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The Multipoint Padé Table and General Recurrences for Rational Interpolation

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Nonlinear Numerical Methods and Rational Approximation II

Part of the book series: Mathematics and Its Applications ((MAIA,volume 296))

Abstract

We first review briefly the Newton-Padé approximation problem and the analogous problem with additional interpolation conditions at infinity, which we call multipoint Padé approximation problem. General recurrence formulas for the Newton-Padé table combine either two pairs of Newton-Padé forms or one such pair and a pair of multipoint Padé forms. We show that, likewise, certain general recurrences for the multipoint Padé table compose two pairs of multipoint Padé forms to get a new pair of multipoint Padé forms. We also discuss the possibility of superfast, i.e.,O(n log2 n) algorithms for certain rational interpolation problems.

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Authors and Affiliations

  1. Interdisciplinary Project Center for Supercomputing, ETH Zurich, ETH-Zentrum, CH-8092, Zurich, Switzerland

    Martin H. Gutknecht

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  1. Martin H. Gutknecht
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Editors and Affiliations

  1. Department of Mathematics and Computer Science, University of Antwerp, Antwerp, Belgium

    Annie Cuyt

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© 1994 Springer Science+Business Media Dordrecht

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Gutknecht, M.H. (1994). The Multipoint Padé Table and General Recurrences for Rational Interpolation. In: Cuyt, A. (eds) Nonlinear Numerical Methods and Rational Approximation II. Mathematics and Its Applications, vol 296. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0970-3_10

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  • DOI: https://doi.org/10.1007/978-94-011-0970-3_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4420-2

  • Online ISBN: 978-94-011-0970-3

  • eBook Packages: Springer Book Archive

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