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http://dx.doi.org/10.4134/BKMS.2009.46.4.701

THE SIMULTANEOUS APPROXIMATION ORDER BY NEURAL NETWORKS WITH A SQUASHING FUNCTION  

Hahm, Nahm-Woo (DEPARTMENT OF MATHEMATIC UNIVERSITY OF INCHEON)
Publication Information
Bulletin of the Korean Mathematical Society / v.46, no.4, 2009 , pp. 701-712 More about this Journal
Abstract
In this paper, we study the simultaneous approximation to functions in $C^m$[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;
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1 P. Cardaliaguet and G. Euvrard, Approximation of a function and its derivative with a neural network, Neural Networks 5 (1992), 207–220   DOI   ScienceOn
2 R. A. DeVore and G. G. Lorentz, Constructive Approximation, Springer Verlag, Heidelberg, 1993
3 B. Gao and Y. Xu, Univariant approximation by superpositions of a sigmoidal function, J. Math. Anal. Appl. 178 (1993), no. 1, 221–226   DOI   ScienceOn
4 Y. Ito, Simultaneous Lp-approximations of polynomials and dervatives on the whole space, Arti. Neural Networks Conf. (1999), 587–592
5 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   DOI   ScienceOn
6 F. Li and Z. Xu, The essential order of simultaneous approximation for neural networks, Appl. Math. Comput. 194 (2007), no. 1, 120–127   DOI   ScienceOn
7 G. G. Lorentz, Bernstein Polynomials, Chelsea, Engelwood Cliffs, 1986
8 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   DOI   ScienceOn
9 M. V. Medvedeva, On sigmoidal functions, Moscow Univ. Math. Bull. 53 (1998), no. 1, 16–19
10 H. N. Mhaskar and N. Hahm, Neural networks for functional approximation and system identification, Neural Computation 9 (1997), no. 1, 143–159   DOI   ScienceOn
11 R. M. Burton and H. G. Dehling, Universal approximation in p-mean by neural networks, Neural Networks 11 (1998), 661–667   DOI   ScienceOn
12 D. E. Rumelhart, G. E. Hinton, and R. J. Williams, Parallel Distributed Processing : explorations in the microstructure of cognition, MIT Press, Massachusetts, 1986
13 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   DOI   ScienceOn
14 X. Li, Simultaneous approximation of a multivariate functions and their derivatives by neural networks with one hidden layer, Neurocomputing 12 (1996), 327–343   DOI   ScienceOn