\daggerCorresponding author. (xuxuefeng@lsec.cc.ac.cn). \ddagger, and (zhangcs@lsec.cc.ac.cn). 512
文献类型：期刊论文
| 作者 | Xu, Xuefeng1; Zhang, Chen-Song2,3,4 |
| 刊名 | SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
 |
| 出版日期 | 2022 |
| 卷号 | 43期号:1页码:512-533 |
| 关键词 | multigrid inexact two-grid methods convergence factor two-sided bounds |
| ISSN号 | 0895-4798 |
| DOI | 10.1137/21M140448X |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000880486100011 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/60701]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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