Cite this article as:
Uzentsova N. S., Sidorov S. P. Simultaneous Approximation of Polynomial Functions and Its Derivatives by Feedforward Artificial Neural Networks with One Hidden Layer N. S.. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2013, vol. 13, iss. 2, pp. 78-82. DOI: https://doi.org/10.18500/1816-9791-2013-13-2-2-78-82
Simultaneous Approximation of Polynomial Functions and Its Derivatives by Feedforward Artificial Neural Networks with One Hidden Layer N. S.
In this paper we propose the algorithm for finding weights of feedforward artificial neural networks with one hidden layer to approximate polynomial functions and its derivatives with a given error. We use the rational sigmoidal function as a transfer function.
1. Galyshkin A. Neironnye seti. Osnovy teorii [Neural
Networks. The foundations of the theory]. Moscow,
Goriachaia Liniia – Telekom, 2012 (in Russian).
2. Haykin S. Neural Networks : A Comprehensive Foundation.
Second ed., New Jersey, Prentice-Hall, Inc.,
1999.
3. Malakooti B., Zhou Y. Q. Approximating Polynomial
Functions by Feedforward Artificial Neural Networks :
Capacity Analysis and Design. Appl. Math. and Comp.,
1998, vol. 90, pp. 27–52.
4. Sidorov S. P. Ob oshibke priblizheniia algebraicheskikh
polinomov neironnymi setiami priamogo rasprostraneniia
[On the error of approximation of algebraical polynomials
by means of artificial feedforward neural networks].
Neirokomp’iutery : razrabotka, primenenie, 2005, no. 5,
pp. 13–17 (in Russian).
