===

Papers in Journals

[88] S. Gratton, C. W. Royer, L. N. Vicente, and Z. Zhang, Complexity and global rates of trust-region methods based on probabilistic mode, to appear in IMA Journal of Numerical Analysis
[87] M. Fisher, S. Gratton, S. Gurol, Y. Trémolet, X. Vasseur Low rank updates in preconditioning the saddle point systems arising from data assimilation problems, to appear in Optimization Methods and Software
[86] S. Gratton, N. Soualmi, and L. N. Vicente, An indicator for the switch from derivative-free to derivative-based optimization, to appear in Operations Research Letters
[85] S. Eisenstadt, S. Gratton, D. Titley Peloquin On the symmetric componentwise relative backward error for linear systems of equations accepted in SIMAX
[84] S. Mercier, S. Gratton, N. Tardieu, X. Vasseur A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics accepted in Computational Mechanics
[83] E. Bergou, Y. Diouane, S. Gratton, On the use of the energy norm in trust-region and adaptive cubic regularization subproblems accepted in COAP.
[82] C. Estatico, S. Gratton, F. Lenti, D. Titley-Peloquin A conjugate gradient like method for p-norm minimization in functional spaces accepted in Numerische Mathematik.
[81] J. Mandel, E. Bergou, S. Gurol, S. Gratton, I. Kasanicky, Hybrid Levenberg-Marquardt and weak constraint ensemble Kalman smoother method, Nonlinear Processes in Geophysics, 23:59-73, 2016.
[80] S.Gratton, J. Tshimanga, On a second-order expansion of the truncated singular subspace decomposition, Numerical Linear Algebra with Applications, 23(3):519-534, 2016.
[79] S.Gratton, S.Mercier, N. Tardieu and X. Vasseur, Limited memory preconditioners for symmetric indefinite problems with application to structural mechanics, Numerical Linear Algebra with Applications, 23(5):865-887, 2016.
[78] E.Bergou, S. Gratton and L. N. Vicente, Levenberg-Marquardt methods based on probabilistic gradient models and inexact subproblem solution, with application to data assimilation SIAM/ASA., 4:924-951, 2016.
[77] Y. Diouane, S. Gratton, X. Vasseur, L. N. Vicente, and H. Calandra, A parallel evolution strategy for an Earth imaging problem in geophysics, Optimization and Engineering, 17(1);3-26, 2016.
[76] S. Gratton, C. W. Royer, and L. N. Vicente, A second-order globally convergent direct-search method and its worst-case complexity, Optimization, 65:1105-1128, 2016.
[75] S.Gratton, P. Henon, P. Jiranek and X. Vasseur, Reducing complexity of algebraic multigrid by aggregation, Numerical Linear Algebra with Applications, 23:501-518, 2016.
[74] Y. Diouane, S. Gratton, and L. N. Vicente, Globally convergent evolution strategies for constrained optimization, Computational Optimization and Applications, 62:323-346, 2015.
[73] Gratton, C. W. Royer, L. N. Vicente, and Z. Zhang, Direct search based on probabilistic descent, SIAM Journal on Optimization, 25:1249-1716, 2015
[72] Y. Diouane, S. Gratton, and L.N. Vicente, Globally convergent evolution strategies, Mathematical Programming, 152:467-490, 2015.
[71] S. Gratton, V. Malmedy, and Ph. L. Toint, Quasi-Newton updates with weighted secant equations, Optimization Methods and Software, 30(4):748-755, 2015.
[70] S. Gratton, M. Rincon-Camacho, E. Simon, and Ph. L. Toint, Observations thinning in data assimilation, EURO Journal on Computational Optimization, (1):31-51, 2015.
[69] G.L. Ramillien, F. Frappart, S. Gratton, and X. Vasseur, Sequential estimation of surface water mass changes from daily satellite gravimetry data, Journal of Geodesy, (89):259-282, 2015.
[68] S. Gratton and L.N. Vicente, A merit function approach for direct search SIAM J. Optim., 24(4):1980-1998, 2014.
[67] S. Gratton and L.N. Vicente, A surrogate management framework using rigorous trust-region steps, Optimization Methods and Software, 29(1):10-23, 2014.
[66] S. Gurol, A. T. Weaver, A. M. Moore, A. Piacentini, H. G. Arango, and S. Gratton, B-preconditioned minimization algorithms for variational data assimilation with the dual formulation, Quarterly Journal of the Royal Meteorological Society, 140(679):539-556, 2014.
[65] S. Gratton, D. Titley-Peloquin, P. Toint, and J. Tshimanga, Differentiating the method of conjugate gradients. SIAM Journal on Matrix Analysis and Applications, 35(1):110-126, 2014.
