Computing eigenpairs of Hermitian matrices in perfect Krylov subspaces

doi:10.1007/s11075-018-00653-y

CSpace

	Computing eigenpairs of Hermitian matrices in perfect Krylov subspaces
	Bai, Zhong-Zhi 1,2; Miao, Cun-Qiang 1,2
	2019-12-01
发表期刊	NUMERICAL ALGORITHMS
ISSN	1017-1398
卷号	82 期号:4 页码:1251-1277
摘要	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.
关键词	Hermitian eigenproblem Krylov subspace method Inexact iteration Convergence property
DOI	10.1007/s11075-018-00653-y
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation[11671393] ; National Natural Science Foundation for Creative Research Groups, People's Republic of China[11321061]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000500985600006
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50409
专题	中国科学院数学与系统科学研究院
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
推荐引用方式 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.