Finding roots of arbitrary high order polynomials based on neural network recursive partitioning method

Abstract

This paper proposes a novel recursive partitioning method based on constrained learning neural networks to find an arbitrary number (less than the order of the polynomial) of (real or complex) roots of arbitrary polynomials. Moreover, this paper also gives a BP network constrained learning algorithm (CLA) used in root-finders based on the constrained relations between the roots and the coefficients of polynomials. At the same time, an adaptive selection method for the parameter δP with the CLA is also given. The experimental results demonstrate that this method can more rapidly and effectively obtain the roots of arbitrary high order polynomials with higher precision than traditional root-finding approaches.