My main topic of interest is the conception of certified tools for numerical analysis, towards the objective of developing a general-purpose library for rigorous numerics with a formal proof layer guaranteeing the correctness of both the methods and the implementation.
Florent Bréhard, Assia Mahboubi, Damien Pous. A certificate-based approach to formally verified approximations. ITP, 2019. Open access version.
Florent Bréhard, Mioara Joldes, Jean-Bernard Lasserre. On a moment problem with holonomic functions. ISSAC, 2019. Open access version.
Denis Arzelier, Florent Bréhard, Mioara Joldes. Exchange algorithm for evaluation and approximation error-optimized polynomials. ARITH, 2019. Open access version.
Romain Serra, Denis Arzelier, Florent Bréhard, Mioara Joldes. Fuel-Optimal Impulsive Fixed-Time Trajectories in the Linearized Circular Restricted 3-Body Problem. IAC, 2018. Open access version.
Florent Bréhard. A Newton-like Validation Method for Chebyshev Approximate Solutions of Linear Ordinary Differential Systems. ISSAC, 2018. Open access version.
Paulo Ricardo Arantes Gilz, Florent Bréhard, Clément Gazzino. Validated Semi-Analytical Transition Matrix for Linearized Relative Spacecraft Dynamics via Chebyshev Polynomials. AIAA SciTech Forum, 2018. Open access version.
Florent Bréhard, Nicolas Brisebarre, Mioara Joldes. Validated and Numerically Efficient Chebyshev Spectral Methods for Linear Ordinary Differential Equations. ACM Trans. Math. Software, 2018. Open access version.
Denis Arzelier, Florent Bréhard, Norbert Deak, Mioara Joldes, Christophe Louembet, Aude Rondepierre, Romain Serra. Linearized Impulsive Fixed-Time Fuel-Optimal Space rendezvous: A New Numerical Approach. ACA, 2016. Open access version.
ChebValid: a C library to compute certified approximations to solutions of Linear Ordinary Differential Equations, using truncated Chebyshev series.
The project's Git repository can be checked out through anonymous access with the following command:
git clone https://scm.gforge.inria.fr/anonscm/git/tchebyapprox/tchebyapprox.git
A COQ framework implementing Chebyshev Models in a certified setting.
Tutorials of the course Théorie de la programmation (Fall 2017) by Philippe Audebaud, together with Adrien Durier and Marc De Visme
Tutorials of the course Optimization and Approximation (Fall 2017) by Nicolas Bousquet, together with Luc Pellissier
Tutorials of the course Théorie de la programmation (Fall 2016) by Philippe Audebaud, together with Adrien Durier and Pierre Pradic
Tutorials of the course Optimization and Approximation (Fall 2016) by Alantha Newman, together with Khang Le Ngoc