. Kapil, . Ahuja, . Peter, E. Benner, L. Sturler et al., Recycling bicgstab with an application to parametric model order reduction, SIAM Journal on Scientific Computing, vol.37, issue.5, pp.429-446, 2015.

. Kevin, V. Carlberg, R. Forstall, and . Tuminaro, Krylov-subspace recycling via the pod-augmented conjugate-gradient method, SIAM Journal on Matrix Analysis and Applications, vol.37, issue.3, pp.1304-1336, 2016.

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, vol.32, issue.4, pp.1212-1235, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00650239

M. A. Christie and M. J. Blunt, Tenth spe comparative solution project : A comparison of upscaling techniques, 2001.

E. De-sturler, Nested krylov methods based on gcr, Journal of Computational and Applied Mathematics, vol.67, issue.1, pp.15-41, 1996.

E. D. Sturler, Truncation strategies for optimal krylov subspace methods, SIAM Journal on Numerical Analysis, vol.36, issue.3, pp.864-889, 1999.

J. Dongarra, V. Eijkhout, and A. Kalhan, Reverse communication interface for linear algebra templates for iterative methods, 1995.

S. Eisenstat, H. Elman, and M. Schultz, Variational iterative methods for nonsymmetric systems of linear equations, SIAM Journal on Numerical Analysis, vol.20, issue.2, pp.345-357, 1983.

J. Erhel, K. Burrage, and B. Pohl, Restarted GMRES preconditioned by deflation, Journal of Computational and Applied Mathematics, vol.69, issue.2, pp.303-318, 1996.

A. Yogi, R. Erlangga, and . Nabben, Deflation and balancing preconditioners for krylov subspace methods applied to nonsymmetric matrices, SIAM Journal on Matrix Analysis and Applications, vol.30, issue.2, pp.684-699, 2008.

J. Frank and C. Vuik, On the construction of deflation-based preconditioners, SIAM Journal on Scientific Computing, vol.23, issue.2, pp.442-462, 2001.

. André, M. H. Gaul, J. Gutknecht, R. Liesen, and . Nabben, A framework for deflated and augmented krylov subspace methods, SIAM Journal on Matrix Analysis and Applications, vol.34, issue.2, pp.495-518, 2013.

L. Giraud, J. Langou, and M. Rozloznik, The loss of orthogonality in the gram-schmidt orthogonalization process, Numerical Methods and Computational Mechanics, vol.50, issue.7, pp.1069-1075, 2005.

L. Giraud, J. Langou, M. Rozlozník, and J. Van-den-eshof, Rounding error analysis of the classical gram-schmidt orthogonalization process, Numerische Mathematik, vol.101, issue.1, pp.87-100, 2005.

G. H. Golub and C. F. Van-loan, Matrix Computations, 1996.

P. Gosselet, C. Rey, and J. Pebrel, Total and selective reuse of krylov subspaces for the resolution of sequences of nonlinear structural problems, International Journal for Numerical Methods in Engineering, vol.94, issue.1, pp.60-83, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00782841

M. R. Hestenes and E. Stiefel, Methods of conjugate gradients for solving linear systems, Journal of research of the National Bureau of Standards, vol.49, pp.409-436, 1952.

, Math kernel library

P. Jolivet and P. Tournier, Block iterative methods and recycling for improved scalability of linear solvers, Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, SC '16, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01357998

J. Langou, Iterative methods for solving linear systems with multiple right-hand sides, CERFACS, 2003.

J. C. Meza, A modification to the GMRES method for ill-conditioned linear systems, 1995.

J. C. Meza and W. W. Symes, Deflated krylov subspace methods for nearly singular linear systems, Journal of Optimization Theory and Applications, vol.72, issue.3, pp.441-457, 1992.

R. B. Morgan, A restarted GMRES method augmented with eigenvectors, SIAM Journal on Matrix Analysis and Applications, vol.16, issue.4, pp.1154-1171, 1995.

R. B. Morgan, GMRES with deflated restarting, SIAM Journal on Scientific Computing, vol.24, issue.1, pp.20-37, 2002.

R. A. Nicolaides, Deflation of conjugate gradients with applications to boundary value problems, SIAM J. Numer. Anal, vol.24, issue.2, pp.355-365, 1987.

D. P. O'leary, The block conjugate gradient algorithm and related methods, Linear Algebra and its Applications, vol.29, pp.293-322, 1980.

C. C. Paige, N. Beresford, H. A. Parlett, . Van-der, and . Vorst, Approximate solutions and eigenvalue bounds from krylov subspaces, Numerical Linear Algebra with Applications, vol.2, issue.2, pp.115-133, 1995.

M. L. Parks, E. De-sturler, G. Mackey, D. D. Johnson, and S. Maiti, Recycling krylov subspaces for sequences of linear systems, SIAM Journal on Scientific Computing, vol.28, issue.5, pp.1651-1674, 2006.

M. Parks, The Iterative Solution of a Sequence of Linear Systems Arising from Nonlinear Finite Element Analysis, 2005.

C. Rey and F. Risler, A rayleigh-ritz preconditioner for the iterative solution to large scale nonlinear problems, Numerical Algorithms, vol.17, issue.3, pp.279-311, 1998.

Y. Saad, Iterative Methods for Sparse Linear Systems, Society for Industrial and Applied Mathematics, 2003.

Y. Saad, M. Yeung, J. Erhel, and F. Guyomarc'h, A deflated version of the conjugate gradient algorithm, SIAM Journal on Scientific Computing, vol.21, issue.5, pp.1909-1926, 2000.
URL : https://hal.archives-ouvertes.fr/inria-00523686

Y. Saad and M. H. 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.

G. Sacchi and V. Simoncini, A GMRES convergence analysis for localized invariant subspace ill-conditioning, SIAM Journal on Matrix Analysis and Applications, vol.40, issue.2, pp.542-563, 2019.

H. Cao, H. A. Schlumberger, . Tchelepi, U. Stanford, J. Wallis-wallis-consulting-inc et al., Parallel scalable unstructured CPR-Type Linear Solver for Resevoir Simulation, SPE, vol.96809, 2005.

V. Simoncini, On the convergence of restarted krylov subspace methods, SIAM Journal on Matrix Analysis and Applications, vol.22, issue.2, pp.430-452, 2000.

M. Snir, S. Otto, S. Huss-lederman, D. Walker, and J. Dongarra, The MPI Core, vol.1, 1998.

M. Kirk, E. Soodhalter, M. De-sturler, and . Kilmer, A survey of subspace recycling iterative methods, 2020.

M. Kirk, D. B. Soodhalter, F. Szyld, and . Xue, Krylov subspace recycling for sequences of shifted linear systems, Applied Numerical Mathematics, vol.81, pp.105-118, 2014.

J. M. Tang, R. Nabben, C. Vuik, and Y. A. Erlangga, Comparison of two-level preconditioners derived from deflation, domain decomposition and multigrid methods, Journal of Scientific Computing, vol.39, issue.3, pp.340-370, 2009.

J. R. Wallis, R. P. Kendall, and T. E. Little, Constrained residual acceleration of conjugate residual methods, SPE 13563, 1985.