Subspace iterative methods for eigenvalue problems

T. Zhang; G. H. Golub; K. H. Law

doi:10.1016/S0024-3795(99)00074-9

Subspace iterative methods for eigenvalue problems

T. Zhang
, G. H. Golub
, K. H. Law

Research output: Contribution to journal › Article › peer-review

Abstract

This paper presents novel perturbation bounds for generalized symmetric positive definite eigenvalue problems. The bounds provide the insights for an observed computational phenomenon that is not easily explained by the existing bounds developed previously. Using the new bounds, we provide an analysis of a subspace Newton type procedure for computing a few extreme eigenpairs for generalized symmetric positive definite systems. A preconditioned version of this subspace iterative method is also studied.

Original language	English (US)
Pages (from-to)	239-258
Number of pages	20
Journal	Linear Algebra and Its Applications
Volume	294
Issue number	1-3
DOIs	https://doi.org/10.1016/S0024-3795(99)00074-9
State	Published - Jun 15 1999
Externally published	Yes

Keywords

Domain decomposition
Eigenvalue problem
Fictitious domain
Inverse iteration
Precondition
Rayleigh quotient
Schwarz
Subspace approximation
Subspace decomposition

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

Online availability

10.1016/S0024-3795(99)00074-9

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title = "Subspace iterative methods for eigenvalue problems",

abstract = "This paper presents novel perturbation bounds for generalized symmetric positive definite eigenvalue problems. The bounds provide the insights for an observed computational phenomenon that is not easily explained by the existing bounds developed previously. Using the new bounds, we provide an analysis of a subspace Newton type procedure for computing a few extreme eigenpairs for generalized symmetric positive definite systems. A preconditioned version of this subspace iterative method is also studied.",

keywords = "Domain decomposition, Eigenvalue problem, Fictitious domain, Inverse iteration, Precondition, Rayleigh quotient, Schwarz, Subspace approximation, Subspace decomposition",

author = "T. Zhang and Golub, \{G. H.\} and Law, \{K. H.\}",

note = "This research is sponsored by the National Science Foundation, Grant Number DMS-9403899. The authors wish to thank the anonymous referee for many constructive comments.",

year = "1999",

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doi = "10.1016/S0024-3795(99)00074-9",

language = "English (US)",

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pages = "239--258",

journal = "Linear Algebra and Its Applications",

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TY - JOUR

T1 - Subspace iterative methods for eigenvalue problems

AU - Zhang, T.

AU - Golub, G. H.

AU - Law, K. H.

N1 - This research is sponsored by the National Science Foundation, Grant Number DMS-9403899. The authors wish to thank the anonymous referee for many constructive comments.

PY - 1999/6/15

Y1 - 1999/6/15

N2 - This paper presents novel perturbation bounds for generalized symmetric positive definite eigenvalue problems. The bounds provide the insights for an observed computational phenomenon that is not easily explained by the existing bounds developed previously. Using the new bounds, we provide an analysis of a subspace Newton type procedure for computing a few extreme eigenpairs for generalized symmetric positive definite systems. A preconditioned version of this subspace iterative method is also studied.

AB - This paper presents novel perturbation bounds for generalized symmetric positive definite eigenvalue problems. The bounds provide the insights for an observed computational phenomenon that is not easily explained by the existing bounds developed previously. Using the new bounds, we provide an analysis of a subspace Newton type procedure for computing a few extreme eigenpairs for generalized symmetric positive definite systems. A preconditioned version of this subspace iterative method is also studied.

KW - Domain decomposition

KW - Eigenvalue problem

KW - Fictitious domain

KW - Inverse iteration

KW - Precondition

KW - Rayleigh quotient

KW - Schwarz

KW - Subspace approximation

KW - Subspace decomposition

UR - https://www.scopus.com/pages/publications/0033454559

UR - https://www.scopus.com/pages/publications/0033454559#tab=citedBy

U2 - 10.1016/S0024-3795(99)00074-9

DO - 10.1016/S0024-3795(99)00074-9

M3 - Article

AN - SCOPUS:0033454559

SN - 0024-3795

VL - 294

SP - 239

EP - 258

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1-3

ER -

Subspace iterative methods for eigenvalue problems

Abstract

Keywords

ASJC Scopus subject areas

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