Publications of Serge GRATTON
Antoine Bernigaud, Serge Gratton, Ehouarn Simon
A non-linear conjugate gradient in dual space for Lp-norm regularized non-linear least squares with application in data assimilation
Numerical Algorithms, 2024, 95, pp.471-497. ⟨10.1007/s11075-023-01578-x⟩
Serge Gratton, Alena Kopaničáková, Philippe L. Toint
Multilevel Objective-Function-Free Optimization with an Application to Neural Networks Training
SIAM Journal on Optimization, 2023, 33 (4), pp.2772-2800. ⟨10.1137/23M1553455⟩
Serge Gratton, Sadok Jerad, Philippe L. Toint
Convergence Properties of an Objective-Function-Free Optimization Regularization Algorithm, Including an \(\boldsymbol{\mathcal{O}(\epsilon^{-3/2})}\) Complexity Bound
SIAM Journal on Optimization, 2023, 33 (3), pp.1621-1646. ⟨10.1137/22M1499522⟩
Adrien Rouviere, Lucas Pascal, Fabien Méry, Ehouarn Simon, Serge Gratton
Neural prediction model for transition onset of a boundary layer in presence of two-dimensional surface defects
FLOW: Applications of Fluid Mechanics (En ligne), 2023, 3, pp.E20. ⟨10.1017/flo.2023.17⟩
Serge Gratton, Sadok Jerad, Philippe L. Toint
An adaptive regularization method in Banach spaces
Optimization Methods and Software, 2023, 38 (6), pp.1163-1179. ⟨10.1080/10556788.2023.2210253⟩
Serge Gratton, Ehouarn Simon, David Titley-Peloquin
Covariance matrix estimation for ensemble-based Kalman filters with multiple ensembles
Mathematical Geosciences, 2023, 55, pp.1147-1168. ⟨10.1007/s11004-023-10063-z⟩
Serge Gratton, Philippe L. Toint
OFFO minimization algorithms for second-order optimality and their complexity
Computational Optimization and Applications, 2022, 84, pp.573-607. ⟨10.1007/s10589-022-00435-2⟩
Serge Gratton, Ehouarn Simon, David Titley-Peloquin, Philippe Toint
A note on inexact inner products in GMRES
SIAM Journal on Matrix Analysis and Applications, 2022, 43 (3)
Mathis Peyron, Anthony Fillion, Selime Gürol, Serge Gratton, Pierre Boudier, Gael Goret
Latent space data assimilation by using deep learning
Quarterly Journal of the Royal Meteorological Society, 2021, 147 (740, Part A), pp.3759-3777. ⟨10.1002/qj.4153⟩
Antoine Bernigaud, Serge Gratton, Flavia Lenti, Ehouarn Simon, Oumaima Sohab
Lp‐norm regularization approaches in variational data assimilation
Quarterly Journal of the Royal Meteorological Society, 2021, 147, pp.2067 – 2081. ⟨10.1002/qj.4010⟩
Serge Gratton, Ehouarn Simon, David Titley-Peloquin, Philippe Toint
Minimizing convex quadratics with variable precision conjugate gradients
Numerical Linear Algebra with Applications, 2021, 28 (e2337)
Henri Calandra, Serge Gratton, Elisa Riccietti, Xavier Vasseur
On high-order multilevel optimization strategies
SIAM Journal on Optimization, 2020, 31 (1), pp.307-330. ⟨10.1137/19M1255355⟩
Henri Calandra, Serge Gratton, Elisa Riccietti, Xavier Vasseur
On a multilevel Levenberg–Marquardt method for the training of artificial neural networks and its application to the solution of partial differential equations
Optimization Methods and Software, 2020, pp.1-26. ⟨10.1080/10556788.2020.1775828⟩
Anthony Fillion, Marc Bocquet, Serge Gratton, Selime Gürol, Pavel Sakov
An Iterative Ensemble Kalman Smoother in Presence of Additive Model Error
SIAM/ASA Journal on Uncertainty Quantification, 2020, 8 (1), pp.198-228. ⟨10.1137/19M1244147⟩
Henri Calandra, Serge Gratton, Elisa Riccietti, Xavier Vasseur
On Iterative Solution of the Extended Normal Equations
SIAM Journal on Matrix Analysis and Applications, 2020, 41 (4), pp.1571-1589. ⟨10.1137/19M1288644⟩
A note on solving nonlinear optimization problems in variable precision
Computational Optimization and Applications, 2020, pp.1-15
Serge Gratton, Ehouarn Simon, Philippe Toint
An algorithm for the minimization of nonsmooth nonconvex functions using inexact evaluations and its worst-case complexity
Mathematical Programming, Series A, 2020, ⟨10.1007/s10107-020-01466-5⟩
Henri Calandra, Serge Gratton, Elisa Riccietti, Xavier Vasseur
On the approximation of the solution of partial differential equations by artificial neural networks trained by a multilevel Levenberg-Marquardt method
