Structures preserved by the QR-algorithm

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

Citing 4
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Structures preserved by the QR-algorithm

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A multiple shift QR-step for structured rank matrices

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Abstract

In this paper we investigate some classes of structures that are preserved by applying a (shifted) QR-step on a matrix A. We will handle two classes of such structures: the first we call polynomial structures, for example a matrix being Hermitian or Hermitian up to a rank one correction, and the second we call rank structures, which are encountered for example in all kinds of what we could call Hessenberg-like and lower semiseparable-like matrices. An advantage of our approach is that we define a structure by decomposing it as a collection of 'building stones' which we call structure blocks. This allows us to state the results in their natural, most general context.