Abstract
The Taylor expansion proposed by Hansen [3] is generalized to degreem and estimates are given for the number of zero entries in the remainder. The expansion is then used to define a Taylor form for the range of a function over an interval and estimates are given for the number of interval variables replaced by real variables due to the special Taylor expansion. The Taylor form is then implemented for factorable functions. Some numerical results are given.
Zusammenfassung
Die Taylor-Entwicklung, die von Hansen [3] eingeführt wurde, wird für den Gradm verallgemeinert. Ferner geben wir Abschätzungen für die Anzahl der Nullen im Restglied. Dann benützen wir die Entwicklung zur Definition einer Taylor-Form für den Wertebereich einer Funktion in einem Intervall. Wir schätzen die Anzahl der Intervall-Variablen ab, die gegen reelle Variable ausgetauscht werden können. Die Form wird dann für faktorisierbare Formationen implementiert und es werden einige numerische Beispiele angegeben.
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Rokne, J.G., Bao, P. Interval Taylor forms. Computing 39, 247–259 (1987). https://doi.org/10.1007/BF02309558
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DOI: https://doi.org/10.1007/BF02309558