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On multistep Rayleigh quotient iterations for Hermitian eigenvalue problems

文献类型：期刊论文

作者Bai, Zhong-Zhi1,2; Miao, Cun-Qiang3; Jian, Shuai1
刊名COMPUTERS & MATHEMATICS WITH APPLICATIONS
出版日期2019-05-01
卷号77期号:9页码:2396-2406
关键词Hermitian eigenvalue problem Rayleigh quotient iteration Multistep modification Inexact solve Preconditioning
ISSN号0898-1221
DOI10.1016/j.camwa.2018.12.025
英文摘要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.
资助项目National Natural Science Foundation[11671393]
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000465065200008
出版者PERGAMON-ELSEVIER SCIENCE LTD
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/34496]  
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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