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|Author(s):||David E. Gilsinn; J E. Lavery;|
|Title:||Shape-Preserving, Multi-Scale Fitting of Bivariate Data by Cubic L1 Smoothing Splines|
|Published:||May 10, 2002|
|Abstract:||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|
|Pages:||pp. 283 - 293|
|Keywords:||bivariate approximation,least absolute regression,least squares regression,sibson elements,smoothing splines,tensor-product grids|
|PDF version:||Click here to retrieve PDF version of paper (230KB)|