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On local quadratic convergence of inexact simplified Jacobi-Davidson method
Bai, Zhong-Zhi1,2; Miao, Cun-Qiang1,2
2017-05-01
Source PublicationLINEAR ALGEBRA AND ITS APPLICATIONS
ISSN0024-3795
Volume520Pages:215-241
AbstractFor the Hermitian eigenproblems, we prove local quadratic convergence of the inexact simplified Jacobi-Davidson method when the involved relaxed correction equation is solved by a standard Krylov subspace iteration. This method then shows local cubic convergence rate when the relaxed correction equation is solved to a prescribed precision proportional to the norm of the current residual. As a by-product, we obtain local cubic convergence of the simplified Jacobi-Davidson method. These results significantly improve the existing ones that show only local linear convergence for the inexact simplified Jacobi-Davidson method, which lead to local quadratic convergence for the simplified Jacobi-Davidson method when the tolerance of the inexact solve is particularly set to be zero. Numerical experiments confirm these theoretical results. (C) 2017 Elsevier Inc. All rights reserved.
KeywordHermitian eigenproblem Jacobi-Davidson method Inexact iteration Standard Krylov subspace iteration Local convergence
DOI10.1016/j.laa.2017.01.018
Language英语
Funding ProjectNational Natural Science Foundation of China for Creative Research Groups[11321061] ; National Natural Science Foundation of China[11671393] ; National Natural Science Foundation of China[91118001] ; National Basic Research Program, PR China[2011CB309703]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000397073100013
PublisherELSEVIER SCIENCE INC
Citation statistics
Cited Times:6[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/25093
Collection计算数学与科学工程计算研究所
Affiliation1.Chinese Acad Sci, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, POB 2719, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Bai, Zhong-Zhi,Miao, Cun-Qiang. On local quadratic convergence of inexact simplified Jacobi-Davidson method[J]. LINEAR ALGEBRA AND ITS APPLICATIONS,2017,520:215-241.
APA Bai, Zhong-Zhi,&Miao, Cun-Qiang.(2017).On local quadratic convergence of inexact simplified Jacobi-Davidson method.LINEAR ALGEBRA AND ITS APPLICATIONS,520,215-241.
MLA Bai, Zhong-Zhi,et al."On local quadratic convergence of inexact simplified Jacobi-Davidson method".LINEAR ALGEBRA AND ITS APPLICATIONS 520(2017):215-241.
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