A General Reliable Quadratic Form: An Extension of Affine Arithmetic

A General Reliable Quadratic Form: An Extension of Affine Arithmetic 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

A General Reliable Quadratic Form: An Extension of Affine Arithmetic

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2006 by Springer Science + Business Media, Inc.
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.
10.1007/s11155-006-7217-4
Publisher site
See Article on Publisher Site

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.

Journal

Reliable ComputingSpringer Journals

Published: Jan 1, 2006

References

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