On multistep Rayleigh quotient iterations for Hermitian eigenvalue problems

doi:10.1016/j.camwa.2018.12.025

	On multistep Rayleigh quotient iterations for Hermitian eigenvalue problems
	Bai, Zhong-Zhi1,2 ; Miao, Cun-Qiang 3; Jian, Shuai 1
	2019-05-01
发表期刊	COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN	0898-1221
卷号	77 期号:9 页码:2396-2406
摘要	We present a multistep Rayleigh quotient iteration, as well as its inexact variant, for computing an eigenpair of a large sparse Hermitian matrix. Theoretical analysis shows that both exact and inexact multistep Rayleigh quotient iterations converge much faster than the exact and inexact Rayleigh quotient iterations, respectively. For the inexact multistep Rayleigh quotient iteration, we use the preconditioned conjugate gradient method to solve the inner linear systems, and find that significant saving in the number of inner iteration steps can be achieved when choosing a proper preconditioner. Numerical examples demonstrate effectiveness and superiority of our methods. (C) 2018 Elsevier Ltd. All rights reserved.
关键词	Hermitian eigenvalue problem Rayleigh quotient iteration Multistep modification Inexact solve Preconditioning
DOI	10.1016/j.camwa.2018.12.025
语种	英语
资助项目	National Natural Science Foundation[11671393]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000465065200008
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/34497
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, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, POB 2719, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266510, Shandong, Peoples R China
推荐引用方式 GB/T 7714	Bai, Zhong-Zhi,Miao, Cun-Qiang,Jian, Shuai. On multistep Rayleigh quotient iterations for Hermitian eigenvalue problems[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2019,77(9):2396-2406.
APA	Bai, Zhong-Zhi,Miao, Cun-Qiang,&Jian, Shuai.(2019).On multistep Rayleigh quotient iterations for Hermitian eigenvalue problems.COMPUTERS & MATHEMATICS WITH APPLICATIONS,77(9),2396-2406.
MLA	Bai, Zhong-Zhi,et al."On multistep Rayleigh quotient iterations for Hermitian eigenvalue problems".COMPUTERS & MATHEMATICS WITH APPLICATIONS 77.9(2019):2396-2406.