Rigorous Polynomial Approximation using Taylor Models in Coq - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :

Rigorous Polynomial Approximation using Taylor Models in Coq

(1) , (2) , (1) , (1, 3) , (1) , (1) , (4) , (4)
1
2
3
4
Nicolas Brisebarre
Mioara Maria Joldes
Érik Martin-Dorel
Jean-Michel Muller
Ioana Pasca
  • Function : Author
  • PersonId : 845903
Laurence Rideau
  • Function : Author
  • PersonId : 832430
Laurent Théry

Abstract

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 certified 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, parameterized by the type of coefficients and the implementation of polynomials, and we instantiate this interface to the case of Taylor models with interval 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 certified and efficient Taylor models.
Fichier principal
Vignette du fichier
coq-approx.pdf (187.29 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

ensl-00653460 , version 1 (19-12-2011)
ensl-00653460 , version 2 (06-04-2012)

Identifiers

  • HAL Id : ensl-00653460 , version 1

Cite

Nicolas Brisebarre, Mioara Maria Joldes, Érik Martin-Dorel, Micaela Mayero, Jean-Michel Muller, et al.. Rigorous Polynomial Approximation using Taylor Models in Coq. 2011. ⟨ensl-00653460v1⟩
801 View
733 Download

Share

Gmail Facebook Twitter LinkedIn More