Optimization Methods and Software, 2020
Serge Gratton, Clément Royer, Luís N. Vicente
A decoupled first/second-order steps technique for nonconvex nonlinear unconstrained optimization with improved complexity bounds
Mathematical Programming, 2020, 179 (1-2), pp.195-222. ⟨10.1007/s10107-018-1328-7⟩
Henri Calandra, Serge Gratton, Elisa Riccietti, Xavier Vasseur
ON THE ITERATIVE SOLUTION OF SYSTEMS OF THE FORM A T Ax = A T b + c
SIAM Journal on Matrix Analysis and Applications, 2020, pp.1-25
Thibaud Vandamme, Emmanuel Caroli, Serge Gratton
How the Invasion Zone Can Contribute to the Estimation of Petrophysical Properties From Log Inversion at Well Scale?
Petrophysics – The SPWLA Journal of Formation Evaluation and Reservoir Description, 2019, 60 (2), pp.306-325. ⟨10.30632/PJV60N2-2019a8⟩
El Houcine Bergou, Serge Gratton, Jan Mandel
On the convergence of a non-linear ensemble Kalman smoother
Applied Numerical Mathematics, 2019, 137, pp.151-168. ⟨10.1016/j.apnum.2018.11.008⟩
Oliver Guillet, Anthony Weaver, Xavier Vasseur, Yann Michel, Serge Gratton, Selime Gurol
Modelling spatially correlated observation errors in variational data assimilation using a diffusion operator on an unstructured mesh
Quarterly Journal of the Royal Meteorological Society, 2019, pp.1-21. ⟨10.1002/qj.3537⟩
Serge Gratton, Clément Royer, Luís N. Vicente, Zaikun Zhang
Direct search based on probabilistic feasible descent for bound and linearly constrained problems
Computational Optimization and Applications, 2019, 72 (3), pp.525-559. ⟨10.1007/s10589-019-00062-4⟩
Serge Gratton, Selime Gürol, Ehouarn Simon, Philippe Toint
Guaranteeing the convergence of the saddle formulation for weakly constrained 4D‐Var data assimilation
Quarterly Journal of the Royal Meteorological Society, 2018, 144 (717), pp.2592-2602. ⟨10.1002/qj.3355⟩
Serge Gratton, Clément Royer, Luis Vicente, Zaikun Zhang
Complexity and global rates of trust-region methods based on probabilistic mode
IMA Journal of Numerical Analysis, 2018, 38 (3), pp.1579-1597. ⟨10.1093/imanum/drx043⟩
Thibaut Lunet, Julien Bodart, Serge Gratton, Xavier Vasseur
Time-parallel simulation of the decay of homogeneous turbulence using Parareal with spatial coarsening
Computing and Visualization in Science, 2018, Special Issue Parallel-in-Time Methods, 19, pp.31-44. ⟨10.1007/s00791-018-0295-0⟩
Serge Gratton, Selime Gürol, Ehouarn Simon, Philippe Toint
A note on preconditioning weighted linear least-squares, with consequences for weakly constrained variational data assimilation
Quarterly Journal of the Royal Meteorological Society, 2018, 144 (712), pp.934-940. ⟨10.1002/qj.3262⟩
Anthony Fillion, Marc Bocquet, Serge Gratton
Quasi-static ensemble variational data assimilation: a theoretical and numerical study with the iterative ensemble Kalman smoother
Nonlinear Processes in Geophysics, 2018, 25, pp.315-334. ⟨10.5194/npg-25-315-2018⟩
Matthew C. Fisher, Serge Gratton, Selime Gurol, Y. Trémolet, Xavier Vasseur
Low rank updates in preconditioning the saddle point systems arising from data assimilation problems
Optimization Methods and Software, 2018, 33 (1), pp.45-69. ⟨10.1080/10556788.2016.1264398⟩
Stefania Bellavia, Serge Gratton, Elisa Riccietti
A Levenberg-Marquardt method for large nonlinear least-squares problems with dynamic accuracy in functions and gradients
Numerische Mathematik, 2018, 140 (3), pp.791-825. ⟨10.1007/s00211-018-0977-z⟩
Serge Gratton, David Titley-Peloquin
Improved Bounds for Small-Sample Estimation
SIAM Journal on Matrix Analysis and Applications, 2018, 39 (2), pp.922-931
Sylvain Mercier, Serge Gratton, Nicolas Tardieu, Xavier Vasseur
A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity
Computational Mechanics, 2017, 60 (6), pp.969-982. ⟨10.1007/s00466-017-1450-z⟩
El Houcine Bergou, Youssef Diouane, Serge Gratton
On the use of the energy norm in trust-region and adaptive cubic regularization subproblems
Computational Optimization and Applications, 2017, vol. 68 (n° 3), pp. 533-554. ⟨10.1007/s10589-017-9929-2⟩
Serge Gratton, Nacer Soualmi, Luis Vicente
An indicator for the switch from derivative-free to derivative-based optimization.
