Abstract
It is well known that the range of polynomialf over an interval is bounded by the smallest and the largest coefficient off with respect to the Bernstein basis over the interval. This defines an interval extensionF off, which is called Bernstein form. In this paper we show that the bernstein form is inclusion monotone, i.e.X⊇Y impliesF(X)⊇F(Y).
Zusammenfassung
Bekanntlich ist der Wertebereich eines Polynomsf über einem Intervall durch den kleinsten und größten Koeffizienten vonf bezüglich der Bernstein Basis auf dem Intervall eingeschränkt. Dadurch wird eine IntervallerweiterungF vonf definiert, die sogenannte Bernstein Form. In dieser Arbeit zeigen wir, daß die Bernstein Form inklusionsmonoton ist, d. h. wenn.X⊇Y dannF(X)⊇F(Y).
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The research was done within the framework of the ACCLAIM project sponsored by European Community Basic Research Action (ESPRIT 7195) and Austrian Science Foundation (P9374-PHY).
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Hong, H., Stahl, V. Bernstein form is inclusion monotone. Computing 55, 43–53 (1995). https://doi.org/10.1007/BF02238236
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DOI: https://doi.org/10.1007/BF02238236