# zbMATH — the first resource for mathematics

## Gratton, Serge

Compute Distance To:
 Author ID: gratton.serge Published as: Gratton, Serge; Gratton, S. Homepage: http://www.cerfacs.fr/~gratton/ External Links: MGP · Math-Net.Ru · ResearchGate · dblp
 Documents Indexed: 84 Publications since 1996
all top 5

#### Co-Authors

 1 single-authored 18 Toint, Philippe L. 17 Vasseur, Xavier 12 Vicente, Luis Nunes 10 Giraud, Luc 9 Titley-Péloquin, David 8 Calandra, Henri 6 Langou, Julien 5 Baboulin, Marc 5 Bergou, El Houcine 5 Diouane, Youssef 5 Pinel, Xavier 5 Royer, Clément W. 4 Jiránek, Pavel 4 Sartenaer, Annick 3 Arioli, Mario 3 Gürol, Selime 3 Lago, Rafael 3 Mouffe, Mélodie 3 Riccietti, Elisa 3 Simon, Ehouarn 3 Zhang, Zaikun 2 Carvalho, Luiz Mariano 2 Chaitin-Chatelin, Françoise 2 Duff, Iain S. 2 El Ghazi, Abdellatif 2 Elhajji, Said 2 Fares, M’Barek 2 Frayssé, Valérie 2 Ilunga, Jean Tshimanga 2 Lawless, Amos S. 2 Malmedy, Vincent 2 Mercier, Sylvain 2 Nichols, Nancy K. 2 Tardieu, Nicolas 2 Tshimanga, Jean 1 Anterrieu, Éric 1 Bellavia, Stefania 1 Bocquet, Marc 1 Bodart, Julien 1 Carpentieri, Bruno 1 Dongarra, Jack J. 1 Eisenstat, Stanley C. 1 Estatico, Claudio 1 Fillion, Anthony 1 Fisher, Mike 1 Hénon, Pascal 1 Lenti, Flavia 1 Lunet, Thibaut 1 Mandel, Jan 1 Picard, B. 1 Pralet, Stéphane 1 Rincon-Camacho, Monserrat 1 Sakov, Pavel 1 Soualmi, N. 1 Tomanos, Dimitri 1 Toumazou, V. 1 Trémolet, Yannick 1 Tröltzsch, Anke 1 Tshimanga-Ilunga, J. 1 Viloche Bazán, Fermín S. 1 Weber-Mendonça, Melissa
all top 5

#### Serials

 13 SIAM Journal on Matrix Analysis and Applications 8 Numerical Linear Algebra with Applications 6 SIAM Journal on Optimization 6 Computational Optimization and Applications 6 SIAM Journal on Scientific Computing 6 Optimization Methods & Software 4 BIT 3 Numerische Mathematik 3 Mathematical Programming. Series A. Series B 3 SIAM/ASA Journal on Uncertainty Quantification 2 IMA Journal of Numerical Analysis 2 Applied Numerical Mathematics 1 Computer Physics Communications 1 International Journal for Numerical Methods in Fluids 1 Inverse Problems 1 ACM Transactions on Mathematical Software 1 Journal of Computational and Applied Mathematics 1 Journal of Optimization Theory and Applications 1 Operations Research Letters 1 Journal of Computational Mathematics 1 Optimization 1 Traitement du Signal 1 Computational Mechanics 1 International Journal of Computer Mathematics 1 Linear Algebra and its Applications 1 ETNA. Electronic Transactions on Numerical Analysis 1 Computing and Visualization in Science 1 Sibirskiĭ Zhurnal Vychislitel’noĭ Matematiki 1 Optimization and Engineering 1 TEMA. Tendências em Matemática Aplicada e Computacional 1 Journal of Algorithms & Computational Technology 1 EURO Journal on Computational Optimization
all top 5

#### Fields

 60 Numerical analysis (65-XX) 32 Operations research, mathematical programming (90-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 8 Partial differential equations (35-XX) 6 Geophysics (86-XX) 4 Systems theory; control (93-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Computer science (68-XX) 3 Mechanics of deformable solids (74-XX) 3 Optics, electromagnetic theory (78-XX) 2 Statistics (62-XX) 2 Fluid mechanics (76-XX) 1 Operator theory (47-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH Open

