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A new technique for rational extrapolation to the limit

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Summary

Two new algorithms are proposed for extrapolation to the limit. Both algorithms are based on the use of continued fractions as interpolating functions and infinity as extrapolation point. Some relationships with the algorithm, of Bulirsch and Stoer (for rational extrapolation) and the ε-algorithm (for defining the limit of a sequence) are given. Some examples illustrate the usefulness of the given algorithms and their convergence.

Zusammenfassung

Es werden zwei neue Extrapolationsverfahren angegeben. Die beiden Verfahren sind entwickelt aus dem Gebrauch von Kettenbrüchen als interpolierende Funktionen und unendlich als Extrapolationspunkt. Einige Beziehungen mit dem Algorithmus von Bulirsch und Stoer (zur rationalen Extrapolation) und dem ε-Algorithmus (zur Bestimmung des Limes einer Folge) werden gezeigt. Einige Beispiele illustrieren den Gebrauch dieser Verfahren und ihre Konvergenz.

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Authors and Affiliations

  1. Faculty of Applied Sciences Applied Mathematics Division, University of Leuven, Celestijnenlaan 200 B, B-3030, Heverlee, Belgium

    L. Wuytack

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  1. L. Wuytack
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Parts of this paper have been presented, as second theme, for obtaining a doctoral degree in mathematics, at the University of Leuven (Belgium). The work was done while the author was an Aspirant of the N.F.W.O. (Nationaal Fonds voor Wetenschappelijk Onderzoek, Belgium).

Now at the University of Göttingen (Germany) as an Alexander von Humboldt-Stipendiat.

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Wuytack, L. A new technique for rational extrapolation to the limit. Numer. Math. 17, 215–221 (1971). https://doi.org/10.1007/BF01436377

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  • DOI: https://doi.org/10.1007/BF01436377

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