Optimal expansion of subspaces for eigenvector approximations

Qiang Ye

doi:10.1016/j.laa.2007.08.021

Optimal expansion of subspaces for eigenvector approximations

Qiang Ye

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

5 Scopus citations

Abstract

We consider the problem of how to expand a given subspace for approximating an eigenvalue and eigenvector of a matrix A. Specifically, we consider which vector in the subspace, after multiplied by A, provides optimal expansion of the existing subspace for the eigenvalue problem. We determine the optimal vector, when the quality of subspace for approximation is measured by the angle between the subspace and the eigenvector. We have also derived some characterization of the angle that might lead to more practically useful choice of the expansion vector.

Original language	English
Pages (from-to)	911-918
Number of pages	8
Journal	Linear Algebra and Its Applications
Volume	428
Issue number	4
DOIs	https://doi.org/10.1016/j.laa.2007.08.021
State	Published - Feb 1 2008

Bibliographical note

Funding Information:
1 Supported in part by the National Science Foundation under Grant DMS-0411502.

Funding

1 Supported in part by the National Science Foundation under Grant DMS-0411502.

Funders	Funder number
National Science Foundation (NSF)	DMS-0411502
Directorate for Mathematical and Physical Sciences	0411502

Keywords

Eigenvector approximations
Projection methods
Subspace expansion

ASJC Scopus subject areas

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

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10.1016/j.laa.2007.08.021

Cite this

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title = "Optimal expansion of subspaces for eigenvector approximations",

abstract = "We consider the problem of how to expand a given subspace for approximating an eigenvalue and eigenvector of a matrix A. Specifically, we consider which vector in the subspace, after multiplied by A, provides optimal expansion of the existing subspace for the eigenvalue problem. We determine the optimal vector, when the quality of subspace for approximation is measured by the angle between the subspace and the eigenvector. We have also derived some characterization of the angle that might lead to more practically useful choice of the expansion vector.",

keywords = "Eigenvector approximations, Projection methods, Subspace expansion",

author = "Qiang Ye",

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AU - Ye, Qiang

N1 - Funding Information: 1 Supported in part by the National Science Foundation under Grant DMS-0411502.

PY - 2008/2/1

Y1 - 2008/2/1

N2 - We consider the problem of how to expand a given subspace for approximating an eigenvalue and eigenvector of a matrix A. Specifically, we consider which vector in the subspace, after multiplied by A, provides optimal expansion of the existing subspace for the eigenvalue problem. We determine the optimal vector, when the quality of subspace for approximation is measured by the angle between the subspace and the eigenvector. We have also derived some characterization of the angle that might lead to more practically useful choice of the expansion vector.

AB - We consider the problem of how to expand a given subspace for approximating an eigenvalue and eigenvector of a matrix A. Specifically, we consider which vector in the subspace, after multiplied by A, provides optimal expansion of the existing subspace for the eigenvalue problem. We determine the optimal vector, when the quality of subspace for approximation is measured by the angle between the subspace and the eigenvector. We have also derived some characterization of the angle that might lead to more practically useful choice of the expansion vector.

KW - Eigenvector approximations

KW - Projection methods

KW - Subspace expansion

UR - https://www.scopus.com/pages/publications/37249062103

UR - https://www.scopus.com/pages/publications/37249062103#tab=citedBy

U2 - 10.1016/j.laa.2007.08.021

DO - 10.1016/j.laa.2007.08.021

M3 - Article

AN - SCOPUS:37249062103

SN - 0024-3795

VL - 428

SP - 911

EP - 918

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 4

ER -

Optimal expansion of subspaces for eigenvector approximations

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

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