2019/09/11 by Simon Telen, Telen, Simon, Marc Van Barel +3
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Polynomial and algebraic computation #Robotic Path Planning Algorithms
paper · pdf · doi:10.48550/arxiv.1909.04984
openalex publication_date 2019/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a new algorithm for numerical path tracking in polynomial homotopy\ncontinuation. The algorithm is `robust' in the sense that it is designed to\nprevent path jumping and in many cases, it can be used in (only) double\nprecision arithmetic. It is based on an adaptive stepsize predictor that uses\nPad 'e techniques to detect local difficulties for function approximation and\ndanger for path jumping. We show the potential of the new path tracking\nalgorithm through several numerical examples and compare with existing\nimplementations.\n