Abstract
Wavelet neural networks (WNN) have recently attracted great interest, because of their advantages over radial basis function networks (RBFN) as they are universal approximators. In this paper we present a novel wavelet neural network, based on Beta wavelets, for 1-D and 2-D function approximation. Our purpose is to approximate an unknown function f: Rn → R from scattered samples (xi; yi = f(x)) i=1.…n, where:
we have little a priori knowledge on the unknown function f which lives in some infinite dimensional smooth function space,the function approximation process is performed iteratively: each new measure on the function (xi; f(xi)) is used to compute a new estimate \documentclass[12pt]{minimal}
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$${\hat f}$$\end{document} as an approximation of the function f.
Simulation results are demonstrated to validate the generalization ability and efficiency of the proposed Beta wavelet network.