P. R. Amestoy, A. Timothy, I. S. Davis, and . Duff, Algorithm 837, ACM Transactions on Mathematical Software, vol.30, issue.3, pp.381-388, 2004.
DOI : 10.1145/1024074.1024081

V. L. Arlazarov, E. A. Dinic, M. A. Kronrod, and I. A. , Farad?ev: The economical construction of the transitive closure of an oriented graph, Dokl. Akad. Nauk SSSR, vol.194, pp.487-488, 1970.

B. Beckermann and G. Labahn, Fraction-Free Computation of Matrix Rational Interpolants and Matrix GCDs, SIAM Journal on Matrix Analysis and Applications, vol.22, issue.1, pp.114-144, 2000.
DOI : 10.1137/S0895479897326912

R. R. Bitmead, D. O. Brian, and . Anderson, Asymptotically fast solution of toeplitz and related systems of linear equations, Linear Algebra and its Applications, vol.34, pp.103-116, 1980.
DOI : 10.1016/0024-3795(80)90161-5

T. J. Boothby and R. W. Bradshaw, Bitslicing and the method of four russians over larger finite fields, 2009.

A. Bostan, C. P. Jeannerod, and . Schost, Solving structured linear systems with large displacement rank, Theoretical Computer Science, vol.407, issue.1-3, pp.155-181, 2008.
DOI : 10.1016/j.tcs.2008.05.014

URL : http://doi.org/10.1016/j.tcs.2008.05.014

J. R. Bunch and J. E. Hopcroft, Triangular factorization and inversion by fast matrix multiplication, Mathematics of Computation, vol.28, issue.125, pp.231-236, 1974.
DOI : 10.1090/S0025-5718-1974-0331751-8

J. Cardinal and . Paul, On a property of Cauchy-like matrices, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.328, issue.11, pp.1089-1093, 1999.
DOI : 10.1016/S0764-4442(99)80330-9

L. Chen, W. Eberly, E. Kaltofen, B. D. Saunders, W. J. Turner et al., Efficient matrix preconditioners for black box linear algebra, Special issue on structured and infinite systems of linear equations, pp.119-146, 2002.
DOI : 10.1016/S0024-3795(01)00472-4

URL : http://doi.org/10.1016/s0024-3795(01)00472-4

D. Coppersmith, Solving linear equations over GF(2): block Lanczos algorithm, Computational linear algebra in algebraic and related problems, pp.33-60, 1992.
DOI : 10.1016/0024-3795(93)90235-G

URL : http://doi.org/10.1016/0024-3795(93)90235-g

D. Coppersmith, Solving Homogeneous Linear Equations Over GF(2) via Block Wiedemann Algorithm, Mathematics of Computation, vol.62, issue.205, pp.333-350, 1994.
DOI : 10.2307/2153413

D. Coppersmith, Rectangular Matrix Multiplication Revisited, Journal of Complexity, vol.13, issue.1, pp.42-49, 1997.
DOI : 10.1006/jcom.1997.0438

URL : http://doi.org/10.1006/jcom.1997.0438

D. Coppersmith and S. Winograd, Matrix multiplication via arithmetic progressions, Proceedings of the nineteenth annual ACM conference on Theory of computing , STOC '87, pp.251-280, 1990.
DOI : 10.1145/28395.28396

J. Dumas and . Guillaume, Q-adic transform revisited, Proceedings of the twenty-first international symposium on Symbolic and algebraic computation, ISSAC '08, pp.63-69, 2008.
DOI : 10.1145/1390768.1390780

URL : https://hal.archives-ouvertes.fr/hal-00173894

J. Dumas, L. Guillaume, B. Fousse, and . Salvy, Simultaneous modular reduction and Kronecker substitution for small finite fields, Journal of Symbolic Computation, vol.46, issue.7, pp.823-840, 2011.
DOI : 10.1016/j.jsc.2010.08.015

URL : https://hal.archives-ouvertes.fr/hal-00315772

J. Dumas, T. Guillaume, M. Gautier, P. Giesbrecht, B. Giorgi et al., LINBOX: A GENERIC LIBRARY FOR EXACT LINEAR ALGEBRA, Mathematical Software, pp.40-50, 2002.
DOI : 10.1142/9789812777171_0005

J. Dumas, T. Guillaume, C. Gautier, and . Pernet, Finite field linear algebra subroutines, Proceedings of the 2002 international symposium on Symbolic and algebraic computation , ISSAC '02, pp.63-74, 2002.
DOI : 10.1145/780506.780515

