Using semiseparable matrices to compute the SVD of a general matrix product/quotient

Authors:
Marc Van Barel;Yvette Vanberghen;Paul Van Dooren
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;Department of Mathematical Engineering, Catholic University of Louvain, Bítiment Euler, Avenue Georges Lemaitre 4, B-1348 Louvain-la-Neuve, Belgium
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 5
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Abstract

In this work we reduce the computation of the singular values of a general product/quotient of matrices to the computation of the singular values of an upper triangular semiseparable matrix. Compared to the reduction into a bidiagonal matrix the reduction into semiseparable form exhibits a nested subspace iteration. Hence, when there are large gaps between the singular values, these gaps manifest themselves already during the reduction algorithm in contrast to the bidiagonal case.