Computing eigenpairs of Hermitian matrices in perfect Krylov subspaces
Bai, Zhong-Zhi1,2; Miao, Cun-Qiang1,2
AbstractFor 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.
KeywordHermitian eigenproblem Krylov subspace method Inexact iteration Convergence property
Indexed BySCI
Funding ProjectNational Natural Science Foundation[11671393] ; National Natural Science Foundation for Creative Research Groups, People's Republic of China[11321061]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000500985600006
Citation statistics
Document Type期刊论文
Corresponding AuthorBai, Zhong-Zhi
Affiliation1.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.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Bai, Zhong-Zhi]'s Articles
[Miao, Cun-Qiang]'s Articles
Baidu academic
Similar articles in Baidu academic
[Bai, Zhong-Zhi]'s Articles
[Miao, Cun-Qiang]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Bai, Zhong-Zhi]'s Articles
[Miao, Cun-Qiang]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.