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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.
KeywordsNeural Network Approximation Theory Sigmoid Function Approximation Operator Synaptic Weight
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