J. Dumas, P. Guillaume, C. Giorgi, and . Pernet, Dense Linear Algebra over Word-Size Prime Fields, ACM Transactions on Mathematical Software, vol.35, issue.3, 2008.
DOI : 10.1145/1391989.1391992

URL : https://hal.archives-ouvertes.fr/hal-00018223

J. Dumas and . Guillaume, Clément Pernet, and Zhendong Wan: Efficient computation of the characteristic polynomial, ISSAC'05, pp.140-147

J. Dumas, G. Guillaume, and . Villard, Computing the rank of sparse matrices over finite fields, Proceedings of the fifth International Workshop on Computer Algebra in Scientific Computing, pp.47-62, 2002.

A. Duran, B. D. Saunders, and Z. Wan, Hybrid algorithms for rank of sparse matrices, SIAM Conference on Applied Linear Algebra, 2003.

W. Eberly, Black box Frobenius decompositions over small fields (extended abstract), Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation (St. Andrews), pp.106-113, 2000.
DOI : 10.1145/345542.345596

W. Eberly, Early termination over small fields, Proceedings of the 2003 international symposium on Symbolic and algebraic computation , ISSAC '03, pp.80-87, 2003.
DOI : 10.1145/860854.860882

W. Eberly, M. Giesbrecht, P. Giorgi, A. Storjohann, and G. Villard, Faster inversion and other black box matrix computations using efficient block projections, Proceedings of the 2007 international symposium on Symbolic and algebraic computation , ISSAC '07, pp.143-150, 2007.
DOI : 10.1145/1277548.1277569

URL : https://hal.archives-ouvertes.fr/hal-00127807

W. Eberly and E. Kaltofen, On randomized Lanczos algorithms, Proceedings of the 1997 international symposium on Symbolic and algebraic computation , ISSAC '97, pp.176-183, 1997.
DOI : 10.1145/258726.258776

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.11.9799

J. Faugère, S. Charles, and . Lachartre, Parallel gaussian elimination for gröbner bases computations in finite fields, PASCO 2010 Proceedings of the 4th International Workshop on Parallel Symbolic Computation, pp.89-97, 2010.

F. R. Gantmacher, The theory of matrices, 1998.

M. Giesbrecht, A. Lobo, and B. D. Saunders, Certifying inconsistency of sparse linear systems, Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation (Rostock), pp.113-119, 1998.

P. Giorgi, C. P. Jeannerod, and G. Villard, On the complexity of polynomial matrix computations, Proceedings of the 2003 international symposium on Symbolic and algebraic computation , ISSAC '03, pp.135-142, 2003.
DOI : 10.1145/860854.860889

K. Goto and R. Van-de-geijn, High-performance implementation of the level-3 BLAS, ACM Transactions on Mathematical Software, vol.35, issue.1, 2009.
DOI : 10.1145/1377603.1377607

B. Hendrickson and E. Rothberg, Improving the Run Time and Quality of Nested Dissection Ordering, SIAM Journal on Scientific Computing, vol.20, issue.2, pp.468-489, 1998.
DOI : 10.1137/S1064827596300656

C. Jeannerod, C. Pierre, and . Mouilleron, Computing specified generators of structured matrix inverses, Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, ISSAC '10, pp.281-288, 2010.
DOI : 10.1145/1837934.1837988

URL : https://hal.archives-ouvertes.fr/ensl-00450272

T. Kailath, S. Y. Kung, and M. Morf, Displacement ranks of a matrix, Bulletin of the American Mathematical Society, vol.1, issue.5, pp.769-773, 1979.
DOI : 10.1090/S0273-0979-1979-14659-7

E. Kaltofen and A. Lobo, Distributed Matrix-Free Solution of Large Sparse Linear Systems over Finite Fields, Algorithmica, vol.24, issue.3-4, pp.3-4331, 1999.
DOI : 10.1007/PL00008266

E. Kaltofen, Asymptotically fast solution of Toeplitz-like singular linear systems, Proceedings of the international symposium on Symbolic and algebraic computation , ISSAC '94, pp.297-304, 1994.
DOI : 10.1145/190347.190431

E. Kaltofen, Analysis of Coppersmith's block Wiedemann algorithm for the parallel solution of sparse linear systems, Math. Comp, vol.64, issue.210, pp.777-806, 1995.

