Multilayer feedforward networks are universal approximators
Neural Networks
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
On simultaneous approximations by radial basis function neural networks
Applied Mathematics and Computation
Uniform approximation by neural networks
Journal of Approximation Theory
Simultaneous Lp-approximation order for neural networks
Neural Networks
Neural networks for optimal approximation of smooth and analytic functions
Neural Computation
Univariate fuzzy-random neural network approximation operators
Computers & Mathematics with Applications
An approximation by neural networkswith a fixed weight
Computers & Mathematics with Applications
Universal approximation bounds for superpositions of a sigmoidal function
IEEE Transactions on Information Theory
Approximation bounds for smooth functions in C(Rd) by neural and mixture networks
IEEE Transactions on Neural Networks
Smooth function approximation using neural networks
IEEE Transactions on Neural Networks
The errors of simultaneous approximation of multivariate functions by neural networks
Computers & Mathematics with Applications
Essential rate for approximation by spherical neural networks
Neural Networks
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There have been many studies on the simultaneous approximation capability of feed-forward neural networks (FNNs). Most of these, however, are only concerned with the density or feasibility of performing simultaneous approximations. This paper considers the simultaneous approximation of algebraic polynomials, employing Taylor expansion and an algebraic constructive approach, to construct a class of FNNs which realize the simultaneous approximation of any smooth univariate function and all its derivatives. We also present an upper bound on the approximation accuracy of the FNNs, expressed in terms of the modulus of continuity of the functions to be approximated. The results obtained in this paper reveal the complexity of simultaneous approximation by FNNs.