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http://dx.doi.org/10.11568/kjm.2014.22.2.307

DEGREE OF APPROXIMATION BY PERIODIC NEURAL NETWORKS  

Hahm, Nahmwoo (Department of Mathematics Incheon National University)
Hong, Bum Il (Department of Applied Mathematics Kyung Hee University)
Publication Information
Korean Journal of Mathematics / v.22, no.2, 2014 , pp. 307-315 More about this Journal
Abstract
We investigate an approximation order of a continuous $2{\pi}$-periodic function by periodic neural networks. By using the De La Vall$\acute{e}$e Poussin sum and the modulus of continuity, we obtain a degree of approximation by periodic neural networks.
Keywords
De la Vall$\acute{e}$e Poussin sum; Neural network; Degree of approximation;
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  • Reference
1 N. Hahm and B. Hong, The Capability of Periodic Neural Network Approximation, Korean J. Math. 18 (2) (2010), 167-174.
2 H. N. Mhaskar and C. A. Micchelli, Degree of Approximation by Neural and Translation Networks with a Single Hidden Layer, Advanced in Appl. Math. 16 (1995), 151-183.   DOI   ScienceOn
3 H. N. Mhaskar and C. A. Micchelli, Approximation by Superposition of a Sigmoidal Function, Uni. of Cambridge Num. Anal. Report (1991), 1-26.
4 I. P. Natanson, Constructive Function Theory-Uniform Approximation, Ungar Publ. (1964).
5 S. Suzuki, Constructive Function-Approximation by Three-Layer Artificial Neu-ral Networks, Neural Networks 11 (1998), 1049-1058.   DOI   ScienceOn
6 Zarita Zainuddin and Ong Pauline, Function Approximation Using Artificial Neural Networks, WSEAS Trans. Math. 6 (7) (2008), 333-338.
7 R. A. Devore and G. G. Lorentz, Constructive Approximation, Springer-Verlag (1993).
8 Zhou Guanzhen, On the Order of Approximation by Periodic Neural Networks Based on Scattered Nodes, Appl. Math. J. Chinese Unib. Ser. B 20 (3) (2005), 352-362.   DOI   ScienceOn