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A Priori Estimates on the Structured Conditioning of Cauchy and Vandermonde Matrices

  • Enrico Bozzo
  • Dario Fasino
Part of the Operator Theory: Advances and Applications book series (OT, volume 199)

Abstract

We analyze the componentwise and normwise sensitivity of inverses of Cauchy, Vandermonde, and Cauchy-Vandermonde matrices, with respect to relative componentwise perturbations in the nodes defining these matrices. We obtain a priori, easily computable upper bounds for these condition numbers. In particular, we improve known estimates for Vandermonde matrices with generic real nodes; twe consider in detail Vandermonde matrices with nonnegative or symmetric nodes; and we extend the analysis to the class of complex Cauchy-Vandermonde matrices.

Mathematics Subject Classification (2000)

Primary 15A12 Secondary 15A57 65F35 

Keywords

Condition number displacement structure Cauchy matrix Vandermonde matrix 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  • Enrico Bozzo
    • 1
  • Dario Fasino
    • 1
  1. 1.Dipartimento di Matematica e InformaticaUniversità di UdineUdineItaly

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