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hal-04955638

Florent Bréhard, Jasmin Krüger, Adrien Poteaux, Arthur Vinciguerra

Validated numerical Hensel's lifting

2025

hal-04709615

Denis Arzelier, Florent Bréhard, Tom Hubrecht, Mioara Joldes

An Exchange Algorithm for Optimizing both Approximation and Finite-Precision Evaluation Errors in Polynomial Approximations

2024

hal-04626388

Florent Bréhard, Adrien Poteaux, Jasmin Krüger, Arthur Vinciguerra

Validated numerical Hensel lifting

2024

hal-04466875

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⟩

hal-04134188

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⟩

hal-03561096

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⟩

hal-04138791

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⟩

hal-04240944

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

hal-03158347

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⟩

hal-03161118

Florent Bréhard

A Symbolic-Numeric Validation Algorithm for Linear ODEs with Newton-Picard Method

Mathematics in Computer Science, In press

hal-03161151

Florent Bréhard

A Symbolic-Numeric Validation Algorithm for Linear ODEs with Newton-Picard Method

2020

hal-02123054

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⟩

hal-02444341

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-02088529

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-02006645

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

tel-02337901

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⟩

hal-02006606

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-02085895

Florent Bréhard, Nicolas Brisebarre, Mioara Joldes, Warwick Tucker

A New Lower Bound on the Hilbert Number for Quartic Systems

2019

hal-02077552

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

hal-01830253

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-01526272

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⟩

hal-01654396

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-01540170

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-01275427

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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