73 Publications have been cited 480 times in 339 Documents Cited by Year
Recursive trust-region methods for multiscale nonlinear optimization. Zbl 1163.90024
Gratton, Serge; Sartenaer, Annick; Toint, Philippe L.
2008
Algorithm 842: A set of GMRES routines for real and complex arithmetics on high performance computers. Zbl 1070.65527
Frayssé, Valéire; Giraud, Luc; Gratton, Serge; Langou, Julien
2005
On a class of limited memory preconditioners for large scale linear systems with multiple right-hand sides. Zbl 1273.65044
Gratton, S.; Sartenaer, A.; Tshimanga, J.
2011
On the condition number of linear least squares problems in a weighted Frobenius norm. Zbl 0878.65030
Gratton, S.
1996
An active-set trust-region method for derivative-free nonlinear bound-constrained optimization. Zbl 1229.90138
Gratton, Serge; Toint, Philippe L.; Tröltzsch, Anke
2011
Approximate Gauss-Newton methods for nonlinear least squares problems. Zbl 1138.65046
Gratton, S.; Lawless, A. S.; Nichols, N. K.
2007
A partial condition number for linear least squares problems. Zbl 1141.65028
Arioli, Mario; Baboulin, Marc; Gratton, Serge
2008
Flexible GMRES with deflated restarting. Zbl 1215.65057
Giraud, L.; Gratton, S.; Pinel, X.; Vasseur, X.
2010
Numerical experience with a recursive trust-region method for multilevel nonlinear bound-constrained optimization. Zbl 1190.90209
Gratton, Serge; Mouffe, Mélodie; Sartenaer, Annick; Toint, Philippe L.; Tomanos, Dimitri
2010
A contribution to the conditioning of the total least-squares problem. Zbl 1242.65087
Baboulin, Marc; Gratton, Serge
2011
Flexible variants of block restarted GMRES methods with application to geophysics. Zbl 1248.65036
Calandra, Henri; Gratton, Serge; Langou, Julien; Pinel, Xavier; Vasseur, Xavier
2012
Incremental spectral preconditioners for sequences of linear systems. Zbl 1123.65031
Giraud, L.; Gratton, S.; Martin, E.
2007
Direct search based on probabilistic descent. Zbl 1327.90395
Gratton, S.; Royer, C. W.; Vicente, L. N.; Zhang, Z.
2015
A recursive $$\ell_{\infty}$$-trust-region method for bound-constrained nonlinear optimization. Zbl 1156.65060
Gratton, Serge; Mouffe, Mélodie; Toint, Philippe L.; Weber-Mendonça, Melissa
2008
An improved two-grid preconditioner for the solution of three-dimensional Helmholtz problems in heterogeneous media. Zbl 1313.65284
Calandra, Henri; Gratton, Serge; Pinel, Xavier; Vasseur, Xavier
2013
On the condition numbers associated with the polar factorization of a matrix. Zbl 1051.65052
Chaitin-Chatelin, F.; Gratton, S.
2000
A modified block flexible GMRES method with deflation at each iteration for the solution of non-Hermitian linear systems with multiple right-hand sides. Zbl 1281.65056
Calandra, Henri; Gratton, Serge; Lago, Rafael; Vasseur, Xavier; Carvalho, Luiz Mariano
2013
Using dual techniques to derive componentwise and mixed condition numbers for a linear function of a linear least squares solution. Zbl 1168.65022
Baboulin, Marc; Gratton, Serge
2009
A flexible generalized conjugate residual method with inner orthogonalization and deflated restarting. Zbl 1244.65047
Carvalho, Luiz M.; Gratton, Serge; Lago, R.; Vasseur, Xavier
2011
Additive and multiplicative two-level spectral preconditioning for general linear systems. Zbl 1145.65023
Carpentieri, B.; Giraud, L.; Gratton, S.
2007
A merit function approach for direct search. Zbl 1318.90077
Gratton, S.; Vicente, L. N.
2014
Computing the conditioning of the components of a linear least-squares solution. Zbl 1224.65104
Baboulin, Marc; Dongarra, Jack; Gratton, Serge; Langou, Julien
2009
Sensitivity and conditioning of the truncated total least squares solution. Zbl 1312.65060
Gratton, Serge; Titley-Peloquin, David; Ilunga, Jean Tshimanga
2013
Two-level preconditioned Krylov subspace methods for the solution of three-dimensional heterogeneous Helmholtz problems in seismics. Zbl 1299.65253
Calandra, Henri; Gratton, Serge; Lago, Rafael; Pinel, Xavier; Vasseur, Xavier
2012
A note on GMRES preconditioned by a perturbed $$LDL^T$$ decomposition with static pivoting. Zbl 1161.65023
Arioli, M.; Duff, I. S.; Gratton, S.; Pralet, S.
2007
A conjugate gradient like method for $$p$$-norm minimization in functional spaces. Zbl 1379.65029
Estatico, Claudio; Gratton, Serge; Lenti, Flavia; Titley-Peloquin, David
2017
On the use of the energy norm in trust-region and adaptive cubic regularization subproblems. Zbl 1390.90511
Bergou, E.; Diouane, Y.; Gratton, S.
2017
Approximate iterative methods for variational data assimilation. Zbl 1066.65066
Lawless, A. S.; Gratton, S.; Nichols, N. K.
2005
Convergence in backward error of relaxed GMRES. Zbl 1142.65031
