Section: Other Grants and Activities
ANR EVA-Flo Project
Participant : all Arenaire.
The EVA-Flo project (Évaluation et Validation Automatiques de calculs Flottants, 2006-2010) is headed by N. Revol (Arénaire). The other teams participating in this project are Dali (LP2A, U. Perpignan), Fluctuat (LIST, CEA Saclay) and Tropics (INRIA Sophia-Antipolis).
This project focuses on the way a mathematical formula (that includes transcendental functions and, possibly, iterations) is evaluated in floating-point arithmetic. Our approach is threefold: study of algorithms for approximating and evaluating mathematical formulae (with accuracy and performance being at stake), validation of such algorithms (especially their numerical accuracy) when developing them, in order to influence the algorithmic choices, and automation of the process.
ANR Gecko Project
Participant : G. Villard.
The Gecko project (Geometrical Approach to Complexity and Applications, 2005-2008, http://gecko.inria.fr ). is funded by ANR and headed by B. Salvy (Algo project, INRIA Rocquencourt). Other teams participating are at the École polytechnique, Université de Nice Sophia-Antipolis, and Université Paul Sabatier in Toulouse. The project is at the meeting point of numerical analysis, effective methods in algebra, symbolic computation and complexity theory. The aim is to improve significantly solution methods for algebraic or linear differential equations by taking geometry into account.
In Lyon we will concentrate on polynomial and matrix problems (with integer or polynomial entries) including some particular classes of structured matrices.
Ministry Grant ACI ``New Interfaces of Mathematics''
The GAAP project (Étude et outils pour la Génération Automatique d'Approximants Polynomiaux efficaces en machine , 2004-2007) is a collaboration with the LaMUSE laboratory (U. Saint-Étienne). A. Tisserand (CNRS, LIRMM, U. Montpellier) also participates to this project. The goal is the development of a C library MEPLib aimed at obtaining very good polynomial approximants under various constraints on the size in bits and the values of the coefficients. The target applications are software and hardware implementations, such as embedded systems for instance.
``Adaptive and Hybrid Algorithms'', Imag-INRIA project
The AHA project (Adaptive and Hybrid Algorithms , March 2005-2007) is headed by J.-L. Roch (Laboratoire ID-Imag), and supported by Imag Grenoble and INRIA. Our motivation is the conception of algorithms that may adapt themselves automatically to the execution context. Arénaire is involved for building reliable algorithms (e.g. adaptive precision, general algorithms versus algorithms specific to interval arithmetic, ...). Other partners of the project will focus on parallel developments for problems in optimization and vision.