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On local quadratic convergence of inexact simplified Jacobi-Davidson method

文献类型：期刊论文

作者Bai, Zhong-Zhi1,2; Miao, Cun-Qiang1,2
刊名LINEAR ALGEBRA AND ITS APPLICATIONS
出版日期2017-05-01
卷号520页码:215-241
关键词Hermitian eigenproblem Jacobi-Davidson method Inexact iteration Standard Krylov subspace iteration Local convergence
ISSN号0024-3795
DOI10.1016/j.laa.2017.01.018
英文摘要For 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.
资助项目National 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研究方向Mathematics
语种英语
WOS记录号WOS:000397073100013
出版者ELSEVIER SCIENCE INC
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/25092]  
专题计算数学与科学工程计算研究所
通讯作者Bai, Zhong-Zhi
作者单位1.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
推荐引用方式
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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