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The multipoint Padé table and general recurrences for rational interpolation

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

    Martin H. Gutknecht

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Gutknecht, M.H. The multipoint Padé table and general recurrences for rational interpolation. Acta Appl Math 33, 165–194 (1993). https://doi.org/10.1007/BF00995487

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