Solving systems of polynomial equations: A novel end condition and root computation method

In this paper we present an improvement of the algorithm based on recursive de Casteljau subdivision over an n-dimensional bounded domain (simplex or box). The modification consists of a novel end condition and a way of calculation the root in subdomain. Both innovations are based on linear approximation of polynomials in a system. This improvement results in that our approach takes almost half of the time of the standard approach: it can be stopped much earlier than using standard diameter condition and getting midpoint of a subdomain as a root.