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Solving Sparse Integer Linear Systems

Wayne Eberly·Mark Giesbrecht·Pascal Giorgi·Arne Storjohann·Gilles Villard
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Abstract

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.

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Wayne Eberly, Mark Giesbrecht, Pascal Giorgi, Arne Storjohann, Gilles Villard. 2006-03-21. Solving Sparse Integer Linear Systems. https://arxiv.org/abs/cs/0603082

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