P. R. Amestoy, I. S. Duff, J. Koster, L. Excellent, and J. , A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling, SIAM Journal on Matrix Analysis and Applications, vol.23, issue.1, pp.15-41, 2001.
DOI : 10.1137/S0895479899358194

URL : https://hal.archives-ouvertes.fr/hal-00808293

P. R. Amestoy, I. S. Duff, J. Y. L-'excellent, L. , and X. S. , Analysis and comparison of two general sparse solvers for distributed memory computers, ACM Trans, pp.71-78, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00856654

H. Andriambololona, Optimisation des essais et recalage de modeles structuraux, p.26

S. Andrieux, A. B. Abda, and H. D. Bui, Sur l'identification de fissures planes via le concept d'´ ecartàecart`ecartà la réciprocité enélasticitéenélasticité, Comptes Rendus de l'Académie des Sciences-Series I-Mathematics, pp.1431-1438, 1997.

M. Arioli, J. W. Demmel, and I. S. Duff, Solving Sparse Linear Systems with Sparse Backward Error, SIAM Journal on Matrix Analysis and Applications, vol.10, issue.2, pp.165-190, 1989.
DOI : 10.1137/0610013

C. Ashcraft, R. G. Grimes, L. , and J. G. , Accurate Symmetric Indefinite Linear Equation Solvers, SIAM Journal on Matrix Analysis and Applications, vol.20, issue.2, pp.513-561, 1998.
DOI : 10.1137/S0895479896296921

J. G. Astier, L. Dutrech, P. Lebailly, and G. Playe, note ht-61/05/006/a projet vital : Impact du suivi de réseau sur le vieillissement des alternateurs 900 mw

M. Baboulin, X. Li, R. , and F. , Using random butterfly transformations to avoid pivoting in sparse direct methods. High Performance Computing for Computational Science, pp.135-144, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01205703

B. Banerjee, T. F. Walsh, W. Aquino, and M. Bonnet, Large scale parameter estimation problems in frequency-domain elastodynamics using an error in constitutive equation functional, Computer Methods in Applied Mechanics and Engineering, vol.253, pp.60-72, 2013.
DOI : 10.1016/j.cma.2012.08.023

URL : https://hal.archives-ouvertes.fr/hal-00732291

D. Barthe, P. Ladevèze, A. Deraemaecker, L. Loch, and S. , Validation and Updating of Industrial Models Based on the Constitutive Relation Error, AIAA Journal, vol.5, issue.7, pp.1427-1434, 2004.
DOI : 10.1016/S0045-7825(01)00421-2

B. Abdallah and J. , Inversion gaussienne appliquéè a la correction paramétrique de modèles structuraux, p.26

Y. Ben-haim, Identification of Certain Polynomial Nonlinear Structures by Adaptive Selectively-Sensitive Excitation, Journal of Vibration and Acoustics, vol.115, issue.3, pp.246-246, 1993.
DOI : 10.1115/1.2930341

M. Benzi, Preconditioning Techniques for Large Linear Systems: A Survey, Journal of Computational Physics, vol.182, issue.2, pp.418-477, 2002.
DOI : 10.1006/jcph.2002.7176

M. Benzi, G. Golub, and J. And-liesen, Numerical solution of saddle point problems, Acta Numerica, vol.14, issue.46, pp.1-137, 2005.
DOI : 10.1017/S0962492904000212

M. Benzi and J. Liu, Block preconditioning for saddle point systems with indefinite (1, 1) block, International Journal of Computer Mathematics, vol.84, issue.8, pp.1117-1129, 2007.
DOI : 10.1137/S0895479894278952

A. Bobillot and E. Balmès, Solving minimum dynamic residual expansion and using results for error localization, Proceeding of IMAC XIX, pp.179-185, 2001.

