18 citations · 24 across the 13 of their papers we have counts for
15 papers
Elimination ideal and bivariate resultant over finite fields
Gilles Villard
A new algorithm is presented for computing the largest degree invariant factor of the Sylvester matrix (with respect either to or ) associated to two polynomials and …
Exact computations with quasiseparable matrices
Clément Pernet, Hippolyte Signargout, Gilles Villard
Quasi-separable matrices are a class of rank-structured matriceswidely used in numerical linear algebra and of growing interestin computer algebra, with applications in e.g. the li…
Computing the Characteristic Polynomial of Generic Toeplitz-like and Hankel-like Matrices
Clément Pernet, Hippolyte Signargout, Pierre Karpman +1
New algorithms are presented for computing annihilating polynomials of Toeplitz, Hankel, and more generally Toeplitz+ Hankel-like matrices over a field. Our approach follows works…
Computing an LLL-reduced basis of the orthogonal lattice
Jingwei Chen, Damien Stehlé, Gilles Villard
As a typical application, the Lenstra-Lenstra-Lovasz lattice basis reduction algorithm (LLL) is used to compute a reduced basis of the orthogonal lattice for a given integer matrix…
Fast computation of approximant bases in canonical form
Claude-Pierre Jeannerod, Vincent Neiger, Gilles Villard
In this article, we design fast algorithms for the computation of approximant bases in shifted Popov normal form. We first recall the algorithm known as PM-Basis, which will be our…
Linear Time Interactive Certificates for the Minimal Polynomial and the Determinant of a Sparse Matrix
Jean-Guillaume Dumas, Erich Kaltofen, Emmanuel Thomé +1
Computational problem certificates are additional data structures for each output, which can be used by a-possibly randomized-verification algorithm that proves the correctness of…