Title: A new method based on artificial neural networks for solving general nonlinear systems

Authors: H. Abbasnejad; A. Jafarian

Addresses: Department of Mathematics, Urmia Branch, Islamic Azad University, Urmia, Iran ' Department of Mathematics, Urmia Branch, Islamic Azad University, Urmia, Iran

Abstract: Implementation of the amazing features of the human brain in an artificial system has long been considered. It seems that simulating the human nervous system is a recent development in applied mathematics and computer sciences. The objective of this research is to introduce an efficient iterative method based on artificial neural networks for numerically solving nonlinear algebraic systems of polynomial equations. The method first performs some simple algebraic manipulations to convert the origin system to an approximated unconstrained optimisation problem. Subsequently, the resulting nonlinear minimisation problem is solved iteratively using the neural networks approach. For this aim, a suitable five-layer feed-back neural architecture is formed and trained using a back-propagation supervised learning algorithm which is based on the gradient descent rule. Ultimately, some numerical examples with comparisons are given to demonstrate the high accuracy and the ease of implementation of the present technique over other classical methods.

Keywords: nonlinear algebraic system; artificial neural networks approach; criterion function; back-propagation learning algorithm.

DOI: 10.1504/IJCSM.2018.093149

International Journal of Computing Science and Mathematics, 2018 Vol.9 No.3, pp.207 - 218

Accepted: 13 Jun 2017
Published online: 29 Jun 2018 *

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