On the complexity of some problems in interval arithmetic

Abstract

We study some problems in interval arithmetic treated in Kreinovich et al. [6]. First, we consider the best linear approximation of a quadratic interval function. Known to be NP-hard in the Turing model, we analyze its complexity in the real number model and the analoguous class NPR. We give new upper complexity bounds by locating the decision version in DΣR2 (a real analogue of Σ2) and solve a problem left open in [6]. © Springer-Verlag Berlin Heidelberg 2003.