Coppersmith's block Wiedemann method for polynomial problems
Résumé
Coppersmith has introduced a block version of Wiedemann's algorithm. The method allows to obtain algorithms with best known complexity bounds for various matrix and polynomial problems. We can mention for example: Determinant of a matrix over a ring; Sparse linear systems and inversion of sparse matrices; Annihilating polynomials of structured matrice; Resultant of bivariate polynomials; Fast modular composition of univariate polynomials; Manipulation of zero-dimensional ideal. We review the general approach and discuss new improvement for the resultant problem, using a combination of techniques for structured matrices and high-order lifting.