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.

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Wayne Eberly, Mark Giesbrecht, Pascal Giorgi, Arne Storjohann, Gilles Villard
• Keywords: Algorithm, CORR 2006, Education, P-adic Lifting Technique, Sparse Linear Systems