The convergence of three L1 spline methods for scattered data interpolation and fitting

The convergences of three L1 spline methods for scattered data interpolation and fitting using bivariate spline spaces are studied in this paper. That is, L1 interpolatory splines, splines of least absolute deviation, and L1 smoothing splines are shown to converge to the given data function under some conditions and hence, the surfaces from these three methods will resemble the given data values.