Wavelet simultaneous approximation from samples affected by noise

Abstract

The authors recently introduced a p th order wavelet regularization method together with the GCV criterion for approximating a function from a finite sample affected by noise. Convergence results of the method were proven for the L 2-norm. The present paper addresses the problem of simultaneous approximation, which is of interest in applications, where derivatives are useful for extracting several features from a signal. It is proved that it is not needed to devise a special method to this purpose, since the convergence of the method devised by the authors also works for the H q -norm, 0 ≤ q < p.