Operations Research Letters, 2017, 45 (4), pp.353-361. ⟨10.1016/j.orl.2017.05.003⟩
Claudio Estatico, Serge Gratton, Flavia Lenti, David Titley-Peloquin
A conjugate gradient like method for p-norm minimization in functional spaces.
Numerische Mathematik, 2017, 137 (4), pp.895-922. ⟨10.1007/s00211-017-0893-7⟩
Stanley Eisenstadt, Serge Gratton, David Titley-Peloquin
On the symmetric componen twise relative backward error for linear systems of equations
SIAM Journal on Matrix Analysis and Applications, 2017, 38 (4), pp.1100-1115. ⟨10.1137/140986566⟩
El Houcine Bergou, Serge Gratton, Luis Vicente
Levenberg-Marquardt methods based on probabilistic gradient models and inexact subproblem solution, with application to data assimilation
SIAM/ASA Journal on Uncertainty Quantification, 2016, 4 (1), pp.924-951. ⟨10.1137/140974687⟩
Jan Mandel, El Houcine Bergou, Selime Gurol, Serge Gratton
Hybrid Levenberg-Marquardt and weak constraint ensemble Kalman smoother method, Nonlinear Processes in Geophysics
Nonlinear Processes in Geophysics, 2016, 23, pp.59–73. ⟨10.5194/npgd-2-865-2015⟩
Serge Gratton, Jean Tshimanga Ilunga
On a second-order expansion of the truncated singular subspace decomposition
Numerical Linear Algebra with Applications, 2016, 23 (3), pp.519–534
Serge Gratton, Sylvain Mercier, Nicolas Tardieu, Xavier Vasseur
Limited memory preconditioners for symmetric indefinite problems with application to structural mechanics
Numerical Linear Algebra with Applications, 2016, 23 (5), pp.865–887. ⟨10.1002/nla.2058⟩
Serge Gratton, Pascal Hénon, Pavel Jiránek, Xavier Vasseur
Reducing complexity of algebraic multigrid by aggregation
Numerical Linear Algebra with Applications, 2016, pp.501–518. ⟨10.1002/nla.2036⟩
Youssef Diouane, Serge Gratton, Xavier Vasseur, L. Nunes Vicente, Henri Calandra
A Parallel Evolution Strategy for an Earth Imaging Problem in Geophysics
Optimization and Engineering, 2015, pp.1-24. ⟨10.1007/s11081-015-9296-8⟩
Serge Gratton, Vincent Malmedy, Philippe Toint
Quasi-Newton updates with weighted secant equations
Optimization Methods and Software, 2015, 30 (4), pp.748-755. ⟨10.1080/10556788.2014.971025⟩
Serge Gratton, Monserrat Rincon-Camacho, Ehouarn Simon, Philippe Toint
Observation thinning in data assimilation computations
EURO Journal on Computational Optimization, 2015, 3 (1), pp.31-51. ⟨10.1007/s13675-014-0025-4⟩
Serge Gratton, Clément Royer, Luis Vicente, Zaikun Zhang
Direct Search Based on Probabilistic Descent
SIAM Journal on Optimization, 2015, vol. 25 (n° 3), pp. 1515-1541. ⟨10.1137/140961602⟩
Serge Gratton, Clément Royer, Luis Vicente
A second-order globally convergent direct-search method and its worst-case complexity
Optimization, 2015, 65 (6), pp.1105-1128. ⟨10.1080/02331934.2015.1124271⟩
Guillaume Ramillien, Frank Frappart, Serge Gratton, Xavier Vasseur
Sequential estimation of surface water mass changes from daily satellite gravimetry data
Journal of Geodesy, 2015, 89 (3), pp.259-282. ⟨10.1007/s00190-014-0772-2⟩
Youssef Diouane, Serge Gratton, L. Nunes Vicente
Globally convergent evolution strategies for constrained optimization
Computational Optimization and Applications, 2015, vol. 62 (n° 2), pp. 323-346. ⟨10.1007/s10589-015-9747-3⟩
Youssef Diouane, Serge Gratton, L. Nunes Vicente