[64] S. Gratton and D. Titley-Peloquin, Stochastic conditioning of matrix functions, SIAM/ASA Journal on Uncertainty Quantification, 2(1):763-783, 2014
[63] S. Gratton, P. Laloyaux, A. Sartenaer, Derivative-free optimization for large-scale nonlinear data assimilation problems, Quarterly Journal of the Royal Meteorological Society, 140(680):943-957, 2014.
[62] E. Bergou, S. Gratton, and J. Tshimanga, The exact condition number of the truncated singular value solution of a linear ill-posed problem, SIAM Journal on Matrix Analysis and Applications, 35(3):1073-1085, 2014
[61] S. Gratton, Ph. L. Toint and J. Tshimanga, Conjugate-gradients versus multigrid solvers for diffusion-based correlation models in data assimilation, Quarterly Journal of the Royal Meteorological Society,139(675):1481-1487, 2013.
[60] S. Gratton, D. Titley-Peloquin, and J. Tshimanga, Sensitivity and conditioning of the truncated total least squares solution, SIAM Journal on Matrix Analysis and Applications, 34(3):1257-1276, 2013.
[59] S. Gratton, P. Jiranek, and X. Vasseur, Energy backward error: interpretation in numerical solution of elliptic partial differential equations and convergence of the conjugate gradient method, ETNA, 40:338-355, 2013.
[58] S. Gratton, P. Jiranek and D. Titley-Peloquin, Simple Backward Error Bounds for Linear Least-Squares Problems, Numerical Linear Algebra and Applications 439(1):78-89, 2013.
[57] S. Gratton, S. Gurol and Ph. L. Toint, Preconditioning and Globalizing Conjugate Gradients in Dual Space for Quadratically Penalized Nonlinear-Least Squares Problems, Computational Optimization and Applications, 54(1),1-25, 2013.
[56] H. Calandra, S. Gratton, X. Pinel, and X. Vasseur. An improved two-grid preconditioner for the solution of three-dimensional helmholtz problems in heterogeneous media. Numerical Linear Algebra with Applications, 20:663-688, 2013.
[55] H. Calandra, S. Gratton, R. Lago, X. Vasseur, and L. M. Carvalho, A modified block flexible gmres method with deflation at each iteration for the solution of non-hermitian linear systems with multiple right-hand sides, SIAM Journal on Scientific Computing, 35(5):S345-S367, 2013.
[54] G. L. Ramillien, L. Seoane, F. Frappart, R. Biancale, S. Gratton, X. Vasseur, and S. Bourgogne, Constrained regional recovery of continental water mass time-variations from GRACE-based geopotential anomalies, Surveys in Geophysics, 33(5):887-905, 2012
[53] S.Gratton, P.Jiranek and D.Titley-Peloquin On the Accuracy of the Karlson--Walden Estimate of the Backward Error for Linear Least Squares Problems SIAM Journal on Matrix Analysis and Applications, 33(3):822-936, 2012.
[52] S.Gratton, V.Malmedy and P.L.Toint, Using approximate secant equations in limited memory methods for multilevel unconstrained optimization, Computational Optimization and Applications, 51(3):967-979, 2012.
[51] H.Calandra, S.Gratton, R.Lago, X.Pinel and X.Vasseur, Two-Level preconditioned {K}rylov subspace methods for the solution of three-dimensional heterogeneous {H}elmholtz problems in seismics Numerical Analysis and Applications, 5(2):175-181, 2012.
[50] H.Calandra, S.~Gratton, J.Langou, X.Pinel and X.Vasseur, Flexible variants of block restarted {GMRES} methods with application to geophysics SIAM Journal on Scientific Computing, 34(2):714-736, 2012.
[49] M.Arioli and S.Gratton, Linear regression models, least-squares problems, normal equations, and stopping criteria for the conjugate gradient method Computer Physics Communications, 183(11): 2322-2336, 2012.
[48] L.M. Carvalho, S. Gratton, R. Lago, and X. Vasseur, A flexible generalized conjugate residual method with inner orthogonalization and deflated restarting, SIAM Journal on Matrix Analysis and Applications, 32(4):1212-1235, 2011.
[47] S. Gratton M. Mouffe et Ph. L. Toint, Stopping rules and backward error analysis for bound-constrained optimization, Numerische Mathematik, 119(163-187), 2011.
[46] S. Gratton, Ph. L. Toint and J. Tshimanga Ilunga, Inexact range-space Krylov solvers for linear systems arising from inverse problems, SIAM Journal on Matrix Analysis and Applications, 32(3):969-986, 2011.
