Publications

Article dans des revues

  • Florent Bréhard. A Symbolic-Numeric Validation Algorithm for Linear ODEs with Newton-Picard Method. Mathematics in Computer Science, Springer, In press. ⟨hal-03161118⟩
  • Denis Arzelier, Florent Bréhard, Mioara Joldes. Comments on "Series for Collision Probability in Short-Encounter Model". Journal of Guidance, Control, and Dynamics, American Institute of Aeronautics and Astronautics, 2020, 43 (5), ⟨10.2514/1.G004560⟩. ⟨hal-02123054⟩
  • Florent Bréhard, Nicolas Brisebarre, Mioara Joldes. Validated and numerically efficient Chebyshev spectral methods for linear ordinary differential equations. ACM Transactions on Mathematical Software, Association for Computing Machinery, 2018, 44 (4), pp.44:1-44:42. ⟨10.1145/3208103⟩. ⟨hal-01526272v3⟩

Communication dans un congrès

  • 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⟩. ⟨hal-02088529v2⟩
  • 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. ⟨hal-02006645⟩
  • 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. ⟨hal-02006606⟩
  • 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. ⟨hal-01830253⟩
  • Florent Bréhard. 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⟩. ⟨hal-01654396v2⟩
  • 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⟩. ⟨hal-01540170v3⟩
  • Denis Arzelier, Florent Bréhard, Norbert Deak, Mioara Joldes, Christophe Louembet, et al.. 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⟩. ⟨hal-01275427⟩

Pré-publication, Document de travail

  • Denis Arzelier, Florent Bréhard, Mioara Joldeş, Jean-Bernard Lasserre, Sohie Laurens, et al.. Polynomial superlevel set approximation of swept-volume for computing collision probability in space encounters. 2021. ⟨hal-03158347⟩
  • Florent Bréhard. A Symbolic-Numeric Validation Algorithm for Linear ODEs with Newton-Picard Method. 2020. ⟨hal-03161151⟩
  • Florent Bréhard, Nicolas Brisebarre, Mioara Joldes, Warwick Tucker. A New Lower Bound on the Hilbert Number for Quartic Systems. 2019. ⟨hal-02085895⟩

Rapport

  • 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. ⟨hal-02444341⟩
  • Denis Arzelier, Florent Bréhard, Mioara Joldes, Jean-Bernard Lasserre, Léo Martire, et al.. Global Probability of Collision: Problem modeling via occupation measures. DAJ/AR/EO-2016-6457, LAAS / CNRS; CNES. 2019. ⟨hal-02077552⟩

Thèse

  • Florent Bréhard. 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⟩. ⟨tel-02337901⟩