Korean J. Math. Vol. 22 No. 2 (2014) pp.307-315
DOI: https://doi.org/10.11568/kjm.2014.22.2.307

Degree of approximation by periodic neural networks

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Published: Jun 15, 2014
Keywords:
De la Vallee Poussin sum, Neural network, Degree of approximation
Mathematics Subject Classification:
41A25, 41A30

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Nahmwoo Hahm
Department of Mathematics Incheon National University
Bum Il Hong
Kyung Hee University

Abstract

We investigate an approximation order of a continuous 2$\pi$-periodic function by periodic neural networks. By using the De La Valle e Poussin sum and the modulus of continuity, we obtain a degree of approximation by periodic neural networks.



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Supporting Agencies

This work was supported by the Incheon National University Research Grant in 2014.

References

[1] R. A. Devore and G. G. Lorentz, Constructive Approximation, Springer-Verlag (1993). Google Scholar

[2] 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. Google Scholar

[3] N. Hahm and B. Hong, The Capability of Periodic Neural Network Approximation, Korean J. Math. 18(2)(2010), 167-174. Google Scholar

[4] 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. Google Scholar

[5] H. N. Mhaskar and C. A. Micchelli, Approximation by Superposition of a Sigmoidal Function, Univ. of Cambridge Num. Anal. Report (1991), 1-26. Google Scholar

[6] I. P. Natanson, Constructive Function Theory-Uniform Approximation, Ungar Publ. (1964). Google Scholar

[7] S. Suzuki, Constructive Function-Approximation by Three-Layer Artificial Neural Networks, Neural Networks 11(1998), 1049-1058. Google Scholar

[8] Zarita Zainuddin and Ong Pauline, Function Approximation Using Artificial Neural Networks, WSEAS Trans. Math. 6(7) (2008), 333-338. Google Scholar