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

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Abstract

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.

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Notes

  1. The originality of this idea has to be attributed to Dr. Miltiades Adamopoulos, an Emeritus Professor of the Technological Educational Institute of Thessaloniki.

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  1. ATEI of Thessaloniki, Sindos, Thessaloniki, Greece

    Athanasios Margaris & Konstantinos Goulianas

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  1. Athanasios Margaris
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  2. Konstantinos Goulianas
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Correspondence to Athanasios Margaris.

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Margaris, A., Goulianas, K. Finding all roots of 2 × 2 nonlinear algebraic systems using back-propagation neural networks. Neural Comput & Applic 21, 891–904 (2012). https://doi.org/10.1007/s00521-010-0488-z

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