O. Boiteau, Mot-clé solveur, p.46

M. Bonnet, Probì emes inverses, p.24, 2004.

M. Bonnet and A. Constantinescu, Inverse problems in elasticity, R1, pp.24-26, 2005.
DOI : 10.1088/0266-5611/21/2/R01

URL : https://hal.archives-ouvertes.fr/hal-00111264

M. Boutayeb, A. , and D. , A strong tracking extended Kalman observer for nonlinear discrete-time systems, IEEE Transactions on Automatic Control, vol.44, issue.8, pp.1550-1556, 1999.
DOI : 10.1109/9.780419

N. Buleev, Numerical method for solving two-and three-dimensional diffusion equations, Matematicheskii Sbornik 93, pp.227-238, 1960.

J. R. Bunch and L. Kaufman, Some stable methods for calculating inertia and solving symmetric linear systems, Mathematics of Computation, vol.31, issue.137, pp.163-179, 1977.
DOI : 10.1090/S0025-5718-1977-0428694-0

J. R. Bunch and B. N. Parlett, Direct Methods for Solving Symmetric Indefinite Systems of Linear Equations, SIAM Journal on Numerical Analysis, vol.8, issue.4, pp.639-655, 1971.
DOI : 10.1137/0708060

S. Campbell, I. Ipsen, C. Kelley, M. , and C. , GMRES and the minimal polynomial, BIT Numerical Mathematics, vol.15, issue.1, pp.664-675, 1996.
DOI : 10.1007/978-3-0348-8547-8

K. Carsten, I. Gould, and A. Wathen, Constraint preconditioning for indefinite linear systems, pp.1300-1317

A. Chouaki, Recalage de modèles dynamiques de structures avec amortissement, p.26

A. Cimetì-ere, F. Delvare, and F. Pons, Une méthode inverse d'ordre un pour lesprobì emes de complétion de données, Comptes rendus mécanique 333, pp.123-126, 2005.

T. F. Coleman and A. Pothen, The Null Space Problem I. Complexity, SIAM Journal on Algebraic Discrete Methods, vol.7, issue.4, pp.527-537, 1986.
DOI : 10.1137/0607059

T. F. Coleman and A. Pothen, The Null Space Problem II. Algorithms, SIAM Journal on Algebraic Discrete Methods, vol.8, issue.4, pp.544-563, 1987.
DOI : 10.1137/0608045

L. Cormen, C. Leiserson, and . Rivest, Introduction to algorithms, p.44, 1990.

A. A. Cot, Une approche de l'identification en dynamique des structures combinant l'erreur en relation de comportement et le filtrage de kalman, pp.28-133
URL : https://hal.archives-ouvertes.fr/pastel-00724815

T. Davis, Matlab primer, p.44

D. Niet, A. Wubs, and F. , Numerically stable LDLT-factorization of F-type saddle point matrices, IMA Journal of Numerical Analysis, vol.29, issue.1, pp.208-234, 2008.
DOI : 10.1093/imanum/drn005

A. Deraemaecker, Sur la maitrise des modèles en dynamique des structuresàstructures`structuresà partir de résultats d'essais, p.19

A. Deraemaecker, P. Ladevèze, and P. Leconte, Reduced bases for model updating in structural dynamics based on constitutive relation error, Computer Methods in Applied Mechanics and Engineering, vol.191, issue.21-22, pp.2427-2444, 2002.
DOI : 10.1016/S0045-7825(01)00421-2

A. Deraemaeker, P. Ladevèze, and P. Leconte, Reduced bases for model updating in structural dynamics based on constitutive relation error Computer methods in applied mechanics and engineering 191, pp.2427-2444, 2002.

H. S. Dollar, Iterative linear algebra for constrained optimization, pp.47-97

H. S. Dollar, Constraint-Style Preconditioners for Regularized Saddle Point Problems, SIAM Journal on Matrix Analysis and Applications, vol.29, issue.2, pp.672-684, 2007.
DOI : 10.1137/050626168

I. Duff, The solution of augmented systems Pitman research notes in mathematics series, pp.40-40, 1994.

I. Duff, The solution of augmented systems, p.164

I. Duff, MA57---a code for the solution of sparse symmetric definite and indefinite systems, ACM Transactions on Mathematical Software, vol.30, issue.2, pp.118-144, 2004.
DOI : 10.1145/992200.992202

