International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 25704, 17 pages
doi:10.1155/2007/25704
Research Article

Matrix Transformations and Quasi-Newton Methods

Boubakeur Benahmed,1,2 Bruno de Malafosse,1 and Adnan Yassine3

1Laboratoire Mathématiques Appliquées du Havre (LMAH) Université du Havre, IUT Le Havre, BP 4006, Le Havre 76610, France
2Département de Mathématiques et d'Informatique, ENSET d'Oran, BP 1523, Oran 31000, Algeria
3Institut Supérieur d'Études Logistique (ISEL), Université du Havre, Quai Frissard, BP 1137, Le Havre 76063, France

Received 23 December 2006; Accepted 18 March 2007

Academic Editor: Narendra K. Govil

Copyright © 2007 Boubakeur Benahmed et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We first recall some properties of infinite tridiagonal matrices considered as matrix transformations in sequence spaces of the forms sξ, sξ∘, sξ(c), or lp(ξ). Then, we give some results on the finite section method for approximating a solution of an infinite linear system. Finally, using a quasi-Newton method, we construct a sequence that converges fast to a solution of an infinite linear system.