Reseña: Rigorous polynomial approximation using Taylor models in Coq
Se ha publicado un nuevo artículo de razonamiento formalizado en Coq sobre cálculo numérico: Rigorous polynomial approximation using Taylor models in Coq.
Sus autores son Nicolas Brisebarre, Mioara Maria Joldes, Érik Martin-Dorel, Micaela Mayero, Jean-Michel Muller, Ioana Pasca,
Laurence Rideau y Laurent Théry. Todos son miembros del grupo CoqApprox.
El trabajo se ha desarrollado dentro del proyecto TaMaDi y se presentó el 5 de abril en el NFM 2012 (4th NASA Formal Methods Symposium).
El resumen del trabajo es
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, 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 proved and efficient Taylor models.
Este trabajo es continuación de la tesis doctoral de Mioara Joldes titulada Rigorous polynomial approximations and applications, dirigida por Nicolas Brisebarre y Jean-Michel Muller presentada el 26 de septiembre de 2011 en la Universidad de Lyon.
El código de las teorías correspondientes al trabajo se encuentra aquí.