Spline approximation of discontinuous multivariate functions from scattered data

The approximation of discontinuous multivariate functions from a set of scattered data points is usually a two-stage process: first, a detection algorithm is applied to localize the discontinuity sets, then the functions are reconstructed using a fitting method. In this paper we propose a new method for the second stage, based on the computation of discrete smoothing Dm-splines. We establish a result of local convergence of the approximations provided by the method. Finally, we give some numerical and graphical examples.