Giraud, L.; Gratton, S.; Langou, J.
2007
A line-search algorithm inspired by the adaptive cubic regularization framework and complexity analysis. Zbl 1417.90097
Bergou, El Houcine; Diouane, Youssef; Gratton, Serge
2018
On the sensitivity of some spectral preconditioners. Zbl 1104.65040
Giraud, L.; Gratton, S.
2006
The exact condition number of the truncated singular value solution of a linear ill-posed problem. Zbl 1308.65059
Bergou, El Houcine; Gratton, Serge; Tshimanga, Jean
2014
Levenberg-Marquardt methods based on probabilistic gradient models and inexact subproblem solution, with application to data assimilation. Zbl 1358.90156
Bergou, E.; Gratton, S.; Vicente, L. N.
2016
Limited memory preconditioners for symmetric indefinite problems with application to structural mechanics. Zbl 1413.65041
Gratton, Serge; Mercier, Sylvain; Tardieu, Nicolas; Vasseur, Xavier
2016
Improved bounds for small-sample estimation. Zbl 1451.65044
Gratton, Serge; Titley-Peloquin, David
2018
Multigrid based preconditioners for the numerical solution of two-dimensional heterogeneous problems in geophysics. Zbl 1123.65030
Duff, I.; Gratton, S.; Pinel, X.; Vasseur, X.
2007
SVD-tail: A new linear-sampling reconstruction method for inverse scattering problems. Zbl 1175.65129
Fares, M’Barek; Gratton, Serge; Toint, Philippe L.
2009
Parallel tools for solving incremental dense least squares problems: application to space geodesy. Zbl 1226.65029
Baboulin, Marc; Giraud, Luc; Gratton, Serge; Langou, Julien
2009
Stopping rules and backward error analysis for bound-constrained optimization. Zbl 1228.65088
Gratton, Serge; Mouffe, Mélodie; Toint, Philippe L.
2011
Globally convergent evolution strategies. Zbl 1334.90209
Diouane, Y.; Gratton, S.; Vicente, L. N.
2015
Globally convergent evolution strategies for constrained optimization. Zbl 1326.90079
Diouane, Y.; Gratton, S.; Vicente, L. N.
2015
On the accuracy of the Karlson-Waldén estimate of the backward error for linear least squares problems. Zbl 1268.65055
Gratton, Serge; Jiránek, Pavel; Titley-Peloquin, David
2012
Stochastic conditioning of matrix functions. Zbl 1306.65199
Gratton, Serge; Titley-Peloquin, David
2014
Direct search based on probabilistic feasible descent for bound and linearly constrained problems. Zbl 1420.90083
Gratton, S.; Royer, C. W.; Vicente, L. N.; Zhang, Z.
2019
A second-order globally convergent direct-search method and its worst-case complexity. Zbl 1338.90463
Gratton, S.; Royer, C. W.; Vicente, L. N.
2016
Reducing complexity of algebraic multigrid by aggregation. Zbl 1413.65444
Gratton, Serge; Hénon, Pascal; Jiránek, Pavel; Vasseur, Xavier
2016
Convergence in finite precision of successive iteration methods under high nonnormality. Zbl 0864.65015
Chaitin-Chatelin, F.; Gratton, S.
1996
Structured backward error and condition number for linear systems of the type $$A^* Ax = b$$. Zbl 0958.65054
Frayssé, V.; Gratton, S.; Toumazou, V.
2000
Approximate invariant subspaces and quasi-Newton optimization methods. Zbl 1202.90272
Gratton, Serge; Toint, Philippe L.
2010
Differentiating the method of conjugate gradients. Zbl 1306.65180
Gratton, Serge; Titley-Peloquin, David; Toint, Philippe; Ilunga, Jean Tshimanga
2014
Range-space variants and inexact matrix-vector products in Krylov solvers for linear systems arising from inverse problems. Zbl 1237.65033
Gratton, S.; Toint, Ph. L.; Ilunga, J. Tshimanga
2011
Preconditioning and globalizing conjugate gradients in dual space for quadratically penalized nonlinear-least squares problems. Zbl 1267.90093
Gratton, Serge; Gürol, Selime; Toint, Philippe L.
2013
Simple backward error bounds for linear least-squares problems. Zbl 1281.65065
Gratton, Serge; Jiránek, Pavel; Titley-Peloquin, David
2013
A surrogate management framework using rigorous trust-region steps. Zbl 1282.65067
Gratton, S.; Vicente, L. N.
2014
A parallel evolution strategy for an Earth imaging problem in geophysics. Zbl 1364.86009
Diouane, Y.; Gratton, S.; Vasseur, X.; Vicente, L. N.; Calandra, H.
2016
A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity. Zbl 1398.65047
Mercier, Sylvain; Gratton, Serge; Tardieu, Nicolas; Vasseur, Xavier
2017
Quasi-Newton updates with weighted secant equations. Zbl 1356.90162
Gratton, S.; Malmedy, V.; Toint, Ph. L.
2015
A Levenberg-Marquardt method for large nonlinear least-squares problems with dynamic accuracy in functions and gradients. Zbl 1461.65129
Bellavia, Stefania; Gratton, Serge; Riccietti, Elisa
2018
On a second-order expansion of the truncated singular subspace decomposition. Zbl 1413.15022
Gratton, S.; Tshimanga-Ilunga, J.
2016
