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

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.

[Walter Roberson]

A homework question?

[Platon]

No not really! But If you have a relevant response I thank you in advance

Answer 1

[Greg Heath]

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