I. Duff, N. Gould, J. Reid, J. Scott, T. et al., The Factorization of Sparse Symmetric Indefinite Matrices, IMA Journal of Numerical Analysis, vol.11, issue.2, pp.181-204, 1991.
DOI : 10.1093/imanum/11.2.181

I. S. Duff, A. M. Erisman, R. , and J. , Direct methods for sparse matrices, p.163
DOI : 10.1093/acprof:oso/9780198508380.001.0001

I. S. Duff, R. , and J. K. , The Multifrontal Solution of Indefinite Sparse Symmetric Linear, ACM Transactions on Mathematical Software, vol.9, issue.3, pp.302-325, 1983.
DOI : 10.1145/356044.356047

I. S. Duff, J. K. Reid, N. Munksgaard, and H. B. Nielsen, Direct Solution of Sets of Linear Equations whose Matrix is Sparse, Symmetric and Indefinite, IMA Journal of Applied Mathematics, vol.23, issue.2, pp.235-250, 1979.
DOI : 10.1093/imamat/23.2.235

L. Dutrech, Note h-61-2008-01569-fr procédure d'analyse modale applicable aux stators 900 mw bobinés en star. rapport technique, EDF R&D, p.132

N. Dyn, F. , and W. , The numerical solution of equality constrained quadratic programming problems, Mathematics of Computation, vol.41, issue.163, pp.165-170, 1983.

H. Elman, D. Silvester, and A. Wathen, Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics, p.36
DOI : 10.1093/acprof:oso/9780199678792.001.0001

D. J. Ewins, Modal Testing: Theory and Practice, Journal of Vibration Acoustics Stress and Reliability in Design, vol.108, issue.1, p.62
DOI : 10.1115/1.3269294

P. Feissel, Vers une stratégie d'identification en dynamique rapide pour des données incertaines, p.26

P. Feissel, A. , and O. , Modified constitutive relation error identification strategy for transient dynamics with corrupted data: the elastic case Computer methods in applied mechanics and engineering 196, pp.1968-1983, 2007.

W. Gansterer, J. Schneid´yschneid´-schneid´y, U. Ueberhuber´y, and C. , Mathematical properties of equilibrium systems, p.44

N. Gould, M. Hribar, and J. Nocedal, On the Solution of Equality Constrained Quadratic Programming Problems Arising in Optimization, SIAM Journal on Scientific Computing, vol.23, issue.4, pp.1376-1395, 2001.
DOI : 10.1137/S1064827598345667

N. Gould, D. Orban, R. , and T. , Projected Krylov Methods for Saddle-Point Systems, SIAM Journal on Matrix Analysis and Applications, vol.35, issue.4, pp.1329-1343, 2014.
DOI : 10.1137/130916394

A. Greenbaum, V. Pták, and Z. Strako?, Any Nonincreasing Convergence Curve is Possible for GMRES, SIAM Journal on Matrix Analysis and Applications, vol.17, issue.3, pp.465-469, 1996.
DOI : 10.1137/S0895479894275030

M. Gutknecht, A Brief Introduction to Krylov Space Methods for Solving Linear Systems, Frontiers of Computational Science, pp.53-62, 2007.
DOI : 10.1007/978-3-540-46375-7_5

K. Hadj-sassi, Une stratégie d'identification conjointe des paramètres et de l'´ etat de structuresàstructures`structuresà comportements non-linéaires. assimilation de données et erreur en loi de comportement, p.26

I. Hajj, P. Yang, and T. N. Trick, Avoiding zero pivots in the modified nodal approach. Circuits and Systems, IEEE Transactions on, vol.28, pp.271-279, 1981.

P. Hénon, P. Ramet, R. , and J. , PaStiX: a high-performance parallel direct solver for sparse symmetric positive definite systems, Parallel Computing, vol.28, issue.2, pp.301-321, 2002.
DOI : 10.1016/S0167-8191(01)00141-7

M. Hestenes and E. Stiefel, Methods of conjugate gradients for solving linear systems, p.50

R. Jimenez, Model based structural damage assessment using vibration measurements, p.26

R. Jimenez, Model based structural damage assessment using vibration measurements, p.63

W. Joubert, On the convergence behavior of the restarted gmres algorithm for solving nonsymmetric linear systems. Numerical linear algebra with applications 1, pp.427-447, 1994.

