Abstract
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.
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© 2006 Birkhäuser Boston
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(2006). Approximation Theory. In: Neural Networks and Sea Time Series. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4459-8_5
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DOI: https://doi.org/10.1007/0-8176-4459-8_5
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4347-8
Online ISBN: 978-0-8176-4459-8
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