Artificial neural networks approach to the bivariate interpolation problem

Neural networks have already been successfully applied to model the real world problems. The main aim of this paper is to offer an efficient bivariate interpolation methodology that is based on the artificial neural networks. To do this, a multi-layer feed-forward neural network on the real set poin...

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Vydáno v:Afrika mathematica Ročník 26; číslo 7-8; s. 1187 - 1197
Hlavní autoři: Jafarian, A., Basiligheh, N.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2015
Témata:
Applications of Mathematics
History of Mathematical Sciences
Mathematics
Mathematics and Statistics
Mathematics Education
03C40
62M45
Cost function
Feed-forward neural network
Approximate solution
Learning algorithm
Bivariate interpolating polynomial
ISSN:1012-9405, 2190-7668
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Shrnutí:Neural networks have already been successfully applied to model the real world problems. The main aim of this paper is to offer an efficient bivariate interpolation methodology that is based on the artificial neural networks. To do this, a multi-layer feed-forward neural network on the real set points is used. The proposed neural network architecture is able to approximate the unknown interpolating polynomial’s coefficients by using a learning algorithm which is based on the gradient descent method. Finally, to demonstrate the efficiency and accuracy of the proposed method, some test problems in comparison with former techniques, are considered.
ISSN:1012-9405
2190-7668
DOI:10.1007/s13370-014-0276-5