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Approximation Theory and its Applications

, Volume 12, Issue 1, pp 31–41 | Cite as

A property of Hermite-Padé interpolation on the roots of unity

  • T. N. T. Goodman
  • A. Sharma
Article
  • 1 Downloads

Abstract

We extend a theorem of Ivanov and Saff to show that for the Hermite-Padé interpolant at the roots of unity to a function meromorphic in the unit disc, its leading coefficients vanish if and only if the corresponding interpolant to a related function vanishes at given points outside the unit disc. The result is then extended to simultaneous Hermite-Padé inter polation to a finite set of functions.

Keywords

Positive Integer Unit Disc Meromorphic Function Distinct Point Approximation Theory 
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References

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    Ivanov, K. G. and Saff, E. B., Behaviour of the Lagrange Interpolants Inthe Roots of Unity, in Computational Methods and Function Theory, Proceedings Valparaiso, 1989, St. Ruscheweyh et al. (eds.), Springer, Berlin (1990), 81–87.CrossRefGoogle Scholar
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Copyright information

© Springer 1996

Authors and Affiliations

  • T. N. T. Goodman
    • 1
  • A. Sharma
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of DundeeDundeeScotland, U. K.
  2. 2.Department of MathematicsUniversity of AlbertaEdmontonCanada

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