Surface fitting and numerical gradient computations by discrete mollification

We review the δ-mollification procedure for automatic fitting of surfaces defined from discrete noisy data functions in R2. As a further application, the stable numerical computation of gradient fields from discrete noisy data is also investigated. The main features of the algorithm are: 1. 1. information about the noise is needed; 2. 2. the mollification parameters are chosen automatically by means of the Generalized Cross Validation (GCV) procedure. A complete error analysis of the method is provided together with several numerical examples of interest.