| 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 |
| PDF version: |
 Click here to retrieve PDF version of paper (225KB) |
