Approximation Theory

Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


In this chapter we discuss and show some results for the use of the neural network (NN) as a complete set of functions. The fact that the combination of the sigmoidal function corresponding to an NN can approximate any function is a simple consequence of the Stone-Weierstrass theorem and so such an approach is a convincing one. Furthermore, in the case of approximation theory the synaptic weights are given by some a priori estimates and in many cases could be directly evaluated from the data. This approach has, as a drawback, more errors than the NN constructed using the procedures described in the previous chapter.


Neural Network Approximation Theory Sigmoid Function Approximation Operator Synaptic Weight 
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© Birkhäuser Boston 2006

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