Second-order convergence properties of trust-region methods using incomplete curvature information, with an application to multigrid optimization. Zbl 1132.65054
Gratton, Serge; Sartenaer, Annick; Toint, Philippe L.
2006
Fast regularized linear sampling for inverse scattering problems. Zbl 1245.65121
Fares, M’Barek; Gratton, Serge; Toint, Philippe L.
2011
Using approximate secant equations in limited memory methods for multilevel unconstrained optimization. Zbl 1245.90122
Gratton, Serge; Malmedy, Vincent; Toint, Philippe L.
2012
Energy backward error: interpretation in numerical solution of elliptic partial differential equations and behaviour in the conjugate gradient method. Zbl 1290.65029
Gratton, Serge; Jiránek, Pavel; Vasseur, Xavier
2013
A geometric multigrid preconditioner for the solution of the Helmholtz equation in three-dimensional heterogeneous media on massively parallel computers. Zbl 1364.86008
Calandra, H.; Gratton, S.; Vasseur, X.
2017
On the symmetric componentwise relative backward error for linear systems of equations. Zbl 1387.65040
Eisenstat, Stanley C.; Gratton, Serge; Titley-Peloquin, David
2017
Observation thinning in data assimilation computations. Zbl 1307.90104
Gratton, Serge; Rincon-Camacho, Monserrat; Simon, Ehouarn; Toint, Philippe L.
2015
A decoupled first/second-order steps technique for nonconvex nonlinear unconstrained optimization with improved complexity bounds. Zbl 1437.90130
Gratton, S.; Royer, C. W.; Vicente, L. N.
2020
Time-parallel simulation of the decay of homogeneous turbulence using Parareal with spatial coarsening. Zbl 1396.76044
Lunet, Thibaut; Bodart, Julien; Gratton, Serge; Vasseur, Xavier
2018
On the convergence of a non-linear ensemble Kalman smoother. Zbl 1409.93066
Bergou, El Houcine; Gratton, Serge; Mandel, Jan
2019
Low rank updates in preconditioning the saddle point systems arising from data assimilation problems. Zbl 1398.90178
Fisher, M.; Gratton, S.; Gürol, S.; Trémolet, Y.; Vasseur, X.
2018
A note on solving nonlinear optimization problems in variable precision. Zbl 1446.90149
Gratton, S.; Toint, Ph. L.
2020
On iterative solution of the extended normal equations. Zbl 1461.65035
Calandra, Henri; Gratton, Serge; Riccietti, Elisa; Vasseur, Xavier
2020
On high-order multilevel optimization strategies. Zbl 1458.90586
Calandra, Henri; Gratton, Serge; Riccietti, Elisa; Vasseur, Xavier
2021
On high-order multilevel optimization strategies. Zbl 1458.90586
Calandra, Henri; Gratton, Serge; Riccietti, Elisa; Vasseur, Xavier
2021
A decoupled first/second-order steps technique for nonconvex nonlinear unconstrained optimization with improved complexity bounds. Zbl 1437.90130
Gratton, S.; Royer, C. W.; Vicente, L. N.
2020
A note on solving nonlinear optimization problems in variable precision. Zbl 1446.90149
Gratton, S.; Toint, Ph. L.
2020
On iterative solution of the extended normal equations. Zbl 1461.65035
Calandra, Henri; Gratton, Serge; Riccietti, Elisa; Vasseur, Xavier
2020
Direct search based on probabilistic feasible descent for bound and linearly constrained problems. Zbl 1420.90083
Gratton, S.; Royer, C. W.; Vicente, L. N.; Zhang, Z.
2019
On the convergence of a non-linear ensemble Kalman smoother. Zbl 1409.93066
Bergou, El Houcine; Gratton, Serge; Mandel, Jan
2019
A line-search algorithm inspired by the adaptive cubic regularization framework and complexity analysis. Zbl 1417.90097
Bergou, El Houcine; Diouane, Youssef; Gratton, Serge
2018
Improved bounds for small-sample estimation. Zbl 1451.65044
Gratton, Serge; Titley-Peloquin, David
2018
A Levenberg-Marquardt method for large nonlinear least-squares problems with dynamic accuracy in functions and gradients. Zbl 1461.65129
Bellavia, Stefania; Gratton, Serge; Riccietti, Elisa
2018
Time-parallel simulation of the decay of homogeneous turbulence using Parareal with spatial coarsening. Zbl 1396.76044
Lunet, Thibaut; Bodart, Julien; Gratton, Serge; Vasseur, Xavier
2018
Low rank updates in preconditioning the saddle point systems arising from data assimilation problems. Zbl 1398.90178
Fisher, M.; Gratton, S.; Gürol, S.; Trémolet, Y.; Vasseur, X.
2018
A conjugate gradient like method for $$p$$-norm minimization in functional spaces. Zbl 1379.65029
Estatico, Claudio; Gratton, Serge; Lenti, Flavia; Titley-Peloquin, David
2017
On the use of the energy norm in trust-region and adaptive cubic regularization subproblems. Zbl 1390.90511
Bergou, E.; Diouane, Y.; Gratton, S.
2017
A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity. Zbl 1398.65047
Mercier, Sylvain; Gratton, Serge; Tardieu, Nicolas; Vasseur, Xavier
2017
