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Polynomial representations from abstract perturbed Krylov methods
Author(s) -
Zemke JensPeter M.
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610343
Subject(s) - krylov subspace , polynomial , sketch , eigenvalues and eigenvectors , computation , mathematics , computer science , algebra over a field , algorithm , iterative method , pure mathematics , mathematical analysis , physics , quantum mechanics
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)