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

Recommended by Narendra K. Govil

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.