Matrix Transformations and Quasi-Newton Methods

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