A geometric multigrid preconditioner for the solution of the Helmholtz equation in three-dimensional heterogeneous media on massively parallel computers. Zbl 1364.86008
Calandra, H.; Gratton, S.; Vasseur, X.
2017
On the symmetric componentwise relative backward error for linear systems of equations. Zbl 1387.65040
Eisenstat, Stanley C.; Gratton, Serge; Titley-Peloquin, David
2017
Levenberg-Marquardt methods based on probabilistic gradient models and inexact subproblem solution, with application to data assimilation. Zbl 1358.90156
Bergou, E.; Gratton, S.; Vicente, L. N.
2016
Limited memory preconditioners for symmetric indefinite problems with application to structural mechanics. Zbl 1413.65041
Gratton, Serge; Mercier, Sylvain; Tardieu, Nicolas; Vasseur, Xavier
2016
A second-order globally convergent direct-search method and its worst-case complexity. Zbl 1338.90463
Gratton, S.; Royer, C. W.; Vicente, L. N.
2016
Reducing complexity of algebraic multigrid by aggregation. Zbl 1413.65444
Gratton, Serge; Hénon, Pascal; Jiránek, Pavel; Vasseur, Xavier
2016
A parallel evolution strategy for an Earth imaging problem in geophysics. Zbl 1364.86009
Diouane, Y.; Gratton, S.; Vasseur, X.; Vicente, L. N.; Calandra, H.
2016
On a second-order expansion of the truncated singular subspace decomposition. Zbl 1413.15022
Gratton, S.; Tshimanga-Ilunga, J.
2016
Direct search based on probabilistic descent. Zbl 1327.90395
Gratton, S.; Royer, C. W.; Vicente, L. N.; Zhang, Z.
2015
Globally convergent evolution strategies. Zbl 1334.90209
Diouane, Y.; Gratton, S.; Vicente, L. N.
2015
Globally convergent evolution strategies for constrained optimization. Zbl 1326.90079
Diouane, Y.; Gratton, S.; Vicente, L. N.
2015
Quasi-Newton updates with weighted secant equations. Zbl 1356.90162
Gratton, S.; Malmedy, V.; Toint, Ph. L.
2015
Observation thinning in data assimilation computations. Zbl 1307.90104
Gratton, Serge; Rincon-Camacho, Monserrat; Simon, Ehouarn; Toint, Philippe L.
2015
A merit function approach for direct search. Zbl 1318.90077
Gratton, S.; Vicente, L. N.
2014
The exact condition number of the truncated singular value solution of a linear ill-posed problem. Zbl 1308.65059
Bergou, El Houcine; Gratton, Serge; Tshimanga, Jean
2014
Stochastic conditioning of matrix functions. Zbl 1306.65199
Gratton, Serge; Titley-Peloquin, David
2014
Differentiating the method of conjugate gradients. Zbl 1306.65180
Gratton, Serge; Titley-Peloquin, David; Toint, Philippe; Ilunga, Jean Tshimanga
2014
A surrogate management framework using rigorous trust-region steps. Zbl 1282.65067
Gratton, S.; Vicente, L. N.
2014
An improved two-grid preconditioner for the solution of three-dimensional Helmholtz problems in heterogeneous media. Zbl 1313.65284
Calandra, Henri; Gratton, Serge; Pinel, Xavier; Vasseur, Xavier
2013
A modified block flexible GMRES method with deflation at each iteration for the solution of non-Hermitian linear systems with multiple right-hand sides. Zbl 1281.65056
Calandra, Henri; Gratton, Serge; Lago, Rafael; Vasseur, Xavier; Carvalho, Luiz Mariano
2013
Sensitivity and conditioning of the truncated total least squares solution. Zbl 1312.65060
Gratton, Serge; Titley-Peloquin, David; Ilunga, Jean Tshimanga
2013
Preconditioning and globalizing conjugate gradients in dual space for quadratically penalized nonlinear-least squares problems. Zbl 1267.90093
Gratton, Serge; Gürol, Selime; Toint, Philippe L.
2013
Simple backward error bounds for linear least-squares problems. Zbl 1281.65065
Gratton, Serge; Jiránek, Pavel; Titley-Peloquin, David
2013
Energy backward error: interpretation in numerical solution of elliptic partial differential equations and behaviour in the conjugate gradient method. Zbl 1290.65029
Gratton, Serge; Jiránek, Pavel; Vasseur, Xavier
2013
Flexible variants of block restarted GMRES methods with application to geophysics. Zbl 1248.65036
Calandra, Henri; Gratton, Serge; Langou, Julien; Pinel, Xavier; Vasseur, Xavier
2012
Two-level preconditioned Krylov subspace methods for the solution of three-dimensional heterogeneous Helmholtz problems in seismics. Zbl 1299.65253
Calandra, Henri; Gratton, Serge; Lago, Rafael; Pinel, Xavier; Vasseur, Xavier
2012
On the accuracy of the Karlson-Waldén estimate of the backward error for linear least squares problems. Zbl 1268.65055
Gratton, Serge; Jiránek, Pavel; Titley-Peloquin, David
2012
Using approximate secant equations in limited memory methods for multilevel unconstrained optimization. Zbl 1245.90122
Gratton, Serge; Malmedy, Vincent; Toint, Philippe L.
2012
On a class of limited memory preconditioners for large scale linear systems with multiple right-hand sides. Zbl 1273.65044
Gratton, S.; Sartenaer, A.; Tshimanga, J.
