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
Uniform approximation by neural networks
Journal of Approximation Theory
The approximation operators with sigmoidal functions
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
Fractional neural network approximation
Computers & Mathematics with Applications
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Here we study the multivariate quantitative constructive approximation of real and complex valued continuous multivariate functions on a box or R^N, N@?N, by the multivariate quasi-interpolation sigmoidal neural network operators. The ''right'' operators for our goal are fully and precisely described. This approximation is derived by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order partial derivatives. Our multivariate operators are defined by using a multidimensional density function induced by the logarithmic sigmoidal function. The approximations are pointwise and uniform. The related feed-forward neural network is with one hidden layer.