Approximation order to a function in C̄(ℝ) by superposition of a sigmoidal function

Applied Mathematics Letters

Volumn 15, Issue 5, 2002, Pages 591-597

  Hong, Bum Il ^a   Hahm, Nahmwoo ^b  

^a Kyung Hee University   (South Korea)

^b SolarLight Ltd   (South Korea)

Author keywords

Approximation; Sigmoidal function; Superposition

Indexed keywords

EID: 31244437685     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(02)80011-8     Document Type: Article

References (8)

1. A.R. Barron, Universal approximation bounds for superposition of a sigmoidal function, IEEE Trans. Information Theory 39, 930-945, (1993).
2. T. Chen and H. Chen, A constructive proof and an extension of Cybenko's approximation theorem, In Computing Science and Statistics, Springer-Verlag, (1992).
3. G. Cybenko, Approximation by superposition of sigmoidal functions, Mathematics of Control, Signal and Systems 2, 303-314, (1989).
4. N. Hahm and B.I. Hong, Extension of localised approximation by neural networks, Bull. Austral. Math. Soc. 59, 121-131, (1999).
5. Y. Ito, Representation of functions by superpositions of a step or sigmoid function and their applications to neural network theory, Neural Networks 4, 385-394, (1991).
6. M. Leshno, V. Lin, A. Pinkus and S. Schocken, Multilayer feedforward networks with a nonpolynomial activation function can approximate any function, Neural Networks 6, 861-867, (1993).
7. M.B. Stinchcombe, Neural network approximation of continuous functional and continuous functions on compactifications, Neural Networks 12, 467-477, (1999).
8. E.W. Cheney and W. Light, A Course in Approximation Theory, Brooks/Cole, New York, (1999).