Parallel Implementation of a Subsystem-by-Subsystem Solver

Solving polynomial systems subsystem-by-subsystem means to solve a system of polynomial equations by first solving subsets of the system and then intersecting the results. The approach leads to numerical representations of all the solution components of a system. The focus of this paper is the development of a parallel implementation to solve large systems involving a recursive divide-and- conquer scheme. Because we concentrate our discussion on the distribution of the path tracking jobs, we have selected applications for which we have optimal homotopies, for which all paths converge to regular solutions.