Degree of approximation by periodic neural networks
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.
Subject classification41A25, 41A30
Sponsor(s)This work was supported by the Incheon National University Research Grant in 2014.
R. A. Devore and G. G. Lorentz, Constructive Approximation, Springer-Verlag (1993). (Google Scholar)
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)
N. Hahm and B. Hong, The Capability of Periodic Neural Network Approximation, Korean J. Math. 18(2)(2010), 167-174. (Google Scholar)
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)
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)
I. P. Natanson, Constructive Function Theory-Uniform Approximation, Ungar Publ. (1964). (Google Scholar)
S. Suzuki, Constructive Function-Approximation by Three-Layer Artificial Neural Networks, Neural Networks 11(1998), 1049-1058. (Google Scholar)
Zarita Zainuddin and Ong Pauline, Function Approximation Using Artificial Neural Networks, WSEAS Trans. Math. 6(7) (2008), 333-338. (Google Scholar)
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