Abstract
If a polynomial is expanded in terms of Bernstein polynomial over an interval then the coefficients of the expansion may be used to provide upper and lower bounds for the value of the polynomial over the interval. When applying this method to interval polynomials straightforwardly, the coefficients of the expansion are computed with an increase in width due to dependency intervals. In this paper we show that if the computations are rearranged suitably then the Bernstein coefficients can be computed with no increase in width due to dependency intervals.
Zusammenfassung
Die Koeffizienten einer Bernstein-Polynomentwicklung geben obere und untere Schranken für den Wertebereich eines Polynoms über einen Intervall. Wenn diese Methode direkt auf Intervall-Polynome angewendet wird, dann sind die Ergebnisse mit einer Aufblähung behaftet. Diese Arbeit zeigt, daß diese Aufblähung der Bernstein-Koeffizienten vermeidbar ist, wenn die Formeln passend verändert werden.
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Rokne, J.: Optimal computation of the Bernstein algorithm for the bound of an interval polynomial. (Freiburger Intervall-Berichte 81/4, University of Freiburg, Federal Republic of Germany.)
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Rokne, J. Optimal computation of the Bernstein algorithm for the bound of an interval polynomial. Computing 28, 239–246 (1982). https://doi.org/10.1007/BF02241751
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DOI: https://doi.org/10.1007/BF02241751