Unitary rank structured matrices

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:
2008

Citing 13
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Abstract

In this paper we describe how one can represent a unitary rank structured matrix in an efficient way as a product of elementary unitary or Givens transformations. We also provide some basic operations for manipulating the representation, such as the transition to zero-creating form, the transition to a unitary/Givens-weight representation, as well as an internal pull-through process of the two branches of the representation. Finally, we characterize how to determine the 'shift' correction term to the rank structure, and we provide some applications to this result.