References
- B. Gao and Y. Xu, Univariant approximation by superpositions of a sigmoidal function, J. Math. Anal. Appl. 178(1993), 221-226 https://doi.org/10.1006/jmaa.1993.1302
-
N. Hahm and B. I. Hong. Approximation order to a function in
$C^1[0,1]$ and its derivative by a feedforward neural network, J. of Appl. Math. and Info. 27(2009), 137-147. -
N. Hahm and B. I. Hong, Approximation order to a function in
$L_{p}$ space by generalized translation netowrks, Honam Math. Jour. 28(2006), 125-133. -
B. I. Hong and N. Hahm, Approximation order to a function in
${\bar{C}}$ (R) by supersposition of a sigmoidal function, Appl. Math. Lett. 15(2002), 591-597. https://doi.org/10.1016/S0893-9659(02)80011-8 - B. L. Kalman and S. C. Kwasny, Why Tanh : Choosing a sigmoidal function, Int. Joint Conf. Oil Neural Networks 4(1992), 578-581.
- G. Lewicki and G. Marino, Approximation of functions of finite variation by superpositions of a sigmoidal function, Appl. Math. Lett. 17(2004), 1147-1152 https://doi.org/10.1016/j.aml.2003.11.006
- X. Li, Simultaneous approximation of a multivariate junctions and their derivatives by neural networks with one hidden layer, Neurocomputing 12(1996), 327-343 https://doi.org/10.1016/0925-2312(95)00070-4
- H. N. Mhaskar and N. Hahm, Neural networks for functional approximation and system identification, Neural Comp. 9(1997), 143-159. https://doi.org/10.1162/neco.1997.9.1.143
- I. P. Natanson, Constructive function theory, Frederick Publ., 1964.
- E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, 1970.
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- THE CAPABILITY OF LOCALIZED NEURAL NETWORK APPROXIMATION vol.35, pp.4, 2013, https://doi.org/10.5831/HMJ.2013.35.4.729