Z. Bai, D. Hu, L. Reichel, N. Basis, and G. Implementation, A Newton basis GMRES implementation, IMA Journal of Numerical Analysis, vol.14, issue.4, pp.563-581, 1994.
DOI : 10.1093/imanum/14.4.563

B. Beckermann, The condition number of real Vandermonde, Krylov and positive definite Hankel matrices, Numerische Mathematik, vol.85, issue.4, pp.553-577, 2000.
DOI : 10.1007/PL00005392

M. Bellalij, G. Meurant, and H. Sadok, The distance of an eigenvector to a Krylov subspace and the convergence of the Arnoldi method for eigenvalue problems, Linear Algebra and its Applications, vol.504, pp.387-405, 2016.
DOI : 10.1016/j.laa.2016.04.018

R. H. Bisseling, T. M. Doup, and L. D. Loyens, A parallel interior point algorithm for linear programming on a network of transputers, Annals of Operations Research, vol.4, issue.2, pp.49-86, 1993.
DOI : 10.1007/BFb0121187

D. Calvetti, J. Petersen, and L. , A parallel implementation of the GMRES method, de Gruyter, pp.31-45, 1993.
DOI : 10.1515/9783110857658.31

E. Carson, Communication-Avoiding Krylov Subspace Methods in Theory and Practice The adaptive s-step conjugate gradient method, 2015.

A. T. Chronopoulos, -Step Iterative Methods for (Non)Symmetric (In)Definite Linear Systems, SIAM Journal on Numerical Analysis, vol.28, issue.6, pp.1776-1789, 1991.
DOI : 10.1137/0728088

R. D. Da-cunha and T. Hopkins, A parallel implementation of the restarted GMRES iterative algorithm for nonsymmetric systems of linear equations, Advances in Computational Mathematics, vol.34, issue.3, pp.261-277, 1994.
DOI : 10.1007/BF02521112

T. A. Davis and Y. Hu, The university of Florida sparse matrix collection, ACM Transactions on Mathematical Software, vol.38, issue.1, 2011.
DOI : 10.1145/2049662.2049663

D. Sturler, H. A. Van, and . Vorst, Reducing the effect of global communication in GMRES(m) and CG on parallel distributed memory computers, Applied Numerical Mathematics, vol.18, issue.4, pp.441-459, 1995.
DOI : 10.1016/0168-9274(95)00079-A

J. Demmel, L. Grigori, M. Hoemmen, and J. Langou, Communication-optimal Parallel and Sequential QR and LU Factorizations, SIAM Journal on Scientific Computing, vol.34, issue.1, pp.206-239, 2012.
DOI : 10.1137/080731992
URL : https://hal.archives-ouvertes.fr/hal-00870930

G. R. Di-brozolo and Y. Robert, Parallel conjugate gradient-like algorithms for solving sparse nonsymmetric linear systems on a vector multiprocessor, Parallel Computing, vol.11, issue.2, pp.223-239, 1989.
DOI : 10.1016/0167-8191(89)90030-6

L. Giraud, J. Langou, M. Rozloznik, and J. Van-den-eshof, Rounding error analysis of the classical Gram-Schmidt orthogonalization process, Numerische Mathematik, vol.13, issue.1, pp.87-100, 2005.
DOI : 10.1007/s00211-005-0615-4

G. H. Golub and C. F. Van-loan, JHUP, Matrix Computations, vol.4, 2013.

L. Grigori and S. Moufawad, Communication Avoiding ILU0 Preconditioner, SIAM Journal on Scientific Computing, vol.37, issue.2, pp.217-246, 2015.
DOI : 10.1137/130930376
URL : https://hal.archives-ouvertes.fr/hal-01241786

