Using Monodromy to Avoid High Precision

When solving polynomial systems with homotopy continuation, the fundamental numerical linear algebra computations become inaccurate when two paths are in close proximity. The current best defense against this ill-conditioning is the use of adaptive precision. While sufficiently high precision indeed overcomes any such loss of accuracy, high precision can be very expensive. In this article, we describe a simple heuristic rooted in monodromy that can be used to avoid the use of high precision.