[45] M. Baboulin, S. Gratton. A contribution to the conditioning of the total least squares problem. SIAM Journal on Matrix Analysis and Applications, 32:685-699, 2011.
[44] S. Gratton, A. Sartenaer, and J. Tshimanga, On a class of limited memory preconditioners for large scale linear systems with multiple right-hand sides SIAM Journal on Optimization, 21(3):912-935, 2011.
[43] S. Gratton, Ph. L. Toint et A. Troeltzch An active-set trust-region method for derivative-free nonlinear bound-constrained optimization, Optimization Methods and sotware, 21(4-5):873-894, 2011.
[42] G. Ramillien, R. Biancale, S. Gratton, X. Vasseur and S. Bourgogne, GRACE-derived surface mass anomalies by energy integral approach. Application to continental hydrology, Journal of Geodesy, 85(6):313-328, 2011.
[41] S. Gratton, P. Laloyaux, A. Sartenaer, and J. Tshimanga, A reduced and limited-memory preconditioned approach for the 4d-var data-assimilation problem. Quarterly Journal of the Royal Meteorological Society, 137(452-466), 2011
[40] B. Fares, S. Gratton and Ph. L. Toint, Fast regularized linear sampling for inverse scattering problems, Numerical Linear Algebra and Applications, vol. 18(1), pp. 55-68, 2011.
[39] A. Lannes and S. Gratton and S. Durand Pseudo-clock biases for precise point positioning. The algebraic approach. Journal of Global Positioning Systems, 9(1):68--77, 2010.
[38] L. Giraud and S. Gratton and X. Pinel and X. Vasseur Flexible GMRES with Deflated Restarting SIAM Journal on Scientific Computing, 32(4):1858--1878, 2010.
[37] S. Gratton and Ph. L. Toint. Approximate Invariant Subspaces and Quasi-Newton Optimization Optimization Methods and Software, 25(4):507--529, 2010.
[36] A. Lannes, S. Gratton. GNSS Networks in Algebraic Graph Theory. Journal of Global Positioning Systems, 8(1):1--23, 2009.
[35] S. Gratton, J. Tshimanga. An observation-space formulation of variational assimilation using a restricted preconditioned conjugate gradient algorithm. Q. J. Roy. Meterol. Soc., 135:1573--1585, 2009.
[34] B. Fares, S. Gratton and Ph. L. Toint. SVD-tail: a new linear-sampling reconstruction method for inverse scattering problems, Inverse Problems, 25(9)095013.1-19, 2009.
[33] A. Lannes, S. Gratton. QR Implementation of GNSS Centralized Approaches. Journal of Global Positioning Systems, 7(2):133--147, 2009.
[32] M. Baboulin, S. Gratton. Using dual techniques to derive componentwise and mixed condition numbers for a linear functional of a linear least squares solution. BIT 49(1):3-19, 2009.
[31] S. Gratton, M. Mouffe, A. Sartenaer, Ph.L. Toint, D. Tomanos. Numerical Experience with a Recursive Trust-Region Method for Multilevel Nonlinear Optimization. Optimization Methods and Software, vol. 25(3), pp. 359-386, 2010.
[30] M. Baboulin, J. Dongarra, S. Gratton, J. Langou. Computing the Conditioning of the Components of a Linear Least Squares Solution. NLAA , 16(7):517-533, 2009.
[29] S. Gratton, M. Mouffe, Ph.L. Toint, M. Weber-Mendonca. A recursive trust-region method in infinity norm for bound-constrained nonlinear optimization, IMA Journal of Numerical Analysis, vol. 28(4), pp. 827-861, 2008.
[28] A. El Ghazi, S.  El Hajji, L.  Giraud, S.  Gratton. Newton's method for the common eigenvector problem, accepted in Journal of Computational and Applied Mathematics. 219(2):398-407, 2008.
[27] J. Tshimanga, S. Gratton, A.T. Weaver, and A. Sartenaer. Limited-memory preconditioners with application to incremental four-dimensional variational data assimilation, Q. J. Roy. Meterol. Soc., 134, 753-771, 2008.
[26] F. Frayssé, L. Giraud, S. Gratton. A set of Flexible GMRES routines for real and complex arithmetics on high performance computers, ACM Trans. Math. Softw. 35(2), 1--12, 2008.
[25] S. Gratton, A. Sartenaer, Ph.L. Toint. Recursive Trust-Region Methods for Multiscale Nonlinear Optimization. SIAM J. on Optimization, (19)1:414--444, 2008.
[24] M. Arioli, I. Duff, S. Gratton, S. Pralet. Note on GMRES Preconditionned by a Perturbed LDLt Decomposition with Static Pivoting. SIAM Journal on Scientific Computing. (25)5:2024--2044, 2007.
[23] D. Mariano-Goulart, P. Marechal, S. Gratton, L. Giraud. A priori selection of the regularization parameters in emission tomography by Fourier synthesis. Computerized Medical Imaging and Graphics. (31)7:502--509, 2007.
