Florent Bréhard
Publications
Florent Bréhard, Jasmin Krüger, Adrien Poteaux, Arthur Vinciguerra
Validated numerical Hensel's lifting
2025
Denis Arzelier, Florent Bréhard, Tom Hubrecht, Mioara Joldes
An Exchange Algorithm for Optimizing both Approximation and Finite-Precision Evaluation Errors in Polynomial Approximations
2024
Florent Bréhard, Adrien Poteaux, Jasmin Krüger, Arthur Vinciguerra
Validated numerical Hensel lifting
2024
Denis Arzelier, Florent Bréhard, Mioara Joldes, Marc Mezzarobba
Rounding Error Analysis of an Orbital Collision Probability Evaluation Algorithm
31st IEEE International Symposium on Computer Arithmetic, Jun 2024, Malaga, Spain. pp.96-103, ⟨10.1109/ARITH61463.2024.00025⟩
Matthieu Masson, Denis Arzelier, Florent Bréhard, Mioara Joldes, Bruno Salvy
Fast and reliable computation of the instantaneous orbital collision probability
Journal of Guidance, Control, and Dynamics, 2024, pp.1-14. ⟨10.2514/1.G008102⟩
Florent Bréhard, Nicolas Brisebarre, Mioara Joldeş, Warwick Tucker
Efficient and Validated Numerical Evaluation of Abelian Integrals
ACM Transactions on Mathematical Software, 2024, 50 (1), pp.1 - 38. ⟨10.1145/3637550⟩
Florent Bréhard, Adrien Poteaux, Léo Soudant
Validated Root Enclosures for Interval Polynomials with Multiplicities
ISSAC'23 : International Symposium on Symbolic and Algebraic Computation 2023, Jul 2023, Tromso, Norway. ⟨10.1145/3597066.3597122⟩
Matthieu Masson, Denis Arzelier, Florent Bréhard, Mioara Joldes
Fast and reliable computation of the instantaneous orbital collision probability
2nd International Stardust Conference STARCON2, ESA European Space Research and Technology Centre (ESTEC), Nov 2022, Noordwijk, Netherlands
Denis Arzelier, Florent Bréhard, Mioara Joldeş, Jean-Bernard Lasserre, Sohie Laurens, Aude Rondepierre
Polynomial superlevel set approximation of swept-volume for computing collision probability in space encounters
60th IEEE Conference on Decision and Control (CDC 2021), IEEE, Dec 2021, Austin, Texas, United States. ⟨10.1109/CDC45484.2021.9683445⟩
A Symbolic-Numeric Validation Algorithm for Linear ODEs with Newton-Picard Method
Mathematics in Computer Science, In press
A Symbolic-Numeric Validation Algorithm for Linear ODEs with Newton-Picard Method
2020
Denis Arzelier, Florent Bréhard, Mioara Joldes
Comments on "Series for Collision Probability in Short-Encounter Model
Journal of Guidance, Control, and Dynamics, 2020, 43 (5), ⟨10.2514/1.G004560⟩
Denis Arzelier, Florent Bréhard, Mioara Joldes, Jean-Bernard Lasserre, Aude Rondepierre
Rigorous derivation of Coppola's formula for the computation of the probability of collision between space objects
[Research Report] Rapport LAAS n° 20008, LAAS-CNRS. 2020
Florent Bréhard, Assia Mahboubi, Damien Pous
A certificate-based approach to formally verified approximations
ITP 2019 - Tenth International Conference on Interactive Theorem Proving, Sep 2019, Portland, United States. pp.1-19, ⟨10.4230/LIPIcs.ITP.2019.8⟩
Florent Bréhard, Mioara Joldes, Jean-Bernard Lasserre
On Moment Problems with Holonomic Functions
44th International Symposium on Symbolic and Algebraic Computation (ISSAC 2019), Jul 2019, Pékin, China. pp.66-73
Calcul numérique certifié dans les espaces fonctionnels : Un trilogue entre approximations polynomiales rigoureuses, calcul symbolique et preuve formelle
Numerical Analysis [cs.NA]. Université de Lyon, 2019. English. ⟨NNT : 2019LYSEN032⟩
Denis Arzelier, Florent Bréhard, Mioara Joldes
Exchange algorithm for evaluation and approximation error-optimized polynomials
ARITH 2019 - 26th IEEE Symposium on Computer Arithmetic, Jun 2019, Kyoto, Japan. pp.1-8
Florent Bréhard, Nicolas Brisebarre, Mioara Joldes, Warwick Tucker
A New Lower Bound on the Hilbert Number for Quartic Systems
2019
Denis Arzelier, Florent Bréhard, Mioara Joldes, Jean-Bernard Lasserre, Léo Martire, Aude Rondepierre
Global Probability of Collision: Problem modeling via occupation measures
DAJ/AR/EO-2016-6457, LAAS / CNRS; CNES. 2019
Damien Pous, Florent Bréhard, Louis Gaillard, Assia Mahboubi
Certified Chebyshev models in Rocq
Romain Serra, Denis Arzelier, Florent Bréhard, Mioara Joldes
Fuel-optimal impulsive fixed-time trajectories in the linearized circular restricted 3-body-problem
IAC 2018 - 69th International Astronautical Congress; IAF Astrodynamics Symposium, International Astronautical Federation, Oct 2018, Bremen, Germany. pp.1-9
Florent Bréhard, Nicolas Brisebarre, Mioara Joldes
Validated and numerically efficient Chebyshev spectral methods for linear ordinary differential equations
ACM Transactions on Mathematical Software, 2018, 44 (4), pp.44:1-44:42. ⟨10.1145/3208103⟩
A Newton-like Validation Method for Chebyshev Approximate Solutions of Linear Ordinary Differential Systems
ISSAC 2018 - 43rd International Symposium on Symbolic and Algebraic Computation, Jul 2018, New York, United States. pp.103-110, ⟨10.1145/3208976.3209000⟩
Paulo Ricardo Arantes Gilz, Florent Bréhard, Clément Gazzino
Validated Semi-Analytical Transition Matrices for Linearized Relative Spacecraft Dynamics via Chebyshev Series Approximations
SCITECH 2018 - AIAA Science and Technology Forum and Exposition, 28th Space Flight Mechanics Meeting, Jan 2018, Kissimmee, United States. pp.1-23, ⟨10.2514/6.2018-1960⟩
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
20th IFAC Symposium on Automatic Control in Aerospace, Aug 2016, Sherbrooke, Canada. ⟨10.1016/j.ifacol.2016.09.064⟩
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