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On some interval methods for algebraic, exponential and trigonometric polynomials

Über Intervallmethoden für algebraische, exponentielle und trigonometrische Polynome

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Abstract

New inclusion methods for the simultaneous determination of the zeros of algebraic, exponential and trigonometric polynomials are presented. These methods are realized in real interval arithmetic and do not use any derivatives. Using Weierstrass' correction some modified methods with the increased convergence rate are constructed. Convergence analysis and numerical example are included.

Zusammenfassung

Die Arbeit behandelt neue Einschliessungsmethoden zur simultanen Berechnung aller Nullstellen von algebraischen, exponentiellen und trigonometrischen Polynomen. Die Verfahren sind für reelle Intervallarithmetik formuliert und benötigen keine Auswertungen von Ableitungen des gegebenen verallgemeinerten Polynomes. Unter Verwendung der sog. Weierstrass-Korrektoren werden verbesserte modifizierte Verfahren konstruiert. Hierzu enthält die Arbeit Konvergenzuntersuchungen und numerische Beispiele.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Hannover, D-30167, Hannover, Federal Republic of Germany

    M. S. Petković

  2. Faculty of Electronic Engineering, University of Niš, 18000, Niš

    C. Carstensen

Authors
  1. C. Carstensen
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  2. M. S. Petković
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Carstensen, C., Petković, M.S. On some interval methods for algebraic, exponential and trigonometric polynomials. Computing 51, 313–326 (1993). https://doi.org/10.1007/BF02238538

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  • DOI: https://doi.org/10.1007/BF02238538

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