. Kaustuv, IPSOL: An Interior Point Solver for Nonconvex Optimization Problems, pp.92-96, 2009.

A. Kuczkowiak, S. Cogan, M. Ouisse, E. Foltete, and M. Corus, Robust Expansion of Experimental Mode Shapes Under Epistemic Uncertainties, Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, pp.419-427, 2014.
DOI : 10.1007/978-3-319-04552-8_42

P. Ladevèze, Comparaison de modeles de milieux continus, pp.25-26

P. Ladevéze and N. Moës, A new a posteriori error estimation for nonlinear time-dependent finite element analysis, Computer Methods in Applied Mechanics and Engineering, vol.157, issue.1-2, pp.45-68, 1998.
DOI : 10.1016/S0045-7825(97)00212-0

P. Ladeveze, G. Puel, A. Deraemaeker, R. , and T. , Validation of structural dynamics models containing uncertainties Computer methods in applied mechanics and engineering 195, pp.373-393, 2006.

P. Ladeveze, M. Reynier, and D. Nedjar, Parametric correction of finite element models using modal tests, Inverse problems in engineering mechanics, pp.91-100, 1993.

P. Ladevèze and J. Waeytens, Model verification in dynamics through strict upper error bounds, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.21-26, pp.1775-1784, 2009.
DOI : 10.1016/j.cma.2008.12.020

X. S. Li, An overview of SuperLU, ACM Transactions on Mathematical Software, vol.31, issue.3
DOI : 10.1145/1089014.1089017

J. W. Liu, Modification of the minimum-degree algorithm by multiple elimination, ACM Transactions on Mathematical Software, vol.11, issue.2, pp.141-153, 1985.
DOI : 10.1145/214392.214398

L. Luksan and J. Vlcek, Indefinitely preconditioned inexact newton method for large sparse equality constrained nonlinear programming problems, pp.219-247, 1998.

S. Lungten, W. Schilders, and J. Maubach, Sparse inverse incidence matrices for Schilders' factorization applied to resistor network modeling, Numerical Algebra, Control and Optimization, vol.4, issue.3, p.48
DOI : 10.3934/naco.2014.4.227

C. Mathieu, Elimination des conditions aux limites dualis?Adualis? dualis?A c es

J. Meijerink and H. Van-der-vorst, An iterative solution method for linear systems of which the coefficient matrix is a symmetric m-matrix, Mathematics of computation, vol.31, issue.137, pp.148-162, 1977.

S. Mercier, Fast nonlinear solvers in solid mechanics, pp.32-36

M. F. Murphy, G. H. Golub, and A. J. Wathen, A Note on Preconditioning for Indefinite Linear Systems, SIAM Journal on Scientific Computing, vol.21, issue.6, pp.1969-1972, 2000.
DOI : 10.1137/S1064827599355153

H. M. Nguyen, O. Allix, and P. Feissel, A robust identification strategy for rate-dependent models in dynamics, Inverse Problems, vol.24, issue.6, pp.65006-65032, 2008.
DOI : 10.1088/0266-5611/24/6/065006

O. 'callahan, J. Avitabile, P. Riemer, and R. , System equivalent reduction expansion process (serep), Proceedings of the 7th international modal analysis conference, pp.29-37, 1989.

C. Paige and M. Saunders, Solution of Sparse Indefinite Systems of Linear Equations, SIAM Journal on Numerical Analysis, vol.12, issue.4, pp.617-629, 1975.
DOI : 10.1137/0712047

J. Pellet, A. Edf-r&d, and R. , Dualisation des conditions limites, pp.33-34, 2011.

I. Perugia, V. Simoncini, and M. Arioli, Linear Algebra Methods in a Mixed Approximation of Magnetostatic Problems, SIAM Journal on Scientific Computing, vol.21, issue.3, pp.1085-1101, 1999.
DOI : 10.1137/S1064827598333211