[22] F. Bazan, S. Gratton. An explicit Jordan Decomposition of companion matrices. Tend. Mat. Apl. Comput. (7)2:209--218, 2006.
[21] M. Baboulin, L. Giraud, S. Gratton, J. Langou. Parallel tools for solving incremental dense least squares problems. Application to space geodesy. University of Tennessee Technical Report UT-CS-06-582 and CERFACS Technical Report TR/PA/06/63. Also appeared as LAPACK Working Note 179, September 2006. To appear in Advances in Engineering Software.
[20] L. Giraud, S. Gratton, E. Martin. Incremental spectral preconditioners for sequences of linear systems. Applied Numerical Mathematics. (57)11-12:1164--1180, 2007.
[19] I. Duff, S. Gratton, X. Pinel, X. Vasseur. Multigrid based preconditioners for the numerical solution of two-dimensional heterogeneous problems in geophysics. International Journal of Computer Mathematics . 84(8):1167--1181, 2007.
[18] B. Carpentieri, L. Giraud, S. Gratton. Additive and multiplicative two-level spectral preconditioning for general linear systems SIAM J. Scientific Computing. 29(4):1593--1612, 2007.
[17] S. Gratton, A. Lawless, N. Nichols. Approximate Gauss-Newton methods for nonlinear least squares problems. SIAM J. on Optimization . 18:106--132, 2007.
[16] L. Giraud, S. Gratton, J. Langou. Convergence in backward error of relaxed GMRES. SIAM J. Scientific Computing. 29(2):710--728, 2007.
[15] M. Arioli, M. Baboulin, S. Gratton. A partial condition number for linear least-squares problems. SIAM J. Matrix Analysis and Applications. 29(2):413--433, 2007.
[14] M. Baboulin, L. Giraud, S. Gratton, J. Langou. A distributed packed storage for large dense in-core parallel calculations Concurrency and Computation: Practice and Experience. 19(04),483--502, 2007.
[13] S. Gratton, A. Sartenaer, Ph.L. Toint. Second-order convergence properties of trust-region methods using incomplete curvature information, with an application to multigrid. Journal of Computational and Applied Mathematics. 24(06),676--692, 2006.
[12] L. Giraud, S. Gratton. On the sensitivity of some spectral preconditioners. SIAM J. Matrix Analysis and Applications, 27(04),1089--1105, 2006.
[11] M. Baboulin, L. Giraud, S. Gratton. A parallel distributed solver for large dense symmetric systems: applications to geodesy and electromagnetism problems. Int. J. High Speed Computing , 19(04),381--410, 2005.
[10] F. Frayssé, L. Giraud, S. Gratton, and J. Langou. A set of GMRES routines for real and complex arithmetics on high performance computers. ACM Trans. Math. Softw. , 31(2),228--238, 2005.
[9] A.S. Lawless, S. Gratton, and N.K. Nichols. An investigation of incremental 4d-var using non-tangent linear models. Quart. J. Royal Met. Soc. , 131,459--476, 2005.
[8] E. Anterrieu, S. Gratton, and B. Picard. Inverse problem in remote sensing by aperture synthesis imaging. Traitement du Signal , 21(1),1--16, 2004.
[7] A.S. Lawless, S. Gratton, and N.K. Nichols. Approximate iterative methods for variational data assimilation. Int. J. Numer. Methods in Fluids, 47,1129--1135, 2005.
[6] L. Giraud, S. Gratton, and J. Langou. A rank-k update procedure for reorthogonalizing the orthogonal factor from modified Gram-Schmidt. SIAM J. Matrix Analysis and Applications, 25(4),1163--1177, 2004.
[5] D. Laurichesse, S. Gratton, F. Mercier, T. Tournier, J.P. Berth ias, J.L. Issler, F. Doliszny, P. Revidon. Use of GNSS-Based Pseudo-Acceleration Measurements and Orbital C onstraints to Initialize Spaceborne Receiver Orbit Solutions Navigation Journal, 50(2),Summer, 2003.
[4] V. Frayssé, S. Gratton, and V. Toumazou. Structured backward error and condition number for linear systems of the type A*A x = b. BIT, 40(1):74-83, 2000.
[3] F. Chaitin-Chatelin and S. Gratton. On the condition number associated with the polar factorization of a rectangular matrix. Numerical Linear Algebra with Applications, (7):337-354, 2000.
[2] S. Gratton. On the condition number of linear least squares problems in a weighted Frobenius norm. BIT, 36:523-530, 1996.
[1] F. Chaitin-Chatelin and S. Gratton. Convergence of successive iteration methods in finite precision under high nonnormality. BIT, 36:455-469, 1996.
===

