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On the R-order of some recurrences with applications to inclusion-methods

Über die R-Ordnung einiger Rekursionsfolgen bei Einschließungsverfahren

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Abstract

In this paper we are considering some classes of recurrences. Estimates for theirR-order are derived. For this purpose we bound the real roots of certain sequences of polynomials. The results are then applied to the determination of efficient inclusion-methods by means of interval analysis.

Zusammenfassung

Wir leiten hier Abschätzungen für dieR-Ordnung von gewissen Klassen von Rekrusionsfolgen her. Dazu werden Abschätzungen für die positiven Wurzeln bestimmter Polynomfolgen benötigt. Damit lassen sich dann effiziente Iterationsverfahren der Intervallrechnung bestimmen.

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References

  1. Alefeld, G., Herzberger, J.: Introduction to Interval Computations. New York: Academic Press 1983.

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  2. Herzberger, J.: Über ein Iterationsverfahren zur Einschließung der inversen Matrix. Computing35, 185–188 (1985).

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  3. Herzberger, J.: Über ein intervallmäßiges Newton-Verfahren. Z. Angew. Math. Mech.66 (to appear).

  4. Scharlach, R.: Private communication 1985.

  5. Schmidt, J. W.: On theR-order of coupled sequences. Computing26, 333–342 (1981).

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  6. Traub, J. F.: Iterative Methods for the Solution of Equations. Englewood Cliffs: Prentice-Hall Inc. 1964.

    Google Scholar 

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Authors and Affiliations

  1. Fachbereich Mathematik, Universität Oldenburg, D-2900, Oldenburg, Federal Republic of Germany

    Jürgen Herzberger

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  1. Jürgen Herzberger
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Herzberger, J. On the R-order of some recurrences with applications to inclusion-methods. Computing 36, 175–180 (1986). https://doi.org/10.1007/BF02238199

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  • DOI: https://doi.org/10.1007/BF02238199

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