2011
An active-set trust-region method for derivative-free nonlinear bound-constrained optimization. Zbl 1229.90138
Gratton, Serge; Toint, Philippe L.; Tröltzsch, Anke
2011
A contribution to the conditioning of the total least-squares problem. Zbl 1242.65087
Baboulin, Marc; Gratton, Serge
2011
A flexible generalized conjugate residual method with inner orthogonalization and deflated restarting. Zbl 1244.65047
Carvalho, Luiz M.; Gratton, Serge; Lago, R.; Vasseur, Xavier
2011
Stopping rules and backward error analysis for bound-constrained optimization. Zbl 1228.65088
Gratton, Serge; Mouffe, Mélodie; Toint, Philippe L.
2011
Range-space variants and inexact matrix-vector products in Krylov solvers for linear systems arising from inverse problems. Zbl 1237.65033
Gratton, S.; Toint, Ph. L.; Ilunga, J. Tshimanga
2011
Fast regularized linear sampling for inverse scattering problems. Zbl 1245.65121
Fares, M&rsquo;Barek; Gratton, Serge; Toint, Philippe L.
2011
Flexible GMRES with deflated restarting. Zbl 1215.65057
Giraud, L.; Gratton, S.; Pinel, X.; Vasseur, X.
2010
Numerical experience with a recursive trust-region method for multilevel nonlinear bound-constrained optimization. Zbl 1190.90209
Gratton, Serge; Mouffe, Mélodie; Sartenaer, Annick; Toint, Philippe L.; Tomanos, Dimitri
2010
Approximate invariant subspaces and quasi-Newton optimization methods. Zbl 1202.90272
Gratton, Serge; Toint, Philippe L.
2010
Using dual techniques to derive componentwise and mixed condition numbers for a linear function of a linear least squares solution. Zbl 1168.65022
Baboulin, Marc; Gratton, Serge
2009
Computing the conditioning of the components of a linear least-squares solution. Zbl 1224.65104
Baboulin, Marc; Dongarra, Jack; Gratton, Serge; Langou, Julien
2009
SVD-tail: A new linear-sampling reconstruction method for inverse scattering problems. Zbl 1175.65129
Fares, M&rsquo;Barek; Gratton, Serge; Toint, Philippe L.
2009
Parallel tools for solving incremental dense least squares problems: application to space geodesy. Zbl 1226.65029
Baboulin, Marc; Giraud, Luc; Gratton, Serge; Langou, Julien
2009
Recursive trust-region methods for multiscale nonlinear optimization. Zbl 1163.90024
Gratton, Serge; Sartenaer, Annick; Toint, Philippe L.
2008
A partial condition number for linear least squares problems. Zbl 1141.65028
Arioli, Mario; Baboulin, Marc; Gratton, Serge
2008
A recursive $$\ell_{\infty}$$-trust-region method for bound-constrained nonlinear optimization. Zbl 1156.65060
Gratton, Serge; Mouffe, Mélodie; Toint, Philippe L.; Weber-Mendonça, Melissa
2008
Approximate Gauss-Newton methods for nonlinear least squares problems. Zbl 1138.65046
Gratton, S.; Lawless, A. S.; Nichols, N. K.
2007
Incremental spectral preconditioners for sequences of linear systems. Zbl 1123.65031
Giraud, L.; Gratton, S.; Martin, E.
2007
Additive and multiplicative two-level spectral preconditioning for general linear systems. Zbl 1145.65023
Carpentieri, B.; Giraud, L.; Gratton, S.
2007
A note on GMRES preconditioned by a perturbed $$LDL^T$$ decomposition with static pivoting. Zbl 1161.65023
Arioli, M.; Duff, I. S.; Gratton, S.; Pralet, S.
2007
Convergence in backward error of relaxed GMRES. Zbl 1142.65031
Giraud, L.; Gratton, S.; Langou, J.
2007
Multigrid based preconditioners for the numerical solution of two-dimensional heterogeneous problems in geophysics. Zbl 1123.65030
Duff, I.; Gratton, S.; Pinel, X.; Vasseur, X.
2007
On the sensitivity of some spectral preconditioners. Zbl 1104.65040
Giraud, L.; Gratton, S.
2006
Second-order convergence properties of trust-region methods using incomplete curvature information, with an application to multigrid optimization. Zbl 1132.65054
Gratton, Serge; Sartenaer, Annick; Toint, Philippe L.
2006
Algorithm 842: A set of GMRES routines for real and complex arithmetics on high performance computers. Zbl 1070.65527
Frayssé, Valéire; Giraud, Luc; Gratton, Serge; Langou, Julien
2005
Approximate iterative methods for variational data assimilation. Zbl 1066.65066
Lawless, A. S.; Gratton, S.; Nichols, N. K.
2005
On the condition numbers associated with the polar factorization of a matrix. Zbl 1051.65052
Chaitin-Chatelin, F.; Gratton, S.
2000
Structured backward error and condition number for linear systems of the type $$A^* Ax = b$$. Zbl 0958.65054
Frayssé, V.; Gratton, S.; Toumazou, V.
2000
On the condition number of linear least squares problems in a weighted Frobenius norm. Zbl 0878.65030
Gratton, S.
1996
Convergence in finite precision of successive iteration methods under high nonnormality. Zbl 0864.65015
Chaitin-Chatelin, F.; Gratton, S.
1996
all top 5

