An interval extension based on occurrence grouping

doi:10.1007/s00607-011-0158-8

An interval extension based on occurrence grouping

2011-11-20

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DOI：10.1007/s00607-011-0158-8

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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.

Keyword:

Intervals

Interval extension

Monotonicity

Occurrence grouping

An interval extension based on occurrence grouping

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