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...

Full description

Saved in:
Bibliographic Details
Published in:Afrika mathematica Vol. 26; no. 7-8; pp. 1187 - 1197
Main Authors: Jafarian, A., Basiligheh, N.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2015
Subjects:
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
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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