Neural network approximation of continuous functionals and continuous functions on compactifications

 STINCHCOMBE M. B.
 Department of Economics, The University of Texas at Austin
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Author(s)

 STINCHCOMBE M. B.
 Department of Economics, The University of Texas at Austin
Journal

 Neural Networks

Neural Networks 12(3), 467477, 19990401
References: 35

1
 A constructive proof of Cybenko's approximation theorem and its extensions

CHEN T. P.
Proceedings of the 22nd Symposium on the Interface, 163168, 1990
Cited by (1)

2
 There exists a neural network that does not make avoidable mistakes

GALLANT A. R.
Proceedings of the Second International Joint Conference on Neural Networks I, 593606, 1988
Cited by (1)

3
 <no title>

GUILLEMIN V.
Differential Topology, 1974
Cited by (2)

4
 Theory of the back propagation neural network

HECHTNIELSON R.
Proceedings of the International Joint Conference on neural networks I, 593606, 1989
Cited by (1)

5
 <no title>

HUANG G. B.
On approximation capability in C(R^n) by multilayer feedforward networks and related problems, photocopy, 1997
Cited by (1)

6
 <no title>

HURD A. E.
An introduction to nonstandard real analysis, 1985
Cited by (1)

7
 <no title>

KELLEY J. L.
General topology, 1955
Cited by (9)

8
 Approximating and learning unknown mappings using multilayer feedforward networks with bounded weights

STINCHCOMBE M.
Proceedings of the International Joint Conference on Neural Networks III, 716, 1990
Cited by (1)

9
 Approximation of a function and its derivative with a neural network

CARDALIAGUET P.
Neural Networks 5(2), 207220, 1992
Cited by (3)

10
 Approximation capability to functions of several variables, nonlinear functions, and operators by radial basis function neural networks

CHEN T.
IEEE Trans. Neural Networks 6, 749755, 1995
Cited by (11)

11
 Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems

CHEN T.
IEEE Transactions on Neural Networks 6(4), 911917, 1995
DOI Cited by (7)

12
 Approximation capability in C(R^^^n) by multilayer feedforward networks and related problems

CHEN T.
IEEE Transactions on Neural Networks 6(1), 2530, 1995
Cited by (3)

13
 Approximation by ridge functions and neural networks with one hidden layer

CHUI C.
Journal of Approximation Theory 70, 131141, 1992
DOI Cited by (3)

14
 Limitations of the approximation capabilities of neural networks with one hidden layer

CHUI C. K.
Advances in Computational Mathematics 5, 233243, 1996
DOI Cited by (2)

15
 Approximation by superpositions of a sigmoidal function

CYBENKO G.
Mathematics of Control, Signals and Systems 2, 303314, 1989
DOI Cited by (93)

16
 Radial Basis Function Neural Networks for Approximation and Estimation of Nonlinear Stochastic Dynamics Systems

ELANAYAR S.
IEEE Trans. Neural Networks 5(4), 594603, 1994
Cited by (4)

17
 <no title>

FUNAHASHI K.
On the Approximate Realization of Continuous Mapping by Neural Networks 2, 183192, 1989
DOI Cited by (203)

18
 Approximation of dynamical systems by continuous time recurrent neural networks

FUNAHASHI K.
Neural Networks 6, 801806, 1993
Cited by (24)

19
 Approximation capabilities of multilayer feedforward networks

HORNIK K.
Neural Networks 4(2), 251257, 1991
Cited by (19)

20
 Some new results on neural network approximation

HORNIK K.
Neural Networks 6, 10691072, 1993
Cited by (12)

21
 Multilayer feedforward neural networks are universal approximators

HORNIK K.
Neural Networks 25, 359366, 1989
DOI Cited by (135)

22
 Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks

HORNIK K.
Neural Networks 35, 551/560, 1990
DOI Cited by (21)

23
 Approximation capability of layered networks with sigmoid units on tow layers

ITO Y.
Neural Computation 6(6), 12331243, 1993
DOI Cited by (1)

24
 Multilayer feedforward networks with a nonpolynomial activation function can approximate any function

LESHNO M.
Neural Networks 6, 861867, 1993
DOI Cited by (23)

25
 Simultaneous approximation of multivariate functions and their derivatives by neural networks with one hidden layer

LI X.
Neurocomputing 12(4), 327343, 1996
DOI Cited by (1)

26
 Approximation properties of a multilayered feedforward artificial neural network

MHASKAR H. N.
Advances in Computational Mathematics 1(1), 6180, 1993
DOI Cited by (3)

27
 Approximation by superposition of sigmoidal and radial basis functions

MHASKAR H. N.
Advances in Applied Mathematics 13, 350373, 1992
DOI Cited by (11)

28
 Degree of approximation by neural and translation networks with a single hidden layer

MHASKAR H. N.
Advances in Applied Mathematics 16, 151183, 1995
DOI Cited by (4)

29
 Approximation and radialbasisfunction networks

PARK J.
Neural Computation 5, 305316, 1993
DOI Cited by (20)

30
 Nonlinear approximations using elliptic basis function networks

PARK J. Y.
Circuits, Systems and Signal Processing 13(1), 99113, 1994
Cited by (1)

31
 Notes on weighted norms and network approximation of functionals

SANDBERG I. W.
IEEE Transactions on Circuits and SystemsI : Fundamental Theory and Applications 43(7), 600601, 1996
Cited by (2)

32
 Network approximation of inputoutput maps and functionals

SANDBERG I. W.
Circuits Systems Signal Processing 15(6), 711725, 1996
Cited by (2)

33
 Precision and approximate flatness in artificial neural networks

STINCHCOMBE M.
Neural Computation 7(5), 10211039, 1995
DOI Cited by (1)

34
 Universal approximation using feedforward networks with nonsigmoid hidden layer activation functions

STINCHOCOMBE M.
Proceedings of the International Joint Conference on Neural Networks I, 613617, 1989
Cited by (2)

35
 Using feedforward networks to distinguish multivariate populations

STINCHCOMBE M.
Proceedings of the International Joint Conference on Neural Networks I, 788793, 1992
Cited by (1)
Cited by: 1

1
 Functional multilayer perceptron : a nonlinear tool for functional data analysis

ROSSI Fabrice , CONANGUEZ Brieuc
Neural networks : the official journal of the International Neural Network Society 18(1), 4560, 20050101
References (31)