Abstract
In this paper an algorithm for the rational interpolation is proposed that avoids the pitfalls of having to divide by zero in calculating the inverse difference quotients. It also helps to detect unattainable points. The resulting function is a general continued fraction and it is evaluated by a Homer-scheme just as a polynomial or an (ordinary) continued fraction.
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Literatur
Claessens, G.: The rational Hermite interpolation problem and some related recurrence formulas. Comp. and Maths. with Appls. 2(1976), 117–123
Haverkamp, R.: Beiträge zur Stetigkeit rationaler Interpolierender. Habilitationsschrift Münster 1977
Meinguet, J.: On the solubility of the Cauchy interpolation problem. In Approximation theory, ed. by A. Talbot, London and New York, Academic Press 1970, p. 137–163
Perron, O.: Die Lehre von den Kettenbrüchen. Band 1, Stuttgart, B.G. Teubner 1954
Thacher, H.C.: Private mündliche Mitteilung im Aug. 1973
Werner, H.: Eine Faktorisierung der bei der rationalen Interpolation auftretenden Matrizen. Numer. Mathem. 18 (1972), 423–431
Werner, H., Schaback, R.: Praktische Mathematik II, 2. Auflage. Berlin-Heidelberg-New York, Springer Verlag 1979
Wetterling, W.: Ein Interpolationsverfahren zur Lösung der linearen Gleichungssysteme, die bei der rationalen Tschebyscheff-Approximation auftreten. Arch. Rat. Mech. Anal. 12(1963), 403–408
Wuytack, L.: On the osculatory rational interpolation problem. Maths. Comp. 29(1975), 837–843
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Werner, H. (1980). Ein Algorithmus zur Rationalen Interpolation. In: Collatz, L., Meinardus, G., Werner, H. (eds) Numerische Methoden der Approximationstheorie / Numerical Methods of Approximation Theory. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série International d’Analyse Numérique, vol 52. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6721-4_22
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DOI: https://doi.org/10.1007/978-3-0348-6721-4_22
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-1103-2
Online ISBN: 978-3-0348-6721-4
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