Multilayer feedforward networks are universal approximators
Neural Networks
Bernstein-Durrmeyer polynomials on a simplex
Journal of Approximation Theory
Approximation by superposition of sigmoidal and radial basis functions
Advances in Applied Mathematics
Approximation by ridge functions and neural networks with one hidden layer
Journal of Approximation Theory
Advances in Applied Mathematics
Improved rates and asymptotic normality for nonparametric neural network estimators
IEEE Transactions on Information Theory
Approximation bounds for smooth functions in C(Rd) by neural and mixture networks
IEEE Transactions on Neural Networks
Constructive approximation to multivariate function by decay RBF neural network
IEEE Transactions on Neural Networks
The multidimensional function approximation based on constructive wavelet RBF neural network
Applied Soft Computing
The errors of simultaneous approximation of multivariate functions by neural networks
Computers & Mathematics with Applications
Approximation bound of mixture networks in Lwp spaces
ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I
The essential approximation order for neural networks with trigonometric hidden layer units
ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I
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Simultaneous approximation of a function and its derivatives are required in many science and engineering applications. There have been many studies on the simultaneous approximation capability of feedforward neural networks (FNNs). Most of the studies are, however, only concerned with density or feasibility of performing simultaneous approximation with FNNs, and no quantitative estimation on approximation accuracy of the simultaneous approximation is given. Moreover, all existing density or feasibility results are established in the uniform metric only, and provide no solution to topology specification of the FNNs used. In this paper, by means of the Bernstein-Durrmeyer operator, a class of FNNs is constructed which realize the simultaneous approximation of any smooth multivariate function and all its existing partial derivatives. We present, by making use of multivariate approximation tools, a quantitative upper bound estimation on approximation accuracy of the simultaneous approximation of the FNNs in terms of the modulus of smoothness of the functions to be approximated. The obtained results reveals that the approximation speed of the constructed FNNs depends not only on the number of hidden units used, but also on the smoothness of functions to be approximated.