Approximation by ridge functions and neural networks with one hidden layer
Journal of Approximation Theory
On simultaneous approximations by radial basis function neural networks
Applied Mathematics and Computation
Simultaneous Lp-approximation order for neural networks
Neural Networks
Pointwise approximation for neural networks
ISNN'05 Proceedings of the Second international conference on Advances in Neural Networks - Volume Part I
Universal approximation bounds for superpositions of a sigmoidal function
IEEE Transactions on Information Theory
The approximation operators with sigmoidal functions
Computers & Mathematics with Applications
Multivariate sigmoidal neural network approximation
Neural Networks
The errors of simultaneous approximation of multivariate functions by neural networks
Computers & Mathematics with Applications
Approximation of curves contained on the surface by freed-forward neural networks
AICI'11 Proceedings of the Third international conference on Artificial intelligence and computational intelligence - Volume Part III
The errors of approximation for feedforward neural networks in the Lp metric
Mathematical and Computer Modelling: An International Journal
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Neural networks are widely used in many applications including astronomical physics, image processing, recognition, robotics and automated target tracking, etc. Their ability to approximate arbitrary functions is the main reason for this popularity. The main result of this paper is a constructive proof of a formula for the upper bound of the approximation error by feedforward neural networks with one hidden layer of sigmoidal units and a linear output. The result can also be used to estimate complexity of the maximum error network. An example to demonstrate the theoretical result is given.