Finding all real roots of 3 × 3 nonlinear algebraic systems using neural networks

Abstract

The objective of this research is the description of a feed-forward neural network capable of solving nonlinear algebraic systems with polynomials equations. The basic features of the proposed structure, include among other things, product units trained by the back-propagation algorithm and a fixed input unit with a constant input of unity. The presented theory is demonstrated by solving complete 3×3 nonlinear algebraic system paradigms, and the accuracy of the method is tested by comparing the experimental results produced by the network, with the theoretical values of the systems roots.