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Computing 44, 273-278 (1990) J by Springer-Verlag 1990
 

Summary: Computing 44, 273-278 (1990)
Computing
«J by Springer-Verlag 1990
On the Approximation of the Range of Values
by Interval Expressions
G. Alefeld, Karlsruhe
Received October 25, 1989
Dedicated to Professor Hans J. SteUer on the occasion ofbis 60th birthday
Abstract - Zusammenfassung
00 tbe Approximation of tbe Range of Values by Interval Aritbmetic Expressioos. Ir the real-valued
mappingfhas a representation oftheformf(x} = qJo+ t(x}'h(x},x E X, wherefor the diameter of h(X}
the inequality d(h(X)} ::::;;ad(X) holds and for the absolute value of t(X) we have 1t(x)1::::;;-rd(Xf, then
we introduce an interval expression for f which approximates the range ofvalues off over the compact
interval X with order n + 1. O!lr result contains as a special case the theorem on higher order centered
forms from [2] and aseries of representations off not discussed before.
AMS Subject Classification:65G10
Key words:Interval arithmetic. interval expressions
Über die Approximation des Wertebereichs durch Intervallausdriicke.Die reele Funktion f besitze über
dem Intervall X eine Darstellung der Form f(x) = f/Jo+ t(x)' h(x), XE X. Für den Durchmesser von
h(X) gelte d(h(X) ::::;;ad(X) und rur den Absolutbetrag von t(X) bestehedieUngleichung It(x)1 ::::;;-rd(Xf.

  

Source: Alefeld, Götz - Institut für Angewandte und Numerische Mathematik & Fakultät für Mathematik, Universität Karlsruhe

 

Collections: Mathematics