| Identifiant de l'article : |
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ensl-00653460, version 2 |
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| Domaine : |
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Informatique/Autre
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| Titre : |
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Rigorous Polynomial Approximation using Taylor Models in Coq |
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| Auteur(s) : |
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Nicolas Brisebarre1, Mioara Maria Joldes2, Érik Martin-Dorel1, Micaela Mayero1, 3, Jean-Michel Muller1, Ioana Pasca1, Laurence Rideau4, Laurent Théry4 |
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| Laboratoire : |
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| 1 : |
Inria Grenoble Rhône-Alpes / LIP Laboratoire de l'Informatique du Parallélisme - ARENAIRE |
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| 2 : |
Department of Mathematics [Uppsala] |
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LIPN - Laboratoire d'informatique de Paris-nord |
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INRIA Sophia Antipolis - MARELLE |
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| Résumé : |
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One of the most common and practical ways of representing a real function on machines is by using a polynomial approximation. It is then important to properly handle the error introduced by such an approximation. The purpose of this work is to offer guaranteed error bounds for a specific kind of rigorous polynomial approximation called Taylor model. We carry out this work in the Coq proof assistant, with a special focus on genericity and efficiency for our implementation. We give an abstract interface for rigorous polynomial approximations, parameter- ized by the type of coefficients and the implementation of polynomials, and we instantiate this interface to the case of Taylor models with inter- val coefficients, while providing all the machinery for computing them. We compare the performances of our implementation in Coq with those of the Sollya tool, which contains an implementation of Taylor models written in C. This is a milestone in our long-term goal of providing fully formally proved and efficient Taylor models. |
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Langue du texte
intégral : |
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Anglais |
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| Mots-clés : |
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certified error bounds – Taylor models – Coq proof assistant – rigorous polynomial approximation |
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| Classification : |
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ACM F.4.1; G.1.2; G.4 |
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