05053888

j

05053888 De Canditiis, Daniela De Feis, Italia Pointwise convergence of Fourier regularization for smoothing data. J. Comput. Appl. Math. 196, No. 2, 540-552 (2006). 2006 Elsevier Science B.V. (North-Holland), Amsterdam EN Smoothing data Fourier regularization Generalized cross validation mean squared error convergence Zbl 0893.65073

doi:10.1016/j.cam.2005.10.009

The authors analyze the pointwise convergence properties of the Fourier regularized approximation considered by {\it U. Amato} and {\it I. De Feis} [J. Comput. Appl. Math. 87, 261--284 (1997; Zbl 0893.65073)]. It is proved that the smoothed solution is locally convergent but not locally optimal. It is also shown that pointwise optimality and superefficiency can be achieved for more regular subspaces. H. P. Dikshit (New Delhi)