Approximation of φ-bounded variations functions by neural network
Xie Ting-fan · 2011
We studied the approximation of φ-bounded variation functions f on by the feed-forward neural network with bounded sigmoidal functions σ,which the degree of approximation by single hidden layer neural network is ‖σ‖φ-1{Vφ(fn)[a,b]/n}.If the active function was Heaviside function,we obtain that the degree of approximation is φ-1{Vφ(f)[a,b]/2n}.Further more,we extend the results to the whole real axis in the section 3.