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The compass (star) identity for vector-valued rational interpolants

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Abstract

The compass identity (Wynn's five point star identity) for Padé approximants connects neighbouring elements called N, S, E, W and C in the Padé table. Its form has been extended to the cases of rational interpolation of ordinary (scalar) data and interpolation of vector-valued data. In this paper, full specifications of the associated five point identity for the scalar denominator polynomials and the vector numerator polynomials of the vector-valued rational interpolants on real data points are given, as well as the related generalisations of Frobenius' identities. Unique minimal forms of the polynomials constituting the interpolants and results about unattainable points correspond closely to their counterparts in the scalar case.

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Authors and Affiliations

  1. Department of Mathematics, University of Bradford, Bradford, BD7 1DP, England

    P.R. Graves-Morris

  2. Laboratoire d'Analyse Numérique et d'Optimisation Université de Lille 1, F-59655, Villeneuve d'Ascq, France

    B. Beckermann

Authors
  1. P.R. Graves-Morris
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  2. B. Beckermann
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Graves-Morris, P., Beckermann, B. The compass (star) identity for vector-valued rational interpolants. Advances in Computational Mathematics 7, 279–294 (1997). https://doi.org/10.1023/A:1018951020406

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