Matrix Transformations and Quasi-Newton Methods

Benahmed, Boubakeur; de Malafosse, Bruno; Yassine, Adnan

doi:https://doi.org/10.1155/2007/25704

International Journal of Mathematics and Mathematical Sciences

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Research Article | Open Access

Volume 2007 | Article ID 025704 | https://doi.org/10.1155/2007/25704

Matrix Transformations and Quasi-Newton Methods

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

Academic Editor: Narendra K. Govil

Received23 Dec 2006

Accepted18 Mar 2007

Published12 Jul 2007

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.

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Copyright

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.

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