#### Cited by 566 Authors

 30 Gratton, Serge 19 Toint, Philippe L. 17 Wei, Yimin 13 Diao, Huaian 13 Vicente, Luis Nunes 11 Cartis, Coralia 9 Vasseur, Xavier 8 Li, Hanyu 8 Wang, Shaoxin 7 Fasano, Giovanni 7 Santos, Sandra Augusta 6 Diouane, Youssef 5 Calandra, Henri 5 Carpentieri, Bruno 5 Gould, Nicholas Ian Mark 5 Grapiglia, Geovani Nunes 5 Karas, Elizabeth W. 5 Martínez, José Mario 5 Roma, Massimo 5 Royer, Clément W. 5 Yang, Hu 5 Zheng, Bing 4 Bergou, El Houcine 4 Carson, Erin Claire 4 Huang, Ting-Zhu 4 Morini, Benedetta 4 Riccietti, Elisa 4 Strakoš, Zdeněk 4 Titley-Péloquin, David 4 Xiang, Hua 4 Yuan, Ya-xiang 3 Al-Baali, Mehiddin 3 Baboulin, Marc 3 Bellavia, Stefania 3 Buccini, Alessandro 3 Caliciotti, Andrea 3 Cools, Siegfried 3 Giraud, Luc 3 Gonçalves, Douglas Soares 3 Higham, Nicholas J. 3 Jing, Yanfei 3 Leem, Koung Hee 3 Parpas, Panos 3 Pedroso, Lucas G. 3 Pelekanos, George 3 Price, Richard H. 3 Qiao, Sanzheng 3 Reichel, Lothar 3 Richtárik, Peter 3 Scheinberg, Katya 3 Sun, Dong-Lin 3 Ueda, Kenji 3 Vanroose, Wim 3 Viloche Bazán, Fermín S. 3 Vuik, Cornelis 3 Yamashita, Nobuo 3 Yuan, Jinyun 3 Zhang, Zaikun 3 Zhu, Detong 2 Arioli, Mario 2 Batiste, Oriol 2 Biegler, Lorenz T. 2 Birgin, Ernesto G. 2 Böß, Caroline 2 Boutet, Nicolas 2 Bunse-Gerstner, Angelika 2 Chaillat, Stéphanie 2 Cholamjiak, Prasit 2 Chu, Delin 2 Conejo, Paulo D. 2 Cucker, Felipe 2 Curtis, Frank E. 2 De Simone, Valentina 2 Degroote, Joris 2 Demanet, Laurent 2 di Serafino, Daniela 2 Dodangeh, M. 2 Dongarra, Jack J. 2 Dreisigmeyer, David W. 2 Duff, Iain S. 2 Estatico, Claudio 2 Fisher, Mike 2 Francisco, Juliano B. 2 Frandi, Emanuele 2 Gander, Martin Jakob 2 Gejadze, Igor Yu. 2 Gondzio, Jacek 2 Greif, Chen 2 Gu, Xian-Ming 2 Gürol, Selime 2 Haelterman, Rob 2 Haidar, Azzam 2 Hallman, Eric 2 Jia, Zhongxiao 2 Kopaničáková, Alena 2 Krause, Rolf H. 2 Kumbhakar, Manotosh 2 Lahaye, Domenico 2 Larson, Jeffrey 2 Lau, Stephen R. ...and 466 more Authors
all top 5

