Solving Systems of Polynomial Equations: a Novel End Condition and Root Computation Method
Citation: Proceedings of the 2014 Federated Conference on Computer Science and Information Systems, M. Ganzha, L. Maciaszek, M. Paprzycki (eds). ACSIS, Vol. 2, pages 543–552 (2014)
Abstract. 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.