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 Dmsplines. We establish a result of local convergence of the approximations provided by the method. Finally, we give some numerical and graphical examples. © 2001 Elsevier Science B.V. All rights reserved.
López De Silanes, M. C., Parra, M. C., Pasadas, M., & Torrens, J. J. (2001). Spline approximation of discontinuous multivariate functions from scattered data. Journal of Computational and Applied Mathematics, 131(1–2), 281–298. https://doi.org/10.1016/S0377-0427(00)00268-5