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Low complexity k-dimensional centered forms

K-dimensionale zentrische Formen niedriger Komplexität

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Abstract

A new method for computing the centered from ink dimensions for polynomials and rational functions is presented. The method is not nearly as computationally intensive as the method proposed in Ratschek-Schroder [7] in that it avoids the calculation of the partial derivatives of the functions. The method is also easier to implement than the slope method proposed by Krawczyk-Neumaier [5]. Some numerical results are given.

Zusammenfassung

Ein neues Verfahren für die zentrische Form für Polynome und rationale Funktionen ist beschrieben. Was die Rechenkosten angeht, ist dieses Verfahren ökonomischer als das Verfahren von Ratschek-Schröder [7], da die partiellen Ableitungen nicht benötigt werden. Das Verfahren ist auch in praktischer Hinsicht einfacher als das Verfahren von Krawczyk-Neumaier [5]. Einige numerische Ergebnisse sind angegeben.

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References

  1. Alefeld, G., Herzberger, J.: Introductions to Interval Computations. New York: Academic Press 1984.

    Google Scholar 

  2. Hansen, E.: The Centered Form. In: Topics in Interval Analysis (Hansen, E., ed.), 102–105. Oxford 1969.

  3. Knuth, D.: The Art of Computer Programming, Vol. 1, Fundamental Algorithms. Second Edition. Addison Wesley 1973.

  4. Krawczyk, R., Nickel, K.: Die zentrische Form in der Intervallarithmetik, ihre quadratische Konvergenz und ihre Inklusionisotonie. Computing28, 117–132 (1982).

    Article  Google Scholar 

  5. Krawczyk, R., Neumaier, A.: Interval slopes for rational functions and associated centered forms. SIAM Journal on Numerical Analysis22, 604–616 (1985).

    Article  Google Scholar 

  6. Moore, R.: Interval Arithmetic. Englewood Cliffs, N. J.: Prentice Hall 1966.

    Google Scholar 

  7. Ratschek, H.,fSchröder, G.: Centered forms for functions in several variables. Journal of Math. Anal. and Applications82, 543–552 (1981).

    Article  Google Scholar 

  8. Ratschek, H.: Centered forms. SIAM Journal on Numerical Analysis17, 656–662 (1980).

    Article  Google Scholar 

  9. Ratschek, H., Rokne, J.: Computer Methods for the Range of Functions. Chichester: Ellis Horwood 1984.

    Google Scholar 

  10. Rokne, J.: A low complexity explicit rational centered form. Computing34, 261–263 (1985).

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, The University of Calgary, 2500 University Drive NW, T2N 1N4, Calgary, Canada

    J. G. Rokne

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  1. J. G. Rokne
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Rokne, J.G. Low complexity k-dimensional centered forms. Computing 37, 247–253 (1986). https://doi.org/10.1007/BF02252515

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  • DOI: https://doi.org/10.1007/BF02252515

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