Abstract
This paper proposes a comparison between wavelet neural networks (WNN), RBF neural network and polynomial approximation in term of 1-D and 2-D functions approximation. We present a novel wavelet neural network, based on Beta wavelets, for 1-D and 2-D functions approximation. Our purpose is to approximate an unknown function f: Rn -> R from scattered samples (x(i); y = f(x(i))) i=1 ... n, where first, we have little a priori knowledge on the unknown function f: it lives in some infinite dimensional smooth function space and second the function approximation process is performed iteratively: each new measure on the function (x(i); f(x(i))) is used to compute a new estimate (f) over cap as an approximation of the function f Simulation results are demonstrated to validate the generalization ability and efficiency of the proposed Beta wavelet network.