Solving Sparse Integer Linear Systems
<|reference_start|>Solving Sparse Integer Linear Systems: We propose a new algorithm to solve sparse linear systems of equations over the integers. This algorithm is based on a $p$-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.<|reference_end|>
@article{eberly2006solving,
    title={Solving Sparse Integer Linear Systems},
    author={Wayne Eberly, Mark Giesbrecht (SCG), Pascal Giorgi (LP2A, SCG), Arne
  Storjohann (SCG), Gilles Villard (LIP)},
    journal={arXiv preprint arXiv:cs/0603082},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0603082},
    primaryClass={cs.SC}
}