Matrix Transformations and Quasi-Newton Methods

Abstract

We first recall some properties of infinite tridiagonal matrices considered as matrix transformations in sequence spaces of the formssξ,sξ∘,sξ(c), orlp(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.