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THE SIMULTANEOUS APPROXIMATION ORDER BY NEURAL NETWORKS WITH A SQUASHING FUNCTION
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 Title & Authors
THE SIMULTANEOUS APPROXIMATION ORDER BY NEURAL NETWORKS WITH A SQUASHING FUNCTION
Hahm, Nahm-Woo;
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 Abstract
In this paper, we study the simultaneous approximation to functions in [0, 1] by neural networks with a squashing function and the complexity related to the simultaneous approximation using a Bernstein polynomial and the modulus of continuity. Our proofs are constructive.
 Keywords
simultaneous approximation;Bernstein polynomial;squashing function;neural network;
 Language
English
 Cited by
 References
1.
R. M. Burton and H. G. Dehling, Universal approximation in p-mean by neural networks, Neural Networks 11 (1998), 661–667 crossref(new window)

2.
P. Cardaliaguet and G. Euvrard, Approximation of a function and its derivative with a neural network, Neural Networks 5 (1992), 207–220 crossref(new window)

3.
R. A. DeVore and G. G. Lorentz, Constructive Approximation, Springer Verlag, Heidelberg, 1993

4.
A. R. Gallant and H. White, On learning the derivatives of an unknown mapping with multilayer feedforward networks, Lett. Math. Phys. 5 (1992), 129–138 crossref(new window)

5.
B. Gao and Y. Xu, Univariant approximation by superpositions of a sigmoidal function, J. Math. Anal. Appl. 178 (1993), no. 1, 221–226 crossref(new window)

6.
Y. Ito, Simultaneous Lp-approximations of polynomials and dervatives on the whole space, Arti. Neural Networks Conf. (1999), 587–592

7.
G. Lewicki and G. Marino, Approximation of functions of finite variation by superpositions of a sigmoidal function, Appl. Math. Lett. 17 (2004), no. 10, 1147–1152 crossref(new window)

8.
F. Li and Z. Xu, The essential order of simultaneous approximation for neural networks, Appl. Math. Comput. 194 (2007), no. 1, 120–127 crossref(new window)

9.
X. Li, Simultaneous approximation of a multivariate functions and their derivatives by neural networks with one hidden layer, Neurocomputing 12 (1996), 327–343 crossref(new window)

10.
G. G. Lorentz, Bernstein Polynomials, Chelsea, Engelwood Cliffs, 1986

11.
B. Malakooti and Y. Q. Zhou, Approximation polynomial functions by feedforward artificial neural networks : capacity analysis and design, Appl. Math. and Comp. 90 (1998), 27–51 crossref(new window)

12.
M. V. Medvedeva, On sigmoidal functions, Moscow Univ. Math. Bull. 53 (1998), no. 1, 16–19

13.
H. N. Mhaskar and N. Hahm, Neural networks for functional approximation and system identification, Neural Computation 9 (1997), no. 1, 143–159 crossref(new window)

14.
D. E. Rumelhart, G. E. Hinton, and R. J. Williams, Parallel Distributed Processing : explorations in the microstructure of cognition, MIT Press, Massachusetts, 1986