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

Producción científica: Article › revisión exhaustiva

10 Citas (Scopus)

Resumen

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.

Idioma original	English
Páginas (desde-hasta)	1697-1715
Número de páginas	19
Publicación	Linear Algebra and Its Applications
Volumen	434
N.º	7
DOI	https://doi.org/10.1016/j.laa.2010.08.001
Estado	Published - abr 1 2011

Nota bibliográfica

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.

Financiación

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.

Financiadores	Número del financiador
National Science Foundation (NSF)	DMS-0915062
Directorate for Mathematical and Physical Sciences	0915062

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.",

keywords = "Eigenvalue problem, Inexact inverse iteration, Inner-outer iteration, Subspace iteration",

author = "Qiang Ye and Ping Zhang",

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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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DO - 10.1016/j.laa.2010.08.001

M3 - Article

AN - SCOPUS:79951680469

SN - 0024-3795

VL - 434

SP - 1697

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

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Nota bibliográfica

Financiación

ASJC Scopus subject areas

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