A General Reliable Quadratic Form: An Extension of Affine Arithmetic

Author： Messine Frédéric   Touhami Ahmed  

Publisher： Springer Publishing Company

ISSN： 1385-3139

Source： Reliable Computing, Vol.12, Iss.3, 2006-06, pp. : 171-192

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Abstract

In this article, a new extension of affine arithmetic is introduced. This technique is based on a quadratic form named general quadratic form. We focus here on the computation of reliable bounds of a function over a hypercube by using this new tool. Some properties of first quadratic functions and then polynomial ones are reported. In order to show the efficiency of such a method, ten polynomial global optimization problems are presented and solved by using an interval branch-and-bound based algorithm.

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