G. Puel, B. Bourgeteau, A. , and D. , Parameter identification of nonlinear time-dependent rubber bushings models towards their integration in multibody simulations of a vehicle chassis, Mechanical Systems and Signal Processing, vol.36, issue.2, pp.354-369, 2013.
DOI : 10.1016/j.ymssp.2012.10.021

URL : https://hal.archives-ouvertes.fr/hal-00799243

Z. Qu, Model order reduction techniques with applications in finite element analysis, p.63

T. Rees and J. Scott, A comparative study of null-space factorizations for sparse symmetric saddle point systems, Numerical Linear Algebra with Applications, vol.23, issue.4, pp.48-49, 2017.
DOI : 10.1137/S0895479897321088

J. Reid, On the method of conjugate gradients for the solution of large sparse systems of linear equations, Pro. the Oxford conference of institute of mathmatics and its applications, pp.231-254, 1971.

M. Reynier, Sur le controle de modélisations parélémentsparéléments finis : recalagè a partir d'essais dynamiques, p.19

M. Rozlozn?k, F. Okulicka-dd-luzewska, and A. Smoktunowicz, Indefinite orthogonalization with rounding errors, p.46

T. Rusten and R. Winther, A Preconditioned Iterative Method for Saddlepoint Problems, SIAM Journal on Matrix Analysis and Applications, vol.13, issue.3, pp.887-904, 1992.
DOI : 10.1137/0613054

Y. Saad, Iterative methods for sparse linear systems, pp.51-54
DOI : 10.1137/1.9780898718003

Y. Saad and M. Schultz, GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems, SIAM Journal on Scientific and Statistical Computing, vol.7, issue.3, pp.856-869, 1986.
DOI : 10.1137/0907058

J. Schöberl and W. Zulehner, Symmetric Indefinite Preconditioners for Saddle Point Problems with Applications to PDE-Constrained Optimization Problems, SIAM Journal on Matrix Analysis and Applications, vol.29, issue.3, pp.752-773, 2007.
DOI : 10.1137/060660977

J. Shewchuk, What is a good linear finite element? interpolation, conditioning, anisotropy, and quality measures (preprint) University of California at, Berkeley, vol.73, p.137, 2002.

J. Sifuentes, Preconditioning the integral formulation of the helmholtz equation via deflation, p.52

V. Simoncini, Block triangular preconditioners for symmetric saddle-point problems, Applied Numerical Mathematics, vol.49, issue.1, pp.63-80, 2004.
DOI : 10.1016/j.apnum.2003.11.012

V. Simoncini and D. Szyld, Recent computational developments in Krylov subspace methods for linear systems, Numerical Linear Algebra with Applications, vol.15, issue.156, pp.1-59, 2007.
DOI : 10.13182/NSE04-1

E. D. Sontag, of texts in applied mathematics, Mathematical control theory, vol.6, p.36

B. Stott, A. , and O. , an overview of sparse matrix techniques for on-line network applications, IFAC Power Systems and Power Plant Control, p.45, 1986.

A. Tarantola, Inverse problem theory and methods for model parameter estimation, pp.24-28
DOI : 10.1137/1.9780898717921

A. Tarantola and B. Valette, Generalized nonlinear inverse problems solved using the least squares criterion, Reviews of Geophysics, vol.10, issue.1, pp.219-232, 1982.
DOI : 10.1111/j.1365-246X.1979.tb03777.x

A. Tikhonov and V. Arsenin, Solutions of ill-posed problems, p.28, 1977.

H. Van-der-vorst, Iterative krylov methods for large linear systems, p.53
DOI : 10.1017/CBO9780511615115

H. Van-der-vorst and C. Vuik, The superlinear convergence behaviour of GMRES, Journal of Computational and Applied Mathematics, vol.48, issue.3, pp.327-341, 1993.
DOI : 10.1016/0377-0427(93)90028-A

S. Vavasis, Stable Numerical Algorithms for Equilibrium Systems, SIAM Journal on Matrix Analysis and Applications, vol.15, issue.4, pp.1108-1131, 1994.
DOI : 10.1137/S0895479892230948