Finding all roots of 2 × 2 nonlinear algebraic systems using backpropagation neural networks
 Athanasios Margaris,
 Konstantinos Goulianas
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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 backpropagation 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 backpropagation 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.
Inside
Within this Article
 Introduction
 Review of previous work
 Theory of nonlinear algebraic systems
 ANNs as nonlinear system solvers
 Building the backpropagation equations
 Experimental results
 Conclusions and future work
 References
 References
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 Title
 Finding all roots of 2 × 2 nonlinear algebraic systems using backpropagation neural networks
 Journal

Neural Computing and Applications
Volume 21, Issue 5 , pp 891904
 Cover Date
 20120701
 DOI
 10.1007/s005210100488z
 Print ISSN
 09410643
 Online ISSN
 14333058
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Nonlinear algebraic systems
 Neural networks
 Generalized delta rule
 Industry Sectors
 Authors

 Athanasios Margaris ^{(1)}
 Konstantinos Goulianas ^{(1)}
 Author Affiliations

 1. ATEI of Thessaloniki, Sindos, Thessaloniki, Greece