Spectral computations: from operators to matrices
Filomena D. d’Almeida, Paulo Beleza Vasconcelos · PAMM · 2007
Abstract In this work we will address the problem of finding spectral values and bases for the corresponding spectral subspaces for a bounded operator on a Banach space. We will make a bridge between the spectral problem for the continuous operator and the computation of the eigenpairs of a matrix. This approximate problem results first from an approximation by a sequence of continuous operators with finite rank, followed by the reduction to a spectral problem for an operator whose domain as well as range are finite dimensional. Some discussion on defect correction procedures will be also presented. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)