Florent Bréhard

Publications

Pré-publication, Document de travail (7)

Validated Numerical Newton-Puiseux Algorithm Florent Bréhard,Fabien Corinaldesi,Adrien Poteaux 2026 Pré-publication, Document de travail hal-05510315v1
Fast and Reliable Evaluation of the Distribution of Quadratic Forms of Gaussian Random Variables Denis Arzelier,Florent Bréhard,Mioara Joldes 2026 Pré-publication, Document de travail hal-05507599v1
Validated numerical Hensel lifting Florent Bréhard,Jasmin Krüger,Adrien Poteaux,Arthur Vinciguerra 2025 Pré-publication, Document de travail hal-04955638v2
Leveraging high performance with Julia for bias reduction in galaxy observations Mike Petrault,Bilal El Safah,Florent Bréhard,Pierre Fortin,Jenny G. Sorce 2025 Pré-publication, Document de travail hal-05393037v1
Validated numerical Hensel lifting Florent Bréhard,Adrien Poteaux,Jasmin Krüger,Arthur Vinciguerra 2024 Pré-publication, Document de travail hal-04626388v1
A Symbolic-Numeric Validation Algorithm for Linear ODEs with Newton-Picard Method Florent Bréhard 2020 Pré-publication, Document de travail hal-03161151v1
A New Lower Bound on the Hilbert Number for Quartic Systems Florent Bréhard,Nicolas Brisebarre,Mioara Joldes,Warwick Tucker 2019 Pré-publication, Document de travail hal-02085895v1

Article dans une revue (6)

An Exchange Algorithm for Optimizing both Approximation and Finite-Precision Evaluation Errors in Polynomial Approximations Denis Arzelier,Florent Bréhard,Tom Hubrecht,Mioara Joldes ACM Transactions on Mathematical Software, In press, ⟨10.1145/3770066⟩ Article dans une revue hal-04709615v2
Fast and reliable computation of the instantaneous orbital collision probability Matthieu Masson,Denis Arzelier,Florent Bréhard,Mioara Joldes,Bruno Salvy Journal of Guidance, Control, and Dynamics, 2024, pp.1-14. ⟨10.2514/1.G008102⟩ Article dans une revue hal-04134188v1
Efficient and Validated Numerical Evaluation of Abelian Integrals Florent Bréhard,Nicolas Brisebarre,Mioara Joldeş,Warwick Tucker ACM Transactions on Mathematical Software, 2024, 50 (1), pp.1 - 38. ⟨10.1145/3637550⟩ Article dans une revue hal-03561096v2
A Symbolic-Numeric Validation Algorithm for Linear ODEs with Newton-Picard Method Florent Bréhard Mathematics in Computer Science, In press Article dans une revue hal-03161118v1
Comments on &quot;Series for Collision Probability in Short-Encounter Model Denis Arzelier,Florent Bréhard,Mioara Joldes Journal of Guidance, Control, and Dynamics, 2020, 43 (5), ⟨10.2514/1.G004560⟩ Article dans une revue hal-02123054v1
Validated and numerically efficient Chebyshev spectral methods for linear ordinary differential equations Florent Bréhard,Nicolas Brisebarre,Mioara Joldes ACM Transactions on Mathematical Software, 2018, 44 (4), pp.44:1-44:42. ⟨10.1145/3208103⟩ Article dans une revue hal-01526272v3

Communication dans un congrès (11)

