904] ; [11971472]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000880486100011
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/60702
专题	中国科学院数学与系统科学研究院
通讯作者	Xu, Xuefeng
作者单位	1.Purdue Univ, Dept Math, W Lafayette, IN 47907 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Xu, Xuefeng,Zhang, Chen-Song. \daggerCorresponding author. (xuxuefeng@lsec.cc.ac.cn). \ddagger, and (zhangcs@lsec.cc.ac.cn). 512[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,2022,43(1):512-533.
APA	Xu, Xuefeng,&Zhang, Chen-Song.(2022).\daggerCorresponding author. (xuxuefeng@lsec.cc.ac.cn). \ddagger, and (zhangcs@lsec.cc.ac.cn). 512.SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,43(1),512-533.
MLA	Xu, Xuefeng,et al."\daggerCorresponding author. (xuxuefeng@lsec.cc.ac.cn). \ddagger, and (zhangcs@lsec.cc.ac.cn). 512".SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 43.1(2022):512-533.