Polynomial representations from abstract perturbed Krylov methods

We present the framework of “abstract perturbed Krylov methods”, a new, unified point of view on different types of Krylov subspace methods. We give a brief informal sketch of polynomial representations of QOR approximations to solutions of linear systems and eigenvectors. The results are applicable to exact arithmetic, finite precision computations including semiduality approaches, and inexact methods. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)