Generalized Intervals and the Dependency Problem

Abstract

Computing enclosures of the range of functions using interval arithmetic often leads to overestimations due to variables (parameters) appearing more than once within the expression to be evaluated (dependency problem). An experimental implementation of a generalized interval arithmetic which has been proposed by Hansen [2] in 1975 is now available [1, 3]. In many cases generalized intervals are well suited to reduce the dependency problem and/or the so called wrapping effect. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)