Bivariate cubic L1 smoothing splines are introduced. The coefficients of a cubic L1 smoothing spline are calculated by minimizing the weighted sum of the L1 norms ofsecond derivatives of the spline and the l1 norm of the residuals of the data-fitting equations. Cubic L1 smoothing splines are compared with conventional cubic smoothingsplines based on the L2 and l2 norms. Computational results for fitting a challengingdata set consisting of discontinuously connected flat and quadratic areas by C1-smooth Sibson-element splines on a tensor-product grid are presented. In these computational results, the cubic L1 smoothing splines preserve the shape of the data while cubic L2 smoothing splines do not.
Citation: Journal of Approximation Theory
Pub Type: Journals
bivariate approximation, least absolute regression, least squares regression, sibson elements, smoothing splines, tensor-product grids