THE CAPABILITY OF PERIODIC NEURAL NETWORK APPROXIMATION

  • Hahm, Nahmwoo (Department of Mathematics University of Incheon) ;
  • Hong, Bum Il (Department of Applied Mathematics Kyung Hee University)
  • 투고 : 2010.04.13
  • 심사 : 2010.06.07
  • 발행 : 2010.06.30

초록

In this paper, we investigate the possibility of $2{\pi}$-periodic continuous function approximation by periodic neural networks. Using the Riemann sum and the quadrature formula, we show the capability of a periodic neural network approximation.

키워드

참고문헌

  1. E. W. Cheney, Introduction to Approximation Theory, Chelsea (1982).
  2. R. A. Devore and G. G. Lorentz, Constructive Approximation, Springer-Verlag (1993).
  3. Zhou Guanzhen, On the Order of Approximation by Periodic Neural Networks Based on Scattered Nodes, Appl. Math. J. Chinese Univ. Ser. B 20(3)(2005), 352-362. https://doi.org/10.1007/s11766-005-0012-x
  4. G. G. Lorentz, Approximaton of Functions, Chelsea(1986).
  5. H. N. Mhaskar and C. A. Micchelli, Degree of Approximmation by Neural and Translation Networks with a Single Hidden Layer, Adv. in Appl. Math. 16(1995), 151-183. https://doi.org/10.1006/aama.1995.1008
  6. H. N. Mhaskar and C. A. Micchelli, Approximation by Superposition of a Sig- moidal Function, Univ. of Cambridge Num. Anal. Report (1991), 1-26.
  7. I. P. Natanson, Constructive Function Theory-Uniform Approximation, Ungar Publ. (1964).
  8. S. Suzuki, Constructive Function-Approximation by Three-Layer Artificial Neural Networks, Neural Networks 11(1998), 1049-1058. https://doi.org/10.1016/S0893-6080(98)00068-9
  9. M. S. Vyazovskaya and N. S. Pupashenko, On the Normalizing Multiplier of the Generalized Jackson Kernel, Math. Notes 80(1)(2006), 19-26. https://doi.org/10.1007/s11006-006-0103-x