Multivariate sigmoidal neural network approximation

Neural Networks

Volumn 24, Issue 4, 2011, Pages 378-386

  Anastassiou, George A ^a  

^a University of Memphis   (United States)

Author keywords

Complex approximation; Multivariate modulus of continuiuty; Multivariate neural network approximation; Multivariate quasi interpolation operator; Sigmoidal function

Indexed keywords

COMPLEX APPROXIMATION; MULTIVARIATE MODULUS OF CONTINUIUTY; MULTIVARIATE NEURAL NETWORK APPROXIMATION; MULTIVARIATE QUASI-INTERPOLATION OPERATOR; SIGMOIDAL FUNCTIONS;

INTERPOLATION;

NEURAL NETWORKS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; DENSITY FUNCTIONAL THEORY; MATHEMATICAL COMPUTING; MULTIVARIATE ANALYSIS; OPERATOR; PRIORITY JOURNAL; QUANTITATIVE ANALYSIS; STATISTICAL ANALYSIS;

ALGORITHMS; ANIMALS; HUMANS; NEURAL NETWORKS (COMPUTER); STATISTICS AS TOPIC;

EID: 79951956614     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neunet.2011.01.003     Document Type: Article

References (26)

1. Anastassiou G.A. Rate of convergence of some neural network operators to the unit-univariate case. Journal of Mathematical Analysis and Applications 1997, 212:237-262.
2. Anastassiou G.A. Rate of convergence of some multivariate neural network operators to the unit. Journal of Computational and Applied Mathematics 2000, 40:1-19.
3. Anastassiou G.A. Quantitative approximations 2001, Chapman & Hall/CRC, Boca Raton, New York.
4. Anastassiou, G. A. (2010). Univariate sigmoidal neural network approximation (submitted for publication).
5. Barron A.R. Universal approximation bounds for superpositions of a sigmoidal function. IEEE Transactions on Information Theory 1993, 39:930-945.
6. Brauer F., Castillo-Chavez C. Mathematical models in population biology and epidemiology 2001, 8-9. Springer-Verlag, New York.
7. Cao F.L., Xie T.F., Xu Z.B. The estimate for approximation error of neural networks: a constructive approach. Neurocomputing 2008, 71:626-630.
8. Chen Z., Cao F. The approximation operators with sigmoidal functions. Computers and Mathematics with Applications 2009, 58:758-765.
9. Chen T.P., Chen H. Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its applications to a dynamic system. IEEE Transactions on Neural Networks 1995, 6:911-917.
10. Chui C.K., Li X. Approximation by ridge functions and neural networks with one hidden layer. Journal of Approximation Theory 1992, 70:131-141.
11. Cybenko G. Approximation by superpositions of sigmoidal function. Mathematics of Control, Signals, and Systems 1989, 2:303-314.
12. Ferrari S., Stengel R.F. Smooth function approximation using neural networks. IEEE Transactions on Neural Networks 2005, 16:24-38.
13. Funahashi K.I. On the approximate realization of continuous mappings by neural networks. Neural Networks 1989, 2:183-192.
14. Hahm N., Hong B.I. An approximation by neural networks with a fixed weight. Computers & Mathematics with Applications 2004, 47:1897-1903.
15. Hornik K., Stinchombe M., White H. Multilayer feedforward networks are universal approximators. Neural Networks 1989, 2:359-366.
16. Hornik K., Stinchombe M., White H. Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks. Neural Networks 1990, 3:551-560.
17. Hritonenko N., Yatsenko Y. Mathematical modeling in economics, ecology and the environment 2006, 92-93. Science Press, Beijing, Reprint.
18. Leshno M., Lin V.Y., Pinks A., Schocken S. Multilayer feedforward networks with a nonpolynomial activation function can approximate any function. Neural Networks 1993, 6:861-867.
19. Lorentz G.G. Approximation of functions 1966, Rinehart and Winston, New York.
20. Maiorov V., Meir R.S. Approximation bounds for smooth functions in C(Rd) by neural and mixture networks. IEEE Transactions on Neural Networks 1998, 9:969-978.
21. Makovoz Y. Uniform approximation by neural networks. Journal of Approximation Theory 1998, 95:215-228.
22. Mhaskar H.N., Micchelli C.A. Approximation by superposition of a sigmoidal function. Advances in Applied Mathematics 1992, 13:350-373.
23. Mhaskar H.N., Micchelli C.A. Degree of approximation by neural networks with a single hidden layer. Advances in Applied Mathematics 1995, 16:151-183.
24. Suzuki S. Constructive function approximation by three-layer artificial neural networks. Neural Networks 1998, 11:1049-1058.
25. Xie T.F., Zhou S.P. Approximation theory of real functions 1998, Hangzhou University Press, Hangzhou.
26. Xu Z.B., Cao F.L. The essential order of approximation for neural networks. Science in China. Series F 2004, 47:97-112.