An interval extension based on occurrence grouping

Ignacio Araya, Bertrand Neveu, Gilles Trombettoni

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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 x a and x b of the occurrences of x: f og is increasing w.r.t. x a and decreasing w.r.t. x b . [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 show the benefits of this new interval extension for solving systems of nonlinear equations.

Original languageEnglish
Pages (from-to)173-188
Number of pages16
Issue number2-4
StatePublished - Mar 2012
Externally publishedYes


  • Interval extension
  • Intervals
  • Monotonicity
  • Occurrence grouping


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