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Title: Solving polynomial systems using a fast adaptive back propagation-type neural network algorithm
Authors: Goulianas, Konstantinos
Margaris, Athanasios
Refanidis, Ioannis
Diamantaras, Konstantinos I.
Type: Article
Subjects: FRASCATI::Natural sciences::Computer and information sciences
Keywords: Neural networks
polynomial systems
numerical analysis
Issue Date: Apr-2018
Publisher: Cambridge University Press
Source: European Journal of Applied Mathematics
Volume: 29
Issue: 2
First Page: 301
Last Page: 337
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.
ISSN: 0956-7925
Electronic ISSN: 1469-4425
Other Identifiers: 10.1017/S0956792517000146
Appears in Collections:Department of Applied Informatics

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