International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 25704, 17 pages
doi:10.1155/2007/25704
Matrix transformations and quasi-Newton methods
Boubakeur Benahmed1
, Bruno de Malafosse1
and Adnan Yassine3
1Laboratoire Mathématiques Appliquées du Havre (LMAH) Université du Havre, IUT Le Havre, BP 4006, Le Havre 76610, France
3Institut Supérieur d'Études Logistique (ISEL), Université du Havre, Quai Frissard, BP 1137, Le Havre 76063, France
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.