. Lastly, concerning the sparse computations, the blackbox algorithms of [27] and of [9], could handle huge sparse matrices (no dense computation is used as in CIA) But one should study how their use of preconditionners, expensive in practice

]. J. Abdeljaoued and G. I. Malaschonok, Efficient algorithms for computing the characteristic polynomial in a domain, Journal of Pure and Applied Algebra, vol.156, issue.2-3, pp.127-145, 2001.
DOI : 10.1016/S0022-4049(99)00158-9

W. Baur and V. Strassen, The complexity of partial derivatives, Theoretical Computer Science, vol.22, issue.3, pp.317-330, 1983.
DOI : 10.1016/0304-3975(83)90110-X

S. J. Berkowitz, On computing the determinant in small parallel time using a small number of processors, Information Processing Letters, vol.18, issue.3, pp.147-150, 1984.
DOI : 10.1016/0020-0190(84)90018-8

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

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

J. Dumas, P. Giorgi, and C. Pernet, FFPACK, Proceedings of the 2004 international symposium on Symbolic and algebraic computation , ISSAC '04
DOI : 10.1145/1005285.1005304
URL : https://hal.archives-ouvertes.fr/hal-00018223

J. Dumas, B. D. Saunders, and G. Villard, On Efficient Sparse Integer Matrix Smith Normal Form Computations, Journal of Symbolic Computation, vol.32, issue.1-2, pp.71-99, 2001.
DOI : 10.1006/jsco.2001.0451

W. Eberly, Black box Frobenius decompositions over small fields, Proceedings of the 2000 international symposium on Symbolic and algebraic computation symbolic and algebraic computation , ISSAC '00, 2000.
DOI : 10.1145/345542.345596

W. Eberly, Reliable Krylov-based algorithms for matrix null space and rank, Proceedings of the 2004 international symposium on Symbolic and algebraic computation , ISSAC '04
DOI : 10.1145/1005285.1005305

J. V. Gathen and J. Gerhard, Modern Computer Algebra, 1999.

M. Giesbrecht and A. Storjohann, Computing Rational Forms of Integer Matrices, Journal of Symbolic Computation, vol.34, issue.3, pp.157-172, 2002.
DOI : 10.1006/jsco.2002.0554

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

O. H. Ibarra, S. Moran, and R. Hui, A generalization of the fast LUP matrix decomposition algorithm and applications, Journal of Algorithms, vol.3, issue.1, pp.45-56, 1982.
DOI : 10.1016/0196-6774(82)90007-4

E. Kaltofen, On computing determinants of matrices without divisions, Papers from the international symposium on Symbolic and algebraic computation , ISSAC '92, 1992.
DOI : 10.1145/143242.143350

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

E. Kaltofen and G. Villard, On the complexity of computing determinants, computational complexity, vol.13, issue.3-4, pp.91-130, 2004.
DOI : 10.1007/s00037-004-0185-3

W. Keller-gehrig, Fast algorithms for the characteristic polynomial. Theoretical computer science, pp.309-317, 1985.

D. E. Knuth, Seminumerical Algorithms, volume 2 of The Art of Computer Programming, 1997.

H. Lombardi and J. Abdeljaoued, Méthodes matricielles -IntroductionàIntroductionà la complexité algébrique, 2004.

C. Pernet, Calcul du polynôme caractéristique sur des corps finis Master's thesis, 2003.

C. Pernet and Z. Wan, LU based algorithms for characteristic polynomial over a finite field, ACM SIGSAM Bulletin, vol.37, issue.3, pp.83-84, 2003.
DOI : 10.1145/990353.990367

A. Storjohann, Algorithms for Matrix Canonical Forms, 2000.

A. Storjohann, Computing the frobenius form of a sparse integer matrix. Paper to be submitted, 2000.

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, A study of Coppersmith's block Wiedemann algorithm using matrix polynomials, 1997.

G. Villard, Computing the Frobenius Normal Form of a Sparse Matrix, p.0, 2000.
DOI : 10.1007/978-3-642-57201-2_30