N. J. Higham, Accuracy and Stability of Numerical Algorithms, SIAM, 2002.
DOI : 10.1137/1.9780898718027

M. F. Hoemmen, Communication-avoiding Krylov subspace methods, 2010.

A. S. Householder, The Theory of Matrices in Numerical Analysis, 1964.

W. Jalby and B. Philippe, Stability Analysis and Improvement of the Block Gram???Schmidt Algorithm, SIAM journal on scientific and statistical computing, pp.1058-1073, 1991.
DOI : 10.1137/0912056
URL : https://hal.archives-ouvertes.fr/inria-00075396

W. D. Joubert and G. F. Carey, Parallelizable restarted iterative methods for non-symmetric linear systems, Part I: Theory, International Journal of Computer Mathematics, pp.44-243, 1992.
DOI : 10.1080/00207169208804107

C. T. Kelley, Iterative Methods for Linear and Nonlinear Equations, SIAM, 1995.
DOI : 10.1137/1.9781611970944

S. Kim and A. T. Chronopoulos, An efficient nonsymmetric Lanczos method on parallel vector computers, Journal of Computational and Applied Mathematics, vol.42, issue.3, pp.357-374, 1992.
DOI : 10.1016/0377-0427(92)90085-C

M. Mohiyuddin, M. Hoemmen, J. Demmel, and K. Yelick, Minimizing communication in sparse matrix solvers, Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis, SC '09, p.36, 2009.
DOI : 10.1145/1654059.1654096

N. Nassif, J. Erhel, and B. Philippe, Introduction to Computational Linear Algebra, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01196689

D. , N. Wakam, and J. Erhel, Parallelism and Robustness in GMRES with the Newton Basis and the Deflated Restarting, Electronic Transactions on Numerical Analysis, vol.40, pp.381-406, 2013.
URL : https://hal.archives-ouvertes.fr/inria-00638247

D. , N. Wakam, and F. Pacull, Memory efficient hybrid algebraic solvers for linear systems arising from compressible flows, Computers and Fluids, pp.158-167, 2013.

B. Philippe and L. , On the generation of Krylov subspace bases, Applied Numerical Mathematics, vol.62, issue.9, pp.1171-1186, 2012.
DOI : 10.1016/j.apnum.2010.12.009
URL : https://hal.archives-ouvertes.fr/inria-00433009

B. Phillipe and R. Sidje, Parallel Algorithms for the Arnoldi Procedure., Iterative Methods in Linear Algebra, II, IMACS Ser, Comput. Appl. Math, pp.156-165, 1994.

K. Rosen, Elementary Number Theory, Pearson Education, 2011.

Y. Saad, Iterative Methods for Sparse Linear Systems, 2003.
DOI : 10.1137/1.9780898718003

Y. Saad and M. H. Schultz, GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems, SIAM Journal on scientific and statistical computing, pp.856-869, 1986.
DOI : 10.1137/0907058
URL : http://www.stat.uchicago.edu/~lekheng/courses/324/saad-schultz.pdf

J. N. Shadid and R. S. Tuminaro, Sparse Iterative Algorithm Software for Large Scale MIMD Machines: An initial discussion and implementation, Concurrency: practice and experience, pp.481-497, 1992.
DOI : 10.1002/cpe.4330040605

R. B. Sidje, Alternatives for Parallel Krylov Basis Computation, Numerical Linear Algebra with Applications, pp.305-331, 1997.
DOI : 10.1002/(sici)1099-1506(199707/08)4:4<305::aid-nla104>3.0.co;2-d

D. N. Wakam, J. Erhel, E. Canot, and G. Atenekeng-kahou, A comparative study of some distributed linear solvers on systems arising from fluid dynamics simulations, in Parallel Computing: from Multicores and GPU's to Petascale (proceedings of PARCO'09), of Advances in parallel computing, pp.51-58, 2010.

H. F. Walker, Implementation of the GMRES Method Using Householder Transformations, SIAM Journal on Scientific and Statistical Computing, vol.9, issue.1, pp.152-163, 1988.
DOI : 10.1137/0909010

J. H. Wilkinson, The Algebraic Eigenvalue Problem, 1965.