We study some problems in interval arithmetic treated in Kreinovich et al. . First, we consider the best linear approximation of a quadratic interval function. Whereas this problem (as decision problem) is known to be NP-hard in the Turing model, we analyze its complexity in the real number model and the analogous class NP ℝ. Our results substantiate that most likely it does not any longer capture the difficulty of NP ℝ in such a real number setting. More precisely, we give upper complexity bounds for the approximation problem for interval functions by locating it in (a real analogue of). This result allows several conclusions:
Reliable Computing – Springer Journals
Published: Oct 18, 2004
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