KMS Of Academy of mathematics and systems sciences, CAS
| On multistep Rayleigh quotient iterations for Hermitian eigenvalue problems | |
Bai, Zhong-Zhi1,2 ; Miao, Cun-Qiang3; Jian, Shuai1
| |
| 2019-05-01 | |
| Source Publication | COMPUTERS & MATHEMATICS WITH APPLICATIONS
 |
| ISSN | 0898-1221 |
| Volume | 77Issue:9Pages:2396-2406 |
| Abstract | 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. |
| Keyword | Hermitian eigenvalue problem Rayleigh quotient iteration Multistep modification Inexact solve Preconditioning |
| DOI | 10.1016/j.camwa.2018.12.025 |
| Language | 英语 |
| Funding Project | National Natural Science Foundation[11671393] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000465065200008 |
| Publisher | PERGAMON-ELSEVIER SCIENCE LTD |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/34497 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Bai, Zhong-Zhi |
| Affiliation | 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 |
| Recommended Citation 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. |
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