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Chapter 5
In one sense, neural networks
are
intrinsically function approximators.
They accept one or more inputs and produce one or more outputs.
Most networks produce a unique output for a given input, so this
qualifies them as functions. Thus, the entire gamut of applications of
neural networks falls into the blanket role of function approximation.
However, for the purposes of this chapter, we will consider the more
specific problem of using neural networks to map real-valued vectors
to real-valued vectors. As will be seen, this is still an extremely broad
category.
Univariate Function Approximation
Every student of numerical analysis