HERMITE SCATTERED DATA FITTING BY THE PENALIZED LEAST SQUARES METHOD

Given a set of scattered data with derivative values. If the data is noisy or there is anextremely large number of data, we use an extension of the penalized least squares methodof von Golitschek and Schumaker [Serdica, 18 (2002), pp.1001-1020] to fit the data. Weshow that the extension of the penalized least squares method produces a unique splineto fit the data. Also we give the error bound for the extension method. Some numericalexamples are presented to demonstrate the effectiveness of the proposed method.