Matrix Transformations and Quasi-Newton Methods

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.