Geodesic
Simultaneous approximation of polynomial functions and its derivatives by feedforward artificial neural networks with one hidden layer
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 2, pp. 78-82.

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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. 
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N. S. Uzentsova; S. P. Sidorov. Simultaneous approximation of polynomial functions and its derivatives by feedforward artificial neural networks with one hidden layer. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 2, pp. 78-82. http://geodesic.mathdoc.fr/item/ISU_2013_13_2_a11/

[1] Galyshkin A., Neural Networks. The foundations of the theory, Goriachaia Liniia – Telekom, Moscow, 2012

[2] Haykin S., Neural networks: a comprehensive foundation, 2 ed., Prentice-Hall, Inc., N.J., 1999

[3] Malakooti B., Zhou Y. Q., “Approximating polynomial functions by feedforward artificial neural networks: capacity analysis and design”, Appl. Math. and Comp., 90 (1998), 27–52 | DOI | MR | Zbl

[4] Sidorov S. P., “On the error of approximation of algebraical polynomials by means of artificial feedforward neural networks”, Neirokomp'iutery: razrabotka, primenenie, 2005, no. 5, 13–17