Semi-infinite multi-index perturbed block Toeplitz systems

In this article Banach algebra techniques are employed to study the numerical solution of linear systems with a semi-infinite multi-index suitably perturbed k×k block Toeplitz matrix. Decay properties of their solutions are studied by using suitably weighted Wiener algebras. A projection-type method for their numerical solution is introduced. Numerical results are presented illustrating both the accuracy of the method for certain perturbed Toeplitz systems and the need for generalizing the theoretical framework to other such systems.