Solving Sparse Integer Linear Systems
Symbolic Computation
2007-05-23 v1
Abstract
We propose a new algorithm to solve sparse linear systems of equations over the integers. This algorithm is based on a -adic lifting technique combined with the use of block matrices with structured blocks. It achieves a sub-cubic complexity in terms of machine operations subject to a conjecture on the effectiveness of certain sparse projections. A LinBox-based implementation of this algorithm is demonstrated, and emphasizes the practical benefits of this new method over the previous state of the art.
Cite
@article{arxiv.cs/0603082,
title = {Solving Sparse Integer Linear Systems},
author = {Wayne Eberly and Mark Giesbrecht and Pascal Giorgi and Arne Storjohann and Gilles Villard},
journal= {arXiv preprint arXiv:cs/0603082},
year = {2007}
}