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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.

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®
12 citations in Scopus®
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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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