An interval extension based on occurrence grouping

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.