Wavelet simultaneous approximation from samples affected by noise

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 less than or equal to q < p. (C) 1998 Elsevier Science Ltd. All rights reserved.