## Section: Other Grants and Activities

### National Initiatives

#### ANR EVA-Flo Project

Keywords : floating-point computation, specification and validation, automation.

Participant : all Arenaire.

The EVA-Flo project (Évaluation et Validation Automatiques de calculs
*Flo*ttants, 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

Keywords : geometry, algorithm analysis, polynomial matrix, integer matrix.

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''

Keywords : polynomial approximation, minimax approximation, floating-point arithmetic, polytope, linear programming.

Participants : N. Brisebarre, S. Chevillard, J.-M. Muller, S. Torres.

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

Keywords : adaptive algorithm, reliable computation, optimization.

Participants : N. Revol, G. Villard.

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.