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

  • K. GOULIANAS (a1), A. MARGARIS (a2), I. REFANIDIS (a3) and K. DIAMANTARAS (a1)
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.

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The research of K. Goulianas, A. Margaris, I. Refanidis, K. Diamantaras and T. Papadimitriou has been co-financed by the European Union (European Social Fund – ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) – Research Funding Program: THALES, Investing in knowledge society through the European Social Fund.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

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European Journal of Applied Mathematics
  • ISSN: 0956-7925
  • EISSN: 1469-4425
  • URL: /core/journals/european-journal-of-applied-mathematics
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