Technical reports

[1] S. Gratton, V. Frayssé, and V. Toumazou. Structured backward error and condition number for linear systems of the type A*A x = b. Technical Report TR/PA/99/05, 1999. Preliminary version of the article published in BIT, vol. 40, nber 1, pp 74-83.
[2] S. Gratton, V. Frayssé, and V. Toumazou. On a structured backward error analysis for linear systems of the type A*A x = b. Technical Report TR/PA/98/01, 1998. Preliminary version of the article published in BIT, vol. 40, nber 1, pp 74-83.
[3] S. Gratton. Outils théoriques d'analyse du calcul à précision finie. Ph.D. dissertation, Institut National Polytechnique de Toulouse, June 1998. TH/PA/98/30.
[4] V. Frayssé, L. Giraud, and S. Gratton. A set of Flexible-GMRES routines for real and complex arithmetics. Technical Report TR/PA/98/20, 1998.
[5] F. Chaitin-Chatelin and S. Gratton. A note on the convergence of Gauss-Newton algorithm. Technical Report TR/PA/98/27, 1998.
[6] F. Chaitin-Chatelin and S. Gratton. About the distance to singularity for polynomials in one variable. Technical Report TR/PA/98/26, 1998.
[7] F. Chaitin-Chatelin and S. Gratton. On the condition number associated with the polar factorization of a rectangular matrix. Technical Report TR/PA/98/25, 1998. Preliminary version of the article published in Numerical Linear Algebra with Applications, vol. 7, pp 337-354.
[8] V. Frayssé, L. Giraud, and S. Gratton. A set of GMRES routines for real and complex arithmetics. Technical Report TR/PA/97/49, 1997.
[9] V. Frayssé, S. Gratton, and V. Toumazou. Note on the conditioning of linear systems of the kind A*Ax = b. Technical Report TR/PA/96/17, 1996.
[10] S. Gratton. On the condition number of linear least squares problems in Frobenius norm. Technical Report TR/PA/95/27, 1995. Preliminary version of the article published in BIT, vol. 36, pp 523-530.
[11] L. Giraud and S. Gratton. Solveurs linéaires performants pour la résolution de systèmes complexes non hermitiens creux de grande taille. Technical Report TR/PA/95/24, 1995.
[12] F. Chaitin-Chatelin and S. Gratton. Convergence in finite precision of successive iteration methods under high nonnormality. Technical Report TR/PA/95/43, 1995. Preliminary version of the article published in BIT, vol. 36, pp 455-469.
[13] S. Gratton. Moindres carrés pour l'orbitographie. Etude de la stabilité. Technical Report TR/PA/94/17, 1994.


