Title: A unification of unitary similarity transforms to compressed representations
Authors: Vandebril, Raf ×
Del Corso, Gianna M. #
Issue Date: Jul-2011
Publisher: Springer
Series Title: Numerische Mathematik vol:119 issue:4 pages:641-665
Abstract: In this paper a new framework for transforming arbitrary matrices to compressed representations is presented. The framework provides a generic way of transforming a matrix via unitary similarity transformations to, e.g., Hessenberg, Hessenberg-like form and combinations of both. The new algorithms are deduced, based on the QR-factorization of the original matrix. Relying on manipulations with rotations, all the algorithms consist of eliminating the correct set of rotations, resulting in a matrix obeying the desired structural constraints. Based on this new reduction procedure we investigate further correspondences such as irreducibility, uniqueness of the reduction procedure and the link with (rational) Krylov methods. The unitary similarity transform to Hessenberg-like form as presented here, differs significantly from the one presented in earlier work. Not only does it use less rotations to obtain the desired structure, also the convergence to rational Ritz-values is not observed in the conventional approach.
ISSN: 0029-599X
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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