Neural Networks are universal approximators, It is true for picewise continuous functions?

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George Cybenko had prouven that NN are universal approximators for continuous functions (see http://en.wikipedia.org/wiki/Universal_approximation_theorem). Can Neural Network approximate piecewise continuous functions? In particular in MATLAB NN tool box?
I need a response with references.

Accepted Answer

Greg Heath
Greg Heath on 8 Jun 2013
Yes. However, like fourier series, values at finite discontinuities will be the average of the left and right values.
If you don't have a text, my guess is that if you search on something like
neural uniform approximation
you should find something.
Try the comp.ai.neural-nets newsgroup and FAQ before Googling.
Hope this helps.
Thank you for formally accepting my answer
Greg

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