# 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.

## Citations

12 citations in Web of Science®
12 citations in Scopus®

## Altmetrics

Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English 1993 29 Nov 2010 16:29 05 Apr 2016 13:28 Springer 0010-485X Conjugate gradient - Rayleigh quotient - eigenvalue - eigenvector https://doi.org/10.1007/BF02243830 http://www.ams.org/mathscinet-getitem?mr=1242660http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0788.65043