, Volume 27, Issue 4, pp 339–348 | Cite as

The centered form for interval polynomials

  • J. Rokne


Centered forms for computing the range of values of a real interval polynomial over an interval are considered. A number of methods are proposed and tested on randomly generated interval polynomials. Theoretical and numerical results show that none of the suggested methods produce the optimal results in all cases. The methods are also compared to evaluation using the Horner scheme


Computational Mathematic Optimal Result Suggested Method Centered Form Interval Polynomial 
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Die zentrierte Form für Intervallpolynome


Es werden zentrierte Formen entwickelt, die den Wertebereich eines Intervallpolynoms über einen Intervall abschätzen. Mehrere Methoden werden vorgeschlagen und an Intervallpolynomen, deren Koeffizienten mit einem Zufallsgenerator erzeugt worden sind, getestet. Theoretische und numerische Ergebnisse zeigen, daß keine der vorgeschlagenen Methoden optimal ist. Die Methoden werden auch mit dem Hornerschema verglichen.


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  1. [1]
    Alefeld, G., Herzberger, J.: Einführung in die Intervallrechnung. Mannheim: Bibliographisches Institut 1974.Google Scholar
  2. [2]
    Hansen, E.: The centered form, in: Topics in Interval Analysis, pp. 102–106. Oxford: 1969.Google Scholar
  3. [3]
    Miller, W.: More on quadratic convergence in interval arithmetic. BIT13, 76–83 (1973).Google Scholar
  4. [4]
    Moore, R.: Interval analysis. Englewood Cliffs, N.J.: Prentice-Hall 1966.Google Scholar
  5. [5]
    Ratschek, H.: Centered forms. SIAM J. on Numerical Analysis17, 656–662 (1980).Google Scholar
  6. [6]
    Ratschek, H., Rokne, J.: About the centered form. SIAM J. on Numerical Analysis17, 333–337 (1980).Google Scholar
  7. [7]
    Ratschek, H.: Über das Produkt von Intervallpolynomen. Computing15, 315–325 (1974).Google Scholar
  8. [8]
    Ratschek, H., Schröder, S.: Centered forms for functions in several variables. J. of Mathematical Analysis and Applications (to appear).Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • J. Rokne
    • 1
  1. 1.The University of CalgaryCalgaryCanada

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