We construct generalized translation networks to uniformly approximate a class of nonlinear, continuous functionals defined on L p ([ 1,1] s ) for integer s 1, 1 p< 1 or C([1 ,1] s ). We obtain lower bounds on the possible order of approximation for such functionals in terms of any approximation process depending continuously upon a given number of parameters. Our networks almost achieve this order of approximation in terms of the number of parameters (neurons) involved in the network. The training is simple and noniterative; in particular, we avoid any optimization such as that involved in the usual back-propagation.
['H. N. Mhaskar', 'Nahmwoo Hahm']
Neural networks for functional approximation and system identification