Computing the Rank of Large Sparse Matrices over Finite Fields

Jean-Guillaume Dumas (1) , Gilles Villard (2)

1 ID-IMAG - Informatique et Distribution
2 LIP - Laboratoire de l'Informatique du Parallélisme

We want to achieve efficient exact computations, such as the rank, of sparse matrices over finite fields. We therefore compare the practical behaviors, on a wide range of sparse matrices of the deterministic Gaussian elimination technique, using reordering heuristics, with the probabilistic, blackbox, Wiedemann algorithm. Indeed, we prove here that the latter is the fastest iterative variant of the Krylov methods to compute the minimal polynomial or the rank of a sparse matrix.

Domaines: Calcul formel [cs.SC]

Jean-Guillaume Dumas, Gilles Villard. Computing the Rank of Large Sparse Matrices over Finite Fields. Computer Algebra in Scientific Computing (CASC) 2002, Victor G. Ganzha, Ernst W. Mayr, Evgenii V. Vorozhtsov, Sep 2002, Yalta, Ukraine. pp.47--62. ⟨hal-02068056⟩