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Yang, H (1993). Conjugate gradient methods for the Rayleigh quotient minimization of generalized eigenvalue problems. Computing, 51(1):79-94.
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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > Software
Physical Sciences > Theoretical Computer Science Physical Sciences > Numerical Analysis Physical Sciences > Computer Science Applications Physical Sciences > Computational Theory and Mathematics Physical Sciences > Computational Mathematics |
| Language: | English |
| Date: | 1993 |
| Deposited On: | 29 Nov 2010 16:29 |
| Last Modified: | 07 Jan 2025 04:43 |
| Publisher: | Springer |
| ISSN: | 0010-485X |
| Additional Information: | Conjugate gradient - Rayleigh quotient - eigenvalue - eigenvector |
| OA Status: | Closed |
| 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 |
Yang, H