Sparse Gaussian Elimination modulo p: an Update - Archive ouverte HAL Access content directly
Conference Papers Year : 2016

Sparse Gaussian Elimination modulo p: an Update

Abstract

This paper considers elimination algorithms for sparse matrices over finite fields. We mostly focus on computing the rank, because it raises the same challenges as solving linear systems, while being slightly simpler. We developed a new sparse elimination algorithm inspired by the Gilbert-Peierls sparse LU factorization, which is well-known in the numerical computation community. We benchmarked it against the usual right-looking sparse gaussian elimination and the Wiedemann algorithm using the Sparse Integer Matrix Collection of Jean-Guillaume Dumas. We obtain large speedups (1000× and more) on many cases. In particular , we are able to compute the rank of several large sparse matrices in seconds or minutes, compared to days with previous methods.
Fichier principal
Vignette du fichier
main.pdf (404.71 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01333670 , version 1 (18-06-2016)

Identifiers

  • HAL Id : hal-01333670 , version 1

Cite

Charles Bouillaguet, Claire Delaplace. Sparse Gaussian Elimination modulo p: an Update. Computer Algebra in Scientific Computing, Sep 2016, Bucharest, Romania. ⟨hal-01333670⟩
312 View
1634 Download

Share

Gmail Facebook X LinkedIn More