Constrained learning algorithms for finding the roots of polynomials: a case study

This paper makes further discussions on the constrained learning algorithms (CLA) proposed by Perantonis et al. which is an efficient constrained back propagation (BP) algorithm formed by imposing the constraint conditions (most of which are from the a priori information of the involved problems) implicit in the problems on the conventional BP algorithm. In addition, for the problem of applying CLAs to finding the roots of polynomials based on the relation between the roots and the coefficients of polynomials, we discuss the computation complexities for different number of constrained conditions. Finally, some computer simulation results are given to support our claims.