Computing smallest singular triplets with implicitly restarted Lanczos bidiagonalization

  • Authors:

  • E. Kokiopoulou;C. Bekas;E. Gallopoulos

  • Affiliations:

  • Computer Science and Engineering Department, University of Minnesota, 200 Union Street SE, Minneapolis, MN;Computer Science and Engineering Department, University of Minnesota, 200 Union Street SE, Minneapolis, MN;Computer Engineering and Informatics Department, University of Patras, 26500 Patras, Greece

  • Venue:
  • Applied Numerical Mathematics - Numerical algorithms, parallelism and applications
  • Year:
  • 2004

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Abstract

A matrix-free algorithm, IRLANB, for the efficient computation of the smallest singular triplets of large and possibly sparse matrices is described. Key characteristics of the approach are its use of Lanczos bidiagonalization, implicit restarting, and harmonic Ritz values. The algorithm also uses a deflation strategy that can be applied directly on Lanczos bidiagonalization. A refinement postprocessing phase is applied to the converged singular vectors. The computational costs of the above techniques are kept small as they make direct use of the bidiagonal form obtained in the course of the Lanczos factorization. Several numerical experiments with the method are presented that illustrate its effectiveness and indicate that it performs well compared to existing codes.