Rounding Error Analysis of an Orbital Collision Probability Evaluation Algorithm Denis Arzelier,Florent Bréhard,Mioara Joldes,Marc Mezzarobba 31st IEEE International Symposium on Computer Arithmetic, Jun 2024, Malaga, Spain. pp.96-103, ⟨10.1109/ARITH61463.2024.00025⟩ Communication dans un congrès hal-04466875v1
Validated Root Enclosures for Interval Polynomials with Multiplicities Florent Bréhard,Adrien Poteaux,Léo Soudant ISSAC'23 : International Symposium on Symbolic and Algebraic Computation 2023, Jul 2023, Tromso, Norway. ⟨10.1145/3597066.3597122⟩ Communication dans un congrès hal-04138791v1
Fast and reliable computation of the instantaneous orbital collision probability Matthieu Masson,Denis Arzelier,Florent Bréhard,Mioara Joldes 2nd International Stardust Conference STARCON2, ESA European Space Research and Technology Centre (ESTEC), Nov 2022, Noordwijk, Netherlands Communication dans un congrès hal-04240944v1
Polynomial superlevel set approximation of swept-volume for computing collision probability in space encounters Denis Arzelier,Florent Bréhard,Mioara Joldeş,Jean-Bernard Lasserre,Sohie Laurenset al. 60th IEEE Conference on Decision and Control (CDC 2021), IEEE, Dec 2021, Austin, Texas, United States. ⟨10.1109/CDC45484.2021.9683445⟩ Communication dans un congrès hal-03158347v1
A certificate-based approach to formally verified approximations Florent Bréhard,Assia Mahboubi,Damien Pous ITP 2019 - Tenth International Conference on Interactive Theorem Proving, Sep 2019, Portland, United States. pp.1-19, ⟨10.4230/LIPIcs.ITP.2019.8⟩ Communication dans un congrès hal-02088529v2
On Moment Problems with Holonomic Functions Florent Bréhard,Mioara Joldes,Jean-Bernard Lasserre 44th International Symposium on Symbolic and Algebraic Computation (ISSAC 2019), Jul 2019, Pékin, China. pp.66-73 Communication dans un congrès hal-02006645v1
Exchange algorithm for evaluation and approximation error-optimized polynomials Denis Arzelier,Florent Bréhard,Mioara Joldes ARITH 2019 - 26th IEEE Symposium on Computer Arithmetic, Jun 2019, Kyoto, Japan. pp.1-8 Communication dans un congrès hal-02006606v1
Fuel-optimal impulsive fixed-time trajectories in the linearized circular restricted 3-body-problem Romain Serra,Denis Arzelier,Florent Bréhard,Mioara Joldes IAC 2018 - 69th International Astronautical Congress; IAF Astrodynamics Symposium, International Astronautical Federation, Oct 2018, Bremen, Germany. pp.1-9 Communication dans un congrès hal-01830253v1
Validated Semi-Analytical Transition Matrices for Linearized Relative Spacecraft Dynamics via Chebyshev Series Approximations Paulo Ricardo Arantes Gilz,Florent Bréhard,Clément Gazzino 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⟩ Communication dans un congrès hal-01540170v3
A Newton-like Validation Method for Chebyshev Approximate Solutions of Linear Ordinary Differential Systems Florent Bréhard ISSAC 2018 - 43rd International Symposium on Symbolic and Algebraic Computation, Jul 2018, New York, United States. pp.103-110, ⟨10.1145/3208976.3209000⟩ Communication dans un congrès hal-01654396v2
Linearized Impulsive Fixed-Time Fuel-Optimal Space rendezvous: A New Numerical Approach Denis Arzelier,Florent Bréhard,Norbert Deak,Mioara Joldes,Christophe Louembetet al. 20th IFAC Symposium on Automatic Control in Aerospace, Aug 2016, Sherbrooke, Canada. ⟨10.1016/j.ifacol.2016.09.064⟩ Communication dans un congrès hal-01275427v1

Rapport (2)

Rigorous derivation of Coppola's formula for the computation of the probability of collision between space objects Denis Arzelier,Florent Bréhard,Mioara Joldes,Jean-Bernard Lasserre,Aude Rondepierre [Research Report] Rapport LAAS n° 20008, LAAS-CNRS. 2020 Rapport (rapport de recherche) hal-02444341v1
Global Probability of Collision: Problem modeling via occupation measures Denis Arzelier,Florent Bréhard,Mioara Joldes,Jean-Bernard Lasserre,Léo Martireet al. DAJ/AR/EO-2016-6457, LAAS / CNRS; CNES. 2019 Rapport hal-02077552v1

Thèse (1)

Calcul numérique certifié dans les espaces fonctionnels : Un trilogue entre approximations polynomiales rigoureuses, calcul symbolique et preuve formelle Florent Bréhard Numerical Analysis [cs.NA]. Université de Lyon, 2019. English. ⟨NNT : 2019LYSEN032⟩ Thèse tel-02337901v1

Logiciel (1)

Certified Chebyshev models in Rocq Damien Pous,Florent Bréhard,Louis Gaillard,Assia Mahboubi 2019, ⟨swh:1:dir:6cdde290b1103523b5da14286df67b8df99b14a4;origin=https://github.com/damien-pous/approx-models;visit=swh:1:snp:0b56d5fef783663a395578bc5fb64f9f8afa0342;anchor=swh:1:rev:2304ba7730fbb293d4cb55f609994d7bdaf4e83f⟩ Logiciel hal-05008009v1