Finding Linear Dependencies in Integration-By-Parts Equations: A Monte Carlo Approach
arXiv:1309.7287 · doi:10.1016/j.cpc.2014.01.017
Abstract
The reduction of a large number of scalar integrals to a small set of master integrals via Laporta's algorithm is common practice in multi-loop calculations. It is also a major bottleneck in terms of running time and memory consumption. It involves solving a large set of linear equations where many of the equations are linearly dependent. We propose a simple algorithm that eliminates all linearly dependent equations from a given system, reducing the time and space requirements of a subsequent run of Laporta's algorithm.
8 pages, 1 figure. Added references. Some minor additions