Adaptive Solution of Infinite Linear Systems by Krylov Subspace Methods

In this paper we consider the problem of approximating the solution of infinite linear systems, finitely expressed by a sparse coefficient matrix. We analyze various algorithms based on Krylov subspace methods embedded in an adaptive enlargement scheme. The management of these algorithms is not trivial due to the irregular convergence behaviour frequently displayed by Krylov subspace methods for nonsymmetric systems. Numerical experiments, carried out on several test problems, indicate that the more robust methods, like GMRES and QMR, together with the adaptive enlargement scheme exhibit good performances.