On local quadratic convergence of inexact simplified Jacobi-Davidson method

doi:10.1016/j.laa.2017.01.018

	On local quadratic convergence of inexact simplified Jacobi-Davidson method
	Bai, Zhong-Zhi1,2 ; Miao, Cun-Qiang 1,2
	2017-05-01
发表期刊	LINEAR ALGEBRA AND ITS APPLICATIONS
ISSN	0024-3795
卷号	520 页码:215-241
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.
关键词	Hermitian eigenproblem Jacobi-Davidson method Inexact iteration Standard Krylov subspace iteration Local convergence
DOI	10.1016/j.laa.2017.01.018
语种	英语
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
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000397073100013
出版者	ELSEVIER SCIENCE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/25093
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.