U. Amato et Dt. Vuza, WAVELET SIMULTANEOUS APPROXIMATION FROM SAMPLES AFFECTED BY NOISE, Computers & mathematics with applications (1987), 36(5), 1998, pp. 101-111
The authors recently introduced a p(th) order wavelet regularization m
ethod together with the GCV criterion for approximating a function fro
m 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 si
gnal. 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 auth
ors also works for the H-q-norm, 0 less than or equal to q < p. (C) 19
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