A ROBUST NUMERICAL PATH TRACKING ALGORITHM FOR POLYNOMIAL HOMOTOPY CONTINUATION

We propose a new algorithm for numerical path tracking in polynomial homotopycontinuation. The algorithm is “robust” in the sense that it is designed toprevent path jumping, and in many cases it can be used in (only) doubleprecision arithmetic. It is based on an adaptive stepsize predictor that usesPadé techniques to detect local difficulties for function approximation anddanger for path jumping. We show the potential of the new path trackingalgorithm through several numerical examples and compare it with existingimplementations.