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Coppersmith's block Wiedemann method for polynomial problems

Abstract

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.
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  • HAL Id : hal-03730740 , version 1

Cite

Gilles Villard. Coppersmith's block Wiedemann method for polynomial problems. International Conference on Applications of Computer Algebra (ACA) 2021, Jul 2021, Virtual, online, Canada. ⟨hal-03730740⟩
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