Inexact inverse subspace iteration for generalized eigenvalue problems

Qiang Ye; Ping Zhang

doi:10.1016/j.laa.2010.08.001

Inexact inverse subspace iteration for generalized eigenvalue problems

Qiang Ye, Ping Zhang

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

10 Scopus citations

Abstract

n this paper, we present an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax=λBx. We first formulate a version of inexact inverse subspace iteration in which the approximation from one step is used as an initial approximation for the next step. We then analyze the convergence property, which relates the accuracy in the inner iteration to the convergence rate of the outer iteration. In particular, the linear convergence property of the inverse subspace iteration is preserved. Numerical examples are given to demonstrate the theoretical results.

Original language	English
Pages (from-to)	1697-1715
Number of pages	19
Journal	Linear Algebra and Its Applications
Volume	434
Issue number	7
DOIs	https://doi.org/10.1016/j.laa.2010.08.001
State	Published - Apr 1 2011

Bibliographical note

Funding Information:
URL: http://www.math.uky.edu/∼qye (Q. Ye). 1 Supported in part by NSF under Grant DMS-0915062. 2 Current Address: Microscape Technology Co., Ltd., No. 80, The 4th Avenue, TEDA, Tianjin 300457, China.

Keywords

Eigenvalue problem
Inexact inverse iteration
Inner-outer iteration
Subspace iteration

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.2010.08.001

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title = "Inexact inverse subspace iteration for generalized eigenvalue problems",

abstract = "n this paper, we present an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax=λBx. We first formulate a version of inexact inverse subspace iteration in which the approximation from one step is used as an initial approximation for the next step. We then analyze the convergence property, which relates the accuracy in the inner iteration to the convergence rate of the outer iteration. In particular, the linear convergence property of the inverse subspace iteration is preserved. Numerical examples are given to demonstrate the theoretical results.",

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AU - Ye, Qiang

AU - Zhang, Ping

N1 - Funding Information: URL: http://www.math.uky.edu/∼qye (Q. Ye). 1 Supported in part by NSF under Grant DMS-0915062. 2 Current Address: Microscape Technology Co., Ltd., No. 80, The 4th Avenue, TEDA, Tianjin 300457, China.

PY - 2011/4/1

Y1 - 2011/4/1

N2 - n this paper, we present an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax=λBx. We first formulate a version of inexact inverse subspace iteration in which the approximation from one step is used as an initial approximation for the next step. We then analyze the convergence property, which relates the accuracy in the inner iteration to the convergence rate of the outer iteration. In particular, the linear convergence property of the inverse subspace iteration is preserved. Numerical examples are given to demonstrate the theoretical results.

AB - n this paper, we present an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax=λBx. We first formulate a version of inexact inverse subspace iteration in which the approximation from one step is used as an initial approximation for the next step. We then analyze the convergence property, which relates the accuracy in the inner iteration to the convergence rate of the outer iteration. In particular, the linear convergence property of the inverse subspace iteration is preserved. Numerical examples are given to demonstrate the theoretical results.

KW - Eigenvalue problem

KW - Inexact inverse iteration

KW - Inner-outer iteration

KW - Subspace iteration

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EP - 1715

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 7

ER -

Inexact inverse subspace iteration for generalized eigenvalue problems

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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