  In this thesis, the numerical solution of three different classes of problems
have been studied. Specifically, new techniques have been proposed and their
theoretical analysis has been performed, accompanied by a wide set of numerical
experiments, for investigating further and comparing the effectiveness and
performance of the presented approach. The first two belong to the research
area of numerical linear algebra and concern the spectral analysis and
preconditioning for Krylov subspace methods of the coefficient matrix of large
structured linear systems. The third concerns a problem from the area of
financial computing namely the pricing of an American put option.