Globally convergent evolution strategies
Mathematical Programming, 2015, vol. 152 (n° 1), pp. 467-490. ⟨10.1007/s10107-014-0793-x⟩
Serge Gratton, Patrick Laloyaux, Annick Sartenaer
Derivative-free optimization for large-scale nonlinear data assimilation problems
Quarterly Journal of the Royal Meteorological Society, 2014, 140 (680), pp.943-957. ⟨10.1002/qj.2169⟩
A merit function approach for direct search
SIAM Journal on Optimization, 2014, 24 (4), pp.1980-1998. ⟨10.1137/130917661⟩
Serge Gratton, David Titley-Peloquin
Stochastic conditionin g of matrix functions
SIAM/ASA Journal on Uncertainty Quantification, 2014, 2 (1), pp.763-783. ⟨10.1137/140973827⟩
Serge Gratton, David Titley-Peloquin, Philippe Toint, Jean Tshimanga Ilunga
Differentiating the Method of Conjugate Gradients
SIAM Journal on Matrix Analysis and Applications, 2014, 35 (1), pp.110–126. ⟨10.1137/120889848⟩
Serge Gratton, Philippe Toint, Jean Tshimanga Ilunga
Conjugate-gradients versus multigrid solvers for diffusion-based correlation models in data assimilation
Quarterly Journal of the Royal Meteorological Society, 2014, 139 (675), pp.1481–1487
El Houcine Bergou, Serge Gratton, Jean Tshimanga Ilunga
The exact condition number of the truncated singular value solution of a linear ill-posed problem
SIAM Journal on Mathematical Analysis, 2014, 35 (3), pp.1073-1085. ⟨10.1137/120869286⟩
Serge Gratton, Pavel Jiranek, Xavier Vasseur
Energy backward error: interpretation in numerical solution of elliptic partial differential equations and convergence of the conjugate gradient method
In : Electronic Transaction on Numerical Analysis, Kent State UNiversity, USA, Vol. 40, pp. 338-355, 2013.
Serge Gratton, David Titley-Peloquin, Jean Tshimanga Ilunga
Sensitivity and conditioning of the truncated total least squares solution
In : SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics (SIAM), USA, Vol. 34 N. 3, pp. 1257-1276, 2013.
Serge Gratton, Selime Gurol, Philippe Toint
Preconditioning and Globalizing Conjugate Gradients in Dual Space for Quadratically Penalized Nonlinear-Least Squares Problems
In : Computational Optimization and Applications, Springer, Vol. 54 N. 1, pp. 1-25, 2013.
Linear regression models, least-squares problems, normal equations, and stopping criteria for the conjugate gradient method
In : Computer Physics Communications (CPC), Elsevier, Vol. 183 N. 11, pp. 2322-2336, 2012.
Guillaume Ramillien, Lucia Soane, Frank Frappart, Serge Gratton, Xavier Vasseur, Stéphane Bourgogne
Constrained regional recovery of continental water mass time-variations from GRACE-based geopotential anomalies
In : Surveys in Geophysics, Springer, Vol. 33 N. 5, pp. 887-905, 2012.
Henry Calandra, Serge Gratton, Raphael Lago, Xavier Pinel, Xavier Vasseur
Two-Level preconditioned Krylov subspace methods for the solution of three-dimensional heterogeneous Helmholtz problems in seismics
In : Numerical Analysis and Applications, Springer, Vol. 5 N. 2, pp. 175-191, May 2012.
Serge Gratton, Pavel Jiranek, David Titley-Peloquin
On the accuracy of the Karlson-Walden estimate of the backward error for linear least squares problems
In : SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics (SIAM), USA, Vol. 33 N. 3, pp. 822-836, 2012.
