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Great Lakes CS Conference on New Research Results in Computer Science

Great Lakes CS 1989: Computing in the 90's pp 286–292Cite as

The HK singular value decomposition of rank deficient matrix triplets

  • Track 8: Numerical Analysis
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 507))

Abstract

In this paper we consider a simultaneous reduction of three matrices. The described method is extended from the work presented in [3] to include rank deficient data. It is shown how, via an initial reduction, the problem becomes one of diagonalizing a product of three matrices. We compare three different algorithms for its computation and show why one is preferred over the others.

Supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract W-31-109-Eng-38

Supported by Army Research Office Grant DAAL 03-86-K-0109

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6 References

  1. R.P. Brent, F.T. Luk and C. Van Loan, “Computation of the singular value decomposition using mesh-connected processors,” J. VLSI Computer Systems, 1 (1985), pp. 250–260.

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  2. L.M. Ewerbring, “A new generalization of the singular value decomposition: algorithms and applications,” Ph.D. dissertation, School of Elec. Eng., Cornell Univ., 1989.

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  3. L.M. Ewerbring and F.T. Luk, “Canonical correlations and generalized SVD: applications and new algorithms,” J. Comput. Applied Math., 27 (1989), pp. 37–52.

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  4. T.N.E. Greville, “Note on the generalized inverse of a matrix product,” SIAM Review, 8 (1966), pp. 518–521.

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Author information

Authors and Affiliations

  1. Mathematics and Computer Science Division, Argonne National Laboratory, 60439, Argonne, Illinois

    L. Magnus Ewerbring

  2. School of Electrical Engineering, Cornell University, 14853, Ithaca, New York

    Franklin T. Luk

Authors
  1. L. Magnus Ewerbring
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  2. Franklin T. Luk
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Editor information

Naveed A. Sherwani Elise de Doncker John A. Kapenga

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© 1991 Springer-Verlag Berlin Heidelberg

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Ewerbring, L.M., Luk, F.T. (1991). The HK singular value decomposition of rank deficient matrix triplets. In: Sherwani, N.A., de Doncker, E., Kapenga, J.A. (eds) Computing in the 90's. Great Lakes CS 1989. Lecture Notes in Computer Science, vol 507. Springer, New York, NY. https://doi.org/10.1007/BFb0038505

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  • DOI: https://doi.org/10.1007/BFb0038505

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-97628-0

  • Online ISBN: 978-0-387-34815-5

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