Numerische Mathematik

, Volume 106, Issue 1, pp 41–68 | Cite as

On the numerical condition of a generalized Hankel eigenvalue problem

Article

Abstract

The generalized eigenvalue problem \(\widetilde H y \,{=}\, \lambda H y\) with H a Hankel matrix and \(\widetilde H\) the corresponding shifted Hankel matrix occurs in number of applications such as the reconstruction of the shape of a polygon from its moments, the determination of abscissa of quadrature formulas, of poles of Padé approximants, or of the unknown powers of a sparse black box polynomial in computer algebra. In many of these applications, the entries of the Hankel matrix are only known up to a certain precision. We study the sensitivity of the nonlinear application mapping the vector of Hankel entries to its generalized eigenvalues. A basic tool in this study is a result on the condition number of Vandermonde matrices with not necessarily real abscissas which are possibly row-scaled.

Mathematics Subject Classification (2000)

15A18 65F35 15A12 30E10 

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Laboratoire Painlevé UMR 8524 (ANO-EDP)UFR Mathématiques – M3Villeneuve d’Ascq CedexFrance
  2. 2.Fletcher Jones Professor of Computer ScienceStanford UniversityStanfordUSA
  3. 3.David R. Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada

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