Serge Gratton, Vincent Malmedy, Philippe Toint
Using approximate secant equations in limited memory methods for multilevel unconstrained optimization
In : Computational Optimization and Applications, Springer, Vol. 51 N. 3, pp. 967-979, 2012.
Henry Calandra, Serge Gratton, Julien Langou, Xavier Pinel, Xavier Vasseur
Flexible variants of block restarted GMRES methods with application to geophysics
In : SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics (SIAM), USA, Vol. 34 N. 2, pp. 714-736, 2012.
Guillaume Ramillien, Richard Biancale, Serge Gratton, Xavier Vasseur, Stéphane Bourgogne
GRACE-derived surface mass anomalies by energy integral approach. Application to continental hydrology
In : Journal of Geodesy, Springer, Vol. 85 N. 6, pp. 313-328, 2012.
Serge Gratton, Philippe Toint, Anke Troeltzsch
An active-set trust-region method for derivative-free nonlinear bound-constrained optimization
In : Optimization Methods and Software, Taylor & Francis Online, Vol. 21 N. 4-5, pp. 873-894, 2011.
Luis Carvalho, Serge Gratton, Raphael Lago, Xavier Vasseur
A flexible generalized conjugate residual method with inner orthogonalization and deflated restarting
In : SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics (SIAM), USA, Vol. 32 N. 4, pp. 1212-1235, 2011.
Serge Gratton, Mélodie Mouffe, Philippe Toint
Stopping rules and backward error analysis for bound-constrained optimization
In : Numerische Mathematik, Springer, Vol. 119, pp. 163-187, 2011.
Serge Gratton, Philippe Toint, Jean Tshimanga Ilunga
Range-Space Variants and Inexact Matrix-Vector Products in Krylov Solvers for Linear Systems Arising from Inverse Problems
In : SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics (SIAM), USA, Vol. 32 N. 3, pp. 969-986, 2011.
A contribution to the conditioning of the total least squares problem. SIAM Journal on Matrix Analysis and Applications
In : SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics (SIAM), USA, Vol. 32, pp. 685-699, 2011.
Serge Gratton, Annick Sartenaer, Jean Tshimanga Ilunga
On a class of limited memory preconditioners for large scale linear systems with multiple right-hand sides
In : SIAM Journal on Optimization, Society for Industrial and Applied Mathematics (SIAM), USA, Vol. 21 N. 3, pp. 912-935, 2011.
Serge Gratton, Patrick Laloyaux, Annick Sartenaer
A reduced and limited-memory preconditioned approach for the 4d-var data-assimilation problem
In : Quarterly Journal of the Royal Meteorological Society, Wiley, Vol. 137, pp. 452-466, 2011.
M’Barek Fares, Serge Gratton, Philippe Toint
Fast regularized linear sampling for inverse scattering problems,
In : Numerical Linear Algebra with Applications, Wiley, Vol. 18(1), pp. 55-68, 2011.
Luc Giraud, Serge Gratton, Xavier Pinel, Xavier Vasseur
Flexible GMRES with Deflated Restarting
In : SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics (SIAM), USA, Vol. 32 N. 4, pp. 1858-1878, 2010.
Mélodie Mouffe, Annick Sartenaer, Serge Gratton, Philippe Toint, Dimitri Tomanos
Numerical Experience with a Recursive Trust-Region Method for Multilevel Nonlinear Optimization.
In : , Vol. 25 N. 3, pp. 359-386, 2010 (to appear).
GNSS Networks in Algebraic Graph Theory
In : Journal of Global Positioning Systems, International Association of Chinese Professionals in Global Positioning Systems, China, Vol. 8 N. 1, pp. 1-23, 2010.
Using dual techniques to derive componentwise and mixed condition numbers for a linear functional of a linear least squares solution
In : BIT Numerical Mathematics, Springer, Vol. 49 N. 1, pp. 3-19, 2009.
Marc Baboulin, Luc Giraud, Serge Gratton, Julien Langou
Parallel tools for solving incremental dense least squares problems. application to space geodesy.
In : Journal of Algorithms and Computational Technology, Multi-Science Publishing, UK, Vol. 31 N. 1, pp. 117-131, 2009.