#### Cited in 87 Serials

 20 Journal of Computational and Applied Mathematics 20 Computational Optimization and Applications 17 Optimization Methods & Software 16 SIAM Journal on Scientific Computing 15 Journal of Computational Physics 15 SIAM Journal on Optimization 15 Numerical Linear Algebra with Applications 14 Mathematical Programming. Series A. Series B 13 Journal of Optimization Theory and Applications 13 Linear Algebra and its Applications 11 SIAM Journal on Matrix Analysis and Applications 11 Numerical Algorithms 10 Applied Mathematics and Computation 8 Computers & Mathematics with Applications 8 Journal of Scientific Computing 6 Computers and Fluids 5 Calcolo 5 Applied Numerical Mathematics 4 Computer Methods in Applied Mechanics and Engineering 4 Numerische Mathematik 4 Optimization 4 International Journal of Computer Mathematics 3 Linear and Multilinear Algebra 3 BIT 3 Advances in Computational Mathematics 3 Optimization and Engineering 3 Optimization Letters 3 EURO Journal on Computational Optimization 2 International Journal for Numerical Methods in Fluids 2 Inverse Problems 2 Mathematics of Computation 2 International Journal for Numerical Methods in Engineering 2 SIAM Journal on Numerical Analysis 2 Operations Research Letters 2 Physica D 2 Journal of Complexity 2 Computational Mechanics 2 Journal of Mathematical Imaging and Vision 2 Engineering Analysis with Boundary Elements 2 Vietnam Journal of Mathematics 2 Mathematical Methods of Operations Research 2 Acta Mathematica Sinica. English Series 2 Journal of Applied Mathematics and Computing 2 Numerical Algebra, Control and Optimization 2 Bulletin of Computational Applied Mathematics 1 International Journal of Engineering Science 1 Theoretical and Computational Fluid Dynamics 1 Computing 1 Mathematics and Computers in Simulation 1 Proceedings of the American Mathematical Society 1 Parallel Computing 1 Numerical Methods for Partial Differential Equations 1 Asia-Pacific Journal of Operational Research 1 Science in China. Series A 1 International Journal of Adaptive Control and Signal Processing 1 European Journal of Operational Research 1 SIAM Review 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 International Journal of Computer Vision 1 Computational and Applied Mathematics 1 INFORMS Journal on Computing 1 ELA. The Electronic Journal of Linear Algebra 1 Abstract and Applied Analysis 1 Chaos 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Communications in Nonlinear Science and Numerical Simulation 1 Computational Geosciences 1 Engineering Computations 1 Foundations of Computational Mathematics 1 Discrete and Continuous Dynamical Systems. Series B 1 SIAM Journal on Applied Dynamical Systems 1 International Journal of Computational Methods 1 Acta Numerica 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 GAMM-Mitteilungen 1 Journal of Fixed Point Theory and Applications 1 Frontiers of Mathematics in China 1 SIAM Journal on Imaging Sciences 1 Mathematical Geosciences 1 Advances in Mathematical Physics 1 Mathematical Programming Computation 1 Science China. Mathematics 1 Communications in Applied and Industrial Mathematics 1 S$$\vec{\text{e}}$$MA Journal 1 Axioms 1 Journal of Mathematics 1 East Asian Journal on Applied Mathematics
all top 5

#### Cited in 31 Fields

 248 Numerical analysis (65-XX) 128 Operations research, mathematical programming (90-XX) 55 Linear and multilinear algebra; matrix theory (15-XX) 37 Calculus of variations and optimal control; optimization (49-XX) 34 Partial differential equations (35-XX) 22 Computer science (68-XX) 22 Fluid mechanics (76-XX) 14 Mechanics of deformable solids (74-XX) 14 Geophysics (86-XX) 8 Operator theory (47-XX) 8 Optics, electromagnetic theory (78-XX) 8 Systems theory; control (93-XX) 7 Statistics (62-XX) 5 Information and communication theory, circuits (94-XX) 3 Ordinary differential equations (34-XX) 3 Approximations and expansions (41-XX) 3 Integral equations (45-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Biology and other natural sciences (92-XX) 2 General topology (54-XX) 2 Mechanics of particles and systems (70-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Relativity and gravitational theory (83-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Potential theory (31-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral transforms, operational calculus (44-XX) 1 Geometry (51-XX) 1 Probability theory and stochastic processes (60-XX) 1 Astronomy and astrophysics (85-XX)