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Ein verallgemeinerter Kettenbruch-Algorithmus zur rationalen Hermite-Interpolation

A generalized continued fraction algorithm for rational Hermite interpolation

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Summary

In this paper we consider rational interpolation for an Hermite Problem, i.e. prescribed values of functionf and its derivatives. The algorithm presented here computes a solutionp/q of the linearized equationsp−fq=0 in form of a generalized continued fraction. Numeratorp and denominatorq of the solution attain minimal degree compatible with the linearized problem. The main advantage of this algorithm lies in the fact that accidental zeros of denominator calculated during the algorithm cannot lead to an unexpected stop of the algorithm. Unattainable points are characterized.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Rheinische Friedrich-Wilhelms-Universität, Wegeler Str. 6, D-5300, Bonn, Germany (Fed. Rep.)

    Herbert Arndt

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  1. Herbert Arndt
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Herrn Prof. Dr. Dr. h.c.mult. L. Collatz zum 70. Geburtstag gewidmet

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Arndt, H. Ein verallgemeinerter Kettenbruch-Algorithmus zur rationalen Hermite-Interpolation. Numer. Math. 36, 99–107 (1980). https://doi.org/10.1007/BF01395991

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  • DOI: https://doi.org/10.1007/BF01395991

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