Abdellatif El Ghazi, Said El Hajji, Luc Giraud, Serge Gratton
Newton’s method for the common eigenvector problem
In : Journal of Computational and Applied Mathematics, Elsevier, Vol. 219 N. 2, pp. 398-407, 2008.
Valérie Frayssé, Luc Giraud, Serge Gratton
Algorithm 881: A set of FGMRES routines for real and complex arithmetics on high performance computers
In : ACM Transactions on Mathematical Software (TOMS), ACM : Association for Computing Machinery, New York, États-Unis, Vol. 35 N. 2, pp. 1-12, 2008.
Mario Arioli, Iain Duff, Serge Gratton, Stéphane Pralet
Note on GMRES Preconditionned by a Perturbed LDLt Decomposition with Static Pivoting. SIAM Journal on Scientific Computing
In : SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics (SIAM), USA, Vol. 25 N. 5, pp. 2024-2044, 2007.
Denis Mariano-Goulart, Pierre Maréchal, Serge Gratton, Luc Giraud, M. Fourcade
A priori selection of the regularization parameters in emission tomography by Fourier
In : Computerized Medical Imaging and Graphics, Elsevier Science, Vol. 31 N. 7, pp. 502-509, October 2007.
Marc Baboulin, Luc Giraud, Serge Gratton, Julien Langou
A distributed packed storage for large dense in-core parallel calculations
In : Concurrency and Computation:Practice and Experience, Wiley, Vol. 19 N. 4, pp. 483-502, 2007.
URL : http://www3.interscience.wiley.com/cgi-bin/jissue/114123131
BibTeXBruno Carpentieri, Luc Giraud, Serge Gratton
Additive and multiplicative two-level spectral preconditioning for general linear systems
In : SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics (SIAM), USA, Vol. 29 N. 4, pp. 1593-1612, 2007.
Luc Giraud, Serge Gratton, Julien Langou
Convergence in backward error of relaxed GMRES
In : SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics (SIAM), USA, Vol. 29 N. 2, pp. 710-728, April 2007.
Luc Giraud, Serge Gratton, Emeric Martin
Incremental spectral preconditioners for sequences of linear systems
In : Applied Numerical Mathematics, Elsevier, Vol. 57 N. 11-12, pp. 1164-1180, November 2007.
On the sensitivity of some spectral preconditioners
In : SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics (SIAM), USA, Vol. 27 N. 4, pp. 1089-1105, 2006.
Abstract URL : http://epubs.siam.org/SIMAX/vol_27_iss_4.html
BibTeXAmos Lawlesss, Serge Gratton, Nancy Nichols
An investigation of incremental 4D-Var using non-tangent linear models
In : Quarterly Journal of the Royal Meteorological Society, Wiley, Vol. 131, pp. 459-476, 2005.
Valérie Frayssé, Luc Giraud, Serge Gratton, Julien Langou
Algorithm 842: A set of GMRES routines for real and complex arithmetics on high performance computers
In : ACM Transactions on Mathematical Software (TOMS), ACM : Association for Computing Machinery, New York, États-Unis, Vol. 31 N. 2, pp. 228-238, 2005.
Luc Giraud, Serge Gratton, Julien Langou
A rank-k update procedure for reorthogonalizing the orthogonal factor from modified Gram-Schmidt
In : SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics (SIAM), USA, Vol. 25 N. 4, pp. 1163-11177, 2004.
On the condition number of linear least squares problems in a weighted Frobenius norm
In : BIT Numerical Mathematics, Springer, Vol. 36, pp. 523-530, 1996.
Adrien Rouvière, Lucas Pascal, Fabien Méry, Ehouarn Simon, Serge Gratton
Neural Prediction Model for Transition Onset of a Boundary-Layer in Presence of 2D Surface Defects (ODAS 2022)
22th ONERA-DLR Aerospace Symposium (ODAS 2022), Jun 2022, Hamburg, Germany. pp.1-10
Adrien Rouviere, Lucas Pascal, Fabien Méry, Ehouarn Simon, Serge Gratton
Neural prediction model for transition onset of a boundary-layer in presence of 2D surface defects
56th 3AF International Conference on Applied Aerodynamics (AERO 2022), Association Aéronautique et Astronautique de France (3AF), Mar 2022, Toulouse, France. pp.1073, ⟨10.2514/6.2022-1073⟩
Serge Gratton, Selime Gürol, Ehouarn Simon, Philippe Toint
Les algorithmes et la puissance de calcul dans les techniques de prévision pour les géosciences en grande dimension vus sous l’angle de l’optimisation mathématique
Colloque Modélisation : succès et limites (2016), Dec 2016, Paris, France. pp.37-47
Sylvain Mercier, Serge Gratton, Nicolas Tardieu, Xavier Vasseur
Enrichissement de préconditionneurs pour la résolution de systèmes linéaires symétriques indéfinis
12e Colloque national en calcul des structures, CSMA, May 2015, Giens, France
Luc Giraud, Serge Gratton, Julien Langou
Convergence in backward error of relaxed GMRES
In : Householder Symposium XVII, Zeuthen, Germany, 01/06/08-06/06/08.
