## Abstract

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 the given domain [B], we try to transform f into a new function f^{og} that is monotonic in 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 overestimation of the image diameter of [f]_{og}. Finally, experiments show the benefits of this new interval extension for solving systems of equations.

Translated title of the contribution | A new extension of the functions at intervals based on the occurrence grouping |
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Original language | French |

Pages | 13-22 |

Number of pages | 10 |

State | Published - 2010 |

Externally published | Yes |

Event | Sixiemes Journees Francophones de Programmation par Contraintes, JFPC 2010 - 6th French Speaking Conference on Constraint Programming, JFPC 2010 - Caen, France Duration: 9 Jun 2010 → 11 Jun 2010 |

### Conference

Conference | Sixiemes Journees Francophones de Programmation par Contraintes, JFPC 2010 - 6th French Speaking Conference on Constraint Programming, JFPC 2010 |
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Country/Territory | France |

City | Caen |

Period | 9/06/10 → 11/06/10 |