Abstract
If the real-valued mappingf has a representation of the formf(x)=f(c)+(x-c) n h(x), xεX, then we introduce an interval expression which approximates the range of values off over the compact intervalX with ordern+1. The well known centered form is the special casen=1 of this result.
Zusammenfassung
Für den Fall, daßf eine Darstellung der Formf(x)=f(c)+(x-c) n h(x), xεX, besitzt, geben wir eine intervallmäßige Auswertung an, die den Wertebereich über dem kompakten IntervalX mit der Ordnungn+1 approximiert. Fürn=1 erhält man die bekannten Aussagen über die zentrierte Form.
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References
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Dedicated to Professor R. Albrecht on the occasion of his 60th birthday
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Alefeld, G., Lohner, R. On higher order centered forms. Computing 35, 177–184 (1985). https://doi.org/10.1007/BF02260503
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DOI: https://doi.org/10.1007/BF02260503