Arithmétique par intervalles

Nathalie Revol 1
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : This paper constitutes an introduction to interval arithmetic. This arithmetic allows on the one hand to take into account the measurement uncertainties on data and on the other hand to determine an enclosure of the computed result that is guaranteed to contain it: indeed, the main advantage of interval arithmetic is its reliability. The goal of this introduction is to emphasize the strong points of interval arithmetic and to explain how to alleviate its problems. The main advantage is to provide global information, such as for instance the range of a function over a whole set. This global information can serve to prove that an iteration is contractant and thus that it has a fixed point. It can also be used to detemine the global optimum of a function without being trapped by a local one.
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Nathalie Revol. Arithmétique par intervalles. Calculateurs Parallèles et Systèmes Répartis, Hermes, 2001, L'arithmétique des ordinateurs, 13 (4-5), pp.387-426. ⟨inria-00545026⟩

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