Rank structures preserved by the QR-algorithm: The singular case

Authors:
Steven Delvaux;Marc Van Barel
Affiliations:
Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Leuven (Heverlee), Belgium;Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Leuven (Heverlee), Belgium
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

Citing 2
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Unitary rank structured matrices

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Abstract

In an earlier paper we introduced the classes of polynomial and rank structures, both of them preserved by applying a (shifted) QR-step on a matrix A. In the present paper we further investigate the case of rank structures. We show that even if A is a singular matrix, a new QR-iterate can be constructed having the same rank structure as the matrix A itself. To this end we introduce the concepts of effectively eliminating QR-decompositions and sparse Givens patterns, both of them being of independent interest.