Neural Computing and Applications

, Volume 21, Issue 5, pp 891–904

Finding all roots of 2 × 2 nonlinear algebraic systems using back-propagation neural networks

Original Article

DOI: 10.1007/s00521-010-0488-z

Cite this article as:
Margaris, A. & Goulianas, K. Neural Comput & Applic (2012) 21: 891. doi:10.1007/s00521-010-0488-z


The objective of this research is the numerical estimation of the roots of a complete 2 × 2 nonlinear algebraic system of polynomial equations using a feed forward back-propagation neural network. The main advantage of this approach is the simple solution of the system, by building a structure—including product units—that simulates exactly the nonlinear system under consideration and find its roots via the classical back-propagation approach. Examples of systems with four or multiple roots were used, in order to test the speed of convergence and the accuracy of the training algorithm. Experimental results produced by the network were compared with their theoretical values.


Nonlinear algebraic systemsNeural networksGeneralized delta rule

Copyright information

© Springer-Verlag London Limited 2010

Authors and Affiliations

  1. 1.ATEI of ThessalonikiThessalonikiGreece