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Publication Citation: Shape-Preserving, Multi-Scale Fitting of Bivariate Data by Cubic L1 Smoothing Splines

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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
Research Areas: Math
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