===

Contract reports

[1] F. Chaitin-Chatelin, V. Frayssé, and S. Gratton. Traitement d'ambiguïtés entières : Rapport intermédiaire. Contract Report IR/PA/98/54, 1998.
[2] F. Chaitin-Chatelin, V. Frayssé, and S. Gratton. Fiabilité des calculs en précision finie : principes et mise en oeuvre. Contract Report FR/PA/97/55, 1997.
[3] F. Chaitin-Chatelin and S. Gratton. Etude de la non convergence de Gauss-Newton. Contract Report IR/PA/97/14, 1997.
[4] S. Gratton. Conditionnement en Optimisation. Etude bibliographique. Contract Report FR/PA/96/36, 1996.
[5] V. Frayssé, L. Giraud, and S. Gratton. Solveurs linéaires itératifs pour la résolution de systèmes complexes non hermitiens creux de grande taille. Contract Report FR/PA/96/34, 1996.
[6] S. Gratton. Moindres carrés pour l'orbitographie - Etude de stabilité. Contract Report IR/PA/95/20, 1995.
[7] F. Collino, S. Ghanemi, L. Giraud, S. Gratton, M. Invernizzi, P. Joly, and A. Piacentini. Rapport de fin de contrat Thomson: Résolution des équations de Maxwell tridimensionnelles dans le domaine fréquentiel sur réseaux hétérogènes de calculateurs. Technical Report FR/EL-PA/95/25, 1995.
[8] V. Frayssé and S. Gratton. Moindres carrés pour l'orbitographie - Etude de stabilité - Partie II. Contract Report FR/PA/95/28, 1995.


===

Proceedings and conferences

[1] J.-P. berthias and P. Broca and S. Gratton and and S. Houry and F. Mercier and A . Piuzzi. Comparison of Jason1 GPS-Doris-Laser orbits. Poster in the Science Working Team Meeting, Biarritz, June 2002
[2] C. Ferrier and S. Gratton and and F. Mercier Radiation pressure modeling of Jason1 and empirical parametrization. Poster in the Science Working Team Meeting, Biarritz, June 2002
[3] J.-P. berthias and P. Broca and S. Gratton and and S. Houry and F. Mercier and A. Piuzzi. Effects of Jason1 attitude processing (measured versus predicted ) Poster in the Science Working Team Meeting, Biarritz, June 2002
[4] J.P. Berthias, P. Broca, A. Comps, S. Gratton, D. Laurichesse, F. Mercier "Lessons Learned From The Use Of A GPS Receiver In Less Than Optimal Conditions" 16th International Symposium on Space Flight Dynamics, Pasadena, 3-7 December 2001.
[5] J. P. Berthias and P. broca and S. Gratton and F. Mercier. Combinig DORIS, SLR and GPS data to obtain maximum accuracy orbit for Jason1. Proceedings of the International Symposium on space Dynamics 26-30 june 2000, Biarritz.

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