E. Kaltofen and B. Saunders, On wiedemann's method of solving sparse linear systems, Lecture Notes in Comput. Sci, vol.539, pp.29-38, 1991.
DOI : 10.1007/3-540-54522-0_93

E. Kaltofen and B. M. Trager, Computing with polynomials given by black boxes for their evaluations: greatest common divisors, factorization, separation of numerators and denominators, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science, pp.301-320, 1990.
DOI : 10.1109/SFCS.1988.21946

E. Kaltofen and G. Villard, On the complexity of computing determinants, Comput. Complexity, vol.13, pp.3-491, 2004.

W. Keller-gehrig, Fast algorithms for the characteristics polynomial, Theoretical Computer Science, vol.36, issue.2-3, pp.309-3170304, 1985.
DOI : 10.1016/0304-3975(85)90049-0

B. A. Lamacchia and A. M. Odlyzko, Solving Large Sparse Linear Systems Over Finite Fields, Lecture Notes in Computer Science, vol.537, pp.109-133, 1991.
DOI : 10.1007/3-540-38424-3_8

R. Lambert, Computational aspects of discrete logarithms, 1996.

J. P. May, D. Saunders, and Z. Wan, Efficient matrix rank computation with application to the study of strongly regular graphs, Proceedings of the 2007 international symposium on Symbolic and algebraic computation , ISSAC '07, pp.277-284, 2007.
DOI : 10.1145/1277548.1277586

M. Morf, Doubling algorithms for teoplitz and related equations, Proc. 1980 Int'l Conf. Acoustics Speech and Signal Processing, pp.954-959, 1980.

T. Mulders and A. Storjohann, Rational solutions of singular linear systems, Proceedings of the 2000 international symposium on Symbolic and algebraic computation symbolic and algebraic computation , ISSAC '00, pp.242-249, 2000.
DOI : 10.1145/345542.345644

. Pan and Y. Victor, Structured matrices and polynomials, Birkhäuser Boston Inc, 2001.
DOI : 10.1007/978-1-4612-0129-8

URL : https://hal.archives-ouvertes.fr/inria-00073171

C. Pernet and A. Storjohann, Faster algorithms for the characteristic polynomial, Proceedings of the 2007 international symposium on Symbolic and algebraic computation , ISSAC '07, pp.307-314, 2007.
DOI : 10.1145/1277548.1277590

A. Storjohann, Deterministic computation of the Frobenius form (extended abstract), 42nd IEEE Symposium on Foundations of Computer Science, pp.368-377, 2001.

A. Storjohann and G. Villard, Algorithms for similarity transforms, 2000.

A. J. Stothers, On the Complexity of Matrix Multiplication, 2010.

E. Thomé, Fast computation of linear generators for matrix sequences and application to the block Wiedemann algorithm, Proceedings of the 2001 international symposium on Symbolic and algebraic computation , ISSAC '01, pp.323-331, 2001.
DOI : 10.1145/384101.384145

W. Turner and . Jonathan, Black box linear algebra with the linbox library, 2002.

V. Williams and V. , Breaking the Coppersmith-Winograd barrier, 2011.

G. Villard, Further analysis of Coppersmith's block Wiedemann algorithm for the solution of sparse linear systems (extended abstract), Proceedings of the 1997 international symposium on Symbolic and algebraic computation , ISSAC '97, pp.32-39, 1997.
DOI : 10.1145/258726.258742

G. Villard, Computing the Frobenius Normal Form of a Sparse Matrix, Computer algebra in scientific computing, pp.395-407, 2000.
DOI : 10.1007/978-3-642-57201-2_30

G. Villard, Algorithmique en algèbre linéaire exacte. Mémoire d'habilitation, 2003.

R. Whaley, A. Clint, J. J. Petitet, and . Dongarra, Automated empirical optimizations of software and the ATLAS project, Parallel Computing, vol.27, issue.1-2, pp.3-35, 2001.
DOI : 10.1016/S0167-8191(00)00087-9

D. H. Wiedemann, Solving sparse linear equations over finite fields, IEEE Transactions on Information Theory, vol.32, issue.1, pp.54-62, 1986.
DOI : 10.1109/TIT.1986.1057137

S. Winograd, On multiplication of 2 ?? 2 matrices, Linear Algebra and its Applications, vol.4, issue.4, pp.381-388, 1971.
DOI : 10.1016/0024-3795(71)90009-7

M. Yannakakis, Computing the Minimum Fill-In is NP-Complete, SIAM Journal on Algebraic Discrete Methods, vol.2, issue.1, pp.77-79, 1981.
DOI : 10.1137/0602010

Z. Zlatev, Computational methods for general sparse matrices, volume 65 of Mathematics and its Applications, 1991.