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An example for the regula-falsi method with an asymptotic cycle

Ein Beispiel für die Regula falsi mit einem asymptotischen Zyklus

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Abstract

In this paper we study the convergence properties of the Regula-falsi method for a specific equation. The set of the starting values for which the Regula-falsi method is convergent has an interesting structure, and the divergence is characterized by an asymptotic cycle of order four.

Zusammenfassung

In der Arbeit wird das Konvergenzverhalten der Regula falsi für eine konkrete Gleichung untersucht. Die Menge der Startwerte, für welche die Regula falsi konvergiert, hat eine interessante Struktur, und die Divergenz ist durch einen asymptotischen Zyklus der Ordnung Vier charakterisiert.

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References

  1. Dietze, S.: Steuer-Approximationsprobleme und Regularisierungsverfahren. Preprints 07-06-81,..., 07-09-81, Technische Universität Dresden 1981.

  2. Dietze, S.: On control-approximation problems in Hilbert spaces and related dual problems: Subdifferentiability properties and estimates. ZAMM63, 29–36 (1983).

    Google Scholar 

  3. Li, T.-Y., Yorke, J. A.: Period three implies chaos. Amer. Math. Monthly82, 985–992 (1975).

    Google Scholar 

  4. Šarkovskii, A. N.: Coexistence of cycles of a continuous map of a line into itself. Ukr. Mat. Z.16, 61–71 (1964).

    Google Scholar 

  5. Schmidt, J. W.: Eine Übertragung der Regula Falsi auf Gleichungen in Banachräumen II. Nichtlineare Gleichungssysteme. ZAMM43, 97–110 (1963).

    Google Scholar 

  6. Saari, D. G., Urenko, J. B.: Newton's method, circle maps, and chaotic motion. Amer. Math. Monthlky91, 3–17 (1984).

    Google Scholar 

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Authors and Affiliations

  1. Sektion Mathematik, Technische Universität, Mommsenstrasse 13, DDR-8027, Dresden, German Democratic Republic

    S. Dietze

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  1. S. Dietze
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Dietze, S. An example for the regula-falsi method with an asymptotic cycle. Computing 33, 75–81 (1984). https://doi.org/10.1007/BF02243077

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  • DOI: https://doi.org/10.1007/BF02243077

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