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Solving polynomial systems using a fast adaptive back propagation-type neural network algorithm

Published online by Cambridge University Press:  20 June 2017

K. GOULIANAS ,
A. MARGARIS ,
I. REFANIDIS  and
K. DIAMANTARAS
K. GOULIANAS
Affiliation:
ATEI of Thessaloniki, Department of Information Technology, GR 574 00, Thessaloniki, Greece emails: gouliana@it.teithe.gr, kdiamant@it.teithe.gr
A. MARGARIS
Affiliation:
TEI of Thessaly, Department of Computer Science and Engineering, GR 411 10, Larissa, Greece email: amarg@uom.gr
I. REFANIDIS
Affiliation:
Department of Applied Informatics, University of Macedonia, GR 540 06, Thessaloniki, Greece email: yrefanid@uom.gr
K. DIAMANTARAS
Affiliation:
ATEI of Thessaloniki, Department of Information Technology, GR 574 00, Thessaloniki, Greece emails: gouliana@it.teithe.gr, kdiamant@it.teithe.gr
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Abstract

This paper proposes a neural network architecture for solving systems of non-linear equations. A back propagation algorithm is applied to solve the problem, using an adaptive learning rate procedure, based on the minimization of the mean squared error function defined by the system, as well as the network activation function, which can be linear or non-linear. The results obtained are compared with some of the standard global optimization techniques that are used for solving non-linear equations systems. The method was tested with some well-known and difficult applications (such as Gauss–Legendre 2-point formula for numerical integration, chemical equilibrium application, kinematic application, neuropsychology application, combustion application and interval arithmetic benchmark) in order to evaluate the performance of the new approach. Empirical results reveal that the proposed method is characterized by fast convergence and is able to deal with high-dimensional equations systems.

Keywords

Neural networkspolynomial systemsnumerical analysis
Type
Papers
Information
European Journal of Applied Mathematics , Volume 29 , Issue 2 , April 2018 , pp. 301 - 337
Copyright
Copyright © Cambridge University Press 2017 

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