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Journal Articles Computing Year : 2012

An Interval Extension Based on Occurrence Grouping

Abstract

In interval arithmetics, special care has been brought to the definition of interval extension functions that compute narrow interval images. In particular, when a function f is monotonic w.r.t. a variable in a given domain, it is well-known that the monotonicity-based interval extension of f computes a sharper image than the natural interval extension does. This paper presents a so-called "occurrence grouping" interval extension [ f ]og of a function f . When f is not monotonic w.r.t. a variable x in a given domain, we try to transform f into a new function f og that is monotonic w.r.t. two subsets xa and xb of the occurrences of x: f og is increasing w.r.t. xa and decreasing w.r.t. xb . [ f ]og is the interval extension by monotonicity of f og and produces a sharper interval image than the natural extension does. For finding a good occurrence grouping, we propose a linear program and an algorithm that minimize a Taylor-based over-estimate of the image diameter of [ f ]og . Experiments showthe benefits of this new interval extension for solving systems of non linear equations
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Dates and versions

hal-00733855 , version 1 (19-09-2012)

Identifiers

  • HAL Id : hal-00733855 , version 1

Cite

Ignacio Araya, Bertrand Neveu, Gilles Trombettoni. An Interval Extension Based on Occurrence Grouping. Computing, 2012, 94 (2), pp.173-188. ⟨hal-00733855⟩
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