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Conjugate gradient methods for the Rayleigh quotient minimization of generalized eigenvalue problems


Yang, H (1993). Conjugate gradient methods for the Rayleigh quotient minimization of generalized eigenvalue problems. Computing, 51(1):79-94.

Abstract

Here we consider a modified version of the Rayleigh quotient conjugate gradient method of Bradbury and Fletcher for the computation of the smallest eigenvalue and a corresponding eigenvector ofAx=Bx, whereA andB are real symmetric andB is positive definite. Global convergence to an eigenpair is proved and, under certain conditions, convergence to the lowest eigenpair is obtained.

Abstract

Here we consider a modified version of the Rayleigh quotient conjugate gradient method of Bradbury and Fletcher for the computation of the smallest eigenvalue and a corresponding eigenvector ofAx=Bx, whereA andB are real symmetric andB is positive definite. Global convergence to an eigenpair is proved and, under certain conditions, convergence to the lowest eigenpair is obtained.

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12 citations in Web of Science®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1993
Deposited On:29 Nov 2010 16:29
Last Modified:05 Apr 2016 13:28
Publisher:Springer
ISSN:0010-485X
Additional Information:Conjugate gradient - Rayleigh quotient - eigenvalue - eigenvector
Publisher DOI:https://doi.org/10.1007/BF02243830
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1242660
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0788.65043

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