Inexactness and flexibility in linear Krylov solvers
In : Matrix analysis and Applications, CIRM Luminy, 15/10/07-19/10/07 (invited speaker).
Luc Giraud, Serge Gratton, Xavier Pinel, Xavier Vasseur
Flexible GMRES with Deflated Restarting with Application for the Solution of the Helmoltz Equations
In : Minisymposium on Domain-Based and Krylov-Based Deflation Methods for Flow in Porous Media at the 2007 SIAM Conference on Mathematical and Computational Issues in the Geosciences, Santa Fe, New Mexico, 19/03/07-22/03/07 (invited speaker).
Luc Giraud, Serge Gratton, Xavier Pinel, Xavier Vasseur
Flexible GMRES with deflated restarting with application to a solution of the Helmholtz equation
In : ICIAM 2007, Minisymposium on Solution methods for sequences of linear systems and applications., Zurich, 16/07/07-20/07/07 (invited speaker).
Serge Gratton, Selime Gurol, Ehouarn Simon, Philippe Toint
Issues in making the weakly-constrained 4DVar formulation computationally efficient
Griewank, Andreas; Reich, Sebastian; Roulstone, Ian; Stuart, Andrew. Mathematical and Algorithmic Aspects of Data Assimilation in the Geosciences, 13 (4), Mathematisches Forschungsinstitut Oberwolfach, pp.2705-2748, 2017, Oberwolfach Reports, ISSN: 1660-8933. ⟨10.4171/OWR/2016/47⟩
Outils théoriques d’analyse du calcul à précision finie
Master’s Thesis, Institut National Polytechnique de Toulouse, June 1998.
Justin Reverdi, Sixin Zhang, Saïd Aoues, Fabrice Gamboa, Serge Gratton, Thomas Pellegrini
CNN-based Compressor Mass Flow Estimator in Industrial Aircraft Vapor Cycle System
2024
Jérémy Briant, Paul Mycek, Mayeul Destouches, Olivier Goux, Serge Gratton, Selime Gürol, Ehouarn Simon, Anthony Weaver
A filtered multilevel Monte Carlo method for estimating the expectation of discretized random fields
2023
Serge Gratton, Sadok Jerad, Philippe L. Toint
Yet another fast variant of Newton’s method for nonconvex optimization
2023
Serge Gratton, Valentin Mercier, Elisa Riccietti, Philippe L Toint
A Block-Coordinate Approach of Multi-level Optimization with an Application to Physics-Informed Neural Networks
2023
Serge Gratton, Philippe L. Toint
OFFO minimization algorithms for second-order optimality and their complexity
2022
Théo Beuzeville, Alfredo Buttari, Serge Gratton, Theo Mary, Erkan Ulker
Adversarial attacks via Sequential Quadratic Programming
2022
Serge Gratton, Sadok Jerad, Philippe L. Toint
Parametric complexity analysis for a class of first-order Adagrad-like algorithms
2022
Serge Gratton, Sadok Jerad, Philippe L. Toint
First-Order Objective-Function-Free Optimization Algorithms and Their Complexity
2022
Serge Gratton, Sadok Jerad, Philippe L. Toint
Convergence properties of an Objective-Function-Free Optimization regularization algorithm, including an $\mathcal{O}(\epsilon^{-3/2})$ complexity bound
2022
Théo Beuzeville, Pierre Boudier, Alfredo Buttari, Serge Gratton, Théo Mary, Stéphane Pralet
Adversarial attacks via backward error analysis
2021
Henri Calandra, Serge Gratton, Elisa Riccietti, Xavier Vasseur
On high-order multilevel optimization strategies
2020
Serge Gratton, Ehouarn Simon, David Titley-Peloquin, Philippe Toint
Exploiting variable precision in GMRES
2020