On a Refined Analysis of Some Problems in Interval Arithmetic Using Real Number Complexity Theory

On a Refined Analysis of Some Problems in Interval Arithmetic Using Real Number Complexity Theory We study some problems in interval arithmetic treated in Kreinovich et al. [13]. 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: http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

On a Refined Analysis of Some Problems in Interval Arithmetic Using Real Number Complexity Theory

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2004 by Kluwer Academic Publishers
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/B:REOM.0000032109.55408.1a
Publisher site
See Article on Publisher Site

Abstract

We study some problems in interval arithmetic treated in Kreinovich et al. [13]. 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:

Journal

Reliable ComputingSpringer Journals

Published: Oct 18, 2004

References

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