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

Van Barel, Marc;Vanberghen, Yvette;Van Dooren, Paul
(2010) Journal of Computational and Applied Mathematics — Vol. 234, n° 11, p. 3175-3180 (2010)

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Authors
  • Van Barel, Marc
    Author
  • Vanberghen, Yvette
    Author
  • Van Dooren, PaulUCLouvain
    Author
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. (C) 2010 Elsevier B.V. All rights reserved.
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Van Barel, M., Vanberghen, Y., & Van Dooren, P. (2010). Using semiseparable matrices to compute the SVD of a general matrix product/quotient. Journal of Computational and Applied Mathematics, 234(11), 3175-3180. https://doi.org/10.1016/j.cam.2010.02.007 (Original work published 2010)