KMS Of Academy of mathematics and systems sciences, CAS
| Computing eigenpairs of Hermitian matrices in perfect Krylov subspaces | |
| Bai, Zhong-Zhi1,2; Miao, Cun-Qiang1,2 | |
| 2019-12-01 | |
| Source Publication | NUMERICAL ALGORITHMS
 |
| ISSN | 1017-1398 |
| Volume | 82Issue:4Pages:1251-1277 |
| Abstract | For computing the smallest eigenvalue and the corresponding eigenvector of a Hermitian matrix, by introducing a concept of perfect Krylov subspace, we propose a class of perfect Krylov subspace methods. For these methods, we prove their local, semilocal, and global convergence properties, and discuss their inexact implementations and preconditioning strategies. In addition, we use numerical experiments to demonstrate the convergence properties and exhibit the competitiveness of these methods with a few state-of-the art iteration methods such as Lanczos, rational Krylov sequence, and Jacobi-Davidson, when they are employed to solve large and sparse Hermitian eigenvalue problems. |
| Keyword | Hermitian eigenproblem Krylov subspace method Inexact iteration Convergence property |
| DOI | 10.1007/s11075-018-00653-y |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | National Natural Science Foundation[11671393] ; National Natural Science Foundation for Creative Research Groups, People's Republic of China[11321061] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000500985600006 |
| Publisher | SPRINGER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/50409 |
| Collection | 中国科学院数学与系统科学研究院 |
| 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 |
| Recommended Citation GB/T 7714 | Bai, Zhong-Zhi,Miao, Cun-Qiang. Computing eigenpairs of Hermitian matrices in perfect Krylov subspaces[J]. NUMERICAL ALGORITHMS,2019,82(4):1251-1277. |
| APA | Bai, Zhong-Zhi,&Miao, Cun-Qiang.(2019).Computing eigenpairs of Hermitian matrices in perfect Krylov subspaces.NUMERICAL ALGORITHMS,82(4),1251-1277. |
| MLA | Bai, Zhong-Zhi,et al."Computing eigenpairs of Hermitian matrices in perfect Krylov subspaces".NUMERICAL ALGORITHMS 82.4(2019):1251-1277. |
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