Please use this identifier to cite or link to this item:
https://ruomo.lib.uom.gr/handle/7000/494
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. |
URI: | https://doi.org/10.1017/S0956792517000146 https://ruomo.lib.uom.gr/handle/7000/494 |
ISSN: | 0956-7925 |
Electronic ISSN: | 1469-4425 |
Other Identifiers: | 10.1017/S0956792517000146 |
Appears in Collections: | Department of Applied Informatics |
Files in This Item:
File | Description | Size | Format | |
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EJAM-D-16-00169_R1 - preprint.pdf | preprint (revision 1) | 334,04 kB | Adobe PDF | View/Open |
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