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ON INTERPOLATION AND APPROXIMATION OF FUNCTIONS USING NEURAL NETWORKS
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Valery Nikolaevich Belovodsky
Ph.D., Associate Professor, DonNTU, Department of Computer Modeling and Design.
283001, 118 b Artyoma str., Donetsk.
Research interests: modeling of technical systems, nonlinear dynamics, fractals and mathematical design, neural networks.
UDC 519.6
DOI 10.24412/2413-7383-2024-3-4-19
Language: Russian
Annotation:
The evolution of neural networks and the ever-expanding field of their application dictate the need to study its theory basics at early stages of student learning. And it is natural to begin this process with consideration of typical problems of the approximation theory of functions in course of computational methods. Such tasks are discussed in this article. Using the example of a two-layer neural network, the possibilities of neural networks for interpolation and approximation of functions of one variable are studied. Computational experiments are being performed with the help of a specially developed program in which the error minimization of the neural network is carried out using a subroutine implementing Levenberg – Marquardt methods. Minimizing errors in the identification of network parameters is carried out by varying their initial values using the Sobol sequence. The results obtained are compared with classical algebraic approaches. The advantages and disadvantages of the neural approach are noted, the generalizations are made.
Keywords: interpolation, approximation, neural network, minimization, Sobol sequence.
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Release: 3(34)'2024
Chapter: MATHEMATICAL MODELING, NUMERICAL METHODS AND SOFTWARE SYSTEMS
How to quote:
Belovodskiy V. N. ON INTERPOLATION AND APPROXIMATION OF FUNCTIONS USING NEURAL NETWORKS [Text]
/ V. N. Belovodskiy
// Problems of artificial intelligence. - 2024. № 3 (34). - P. 4-19. - http://paijournal.guiaidn.ru/ru/2024/3(34)-1.html
