Year: 2004
Journal of Computational Mathematics, Vol. 22 (2004), Iss. 4 : pp. 489–500
Abstract
A derivative-free frame-based conjugate gradients algorithm is presented. Convergence is shown for $C^1$ functions, and this is verified in numerical trials. The algorithm is tested on a variety of low dimensional problems, some of which are ill-conditioned, and is also tested on problems of high dimension. Numerical results show that the algorithm is effective on both classes of problems. The results are compared with those from a discrete quasi-Newton method, showing that the conjugate gradients algorithm is competitive. The algorithm exhibits the conjugate gradients speed-up on problems for which the Hessian at the solution has repeated or clustered eigenvalues. The algorithm is easily parallelizable.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2004-JCM-8858
Journal of Computational Mathematics, Vol. 22 (2004), Iss. 4 : pp. 489–500
Published online: 2004-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Conjugate gradients Derivative-free Frame-based methods Numerical results.