Bivariate Free Knot Splines |
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Authors: | Torsten Schütze Hubert Schwetlick |
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Institution: | (1) Siemens AG, Corporate Technology, Information & Communications, Security (CT IC 3), D-81730 Munich, Germany;(2) Department of Mathematics, Dresden University of Technology, D-01062 Dresden, Germany |
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Abstract: | We consider the least squares approximation of gridded 2D data by tensor product splines with free knots. The smoothing functional to be minimized—a generalization of the univariate Schoenberg functional—is chosen in such a way that the solution of the bivariate problem separates into the solution of a sequence of univariate problems in case of fixed knots. The resulting optimization problem is a constrained separable least squares problem with tensor product structure. Based on some ideas developed by the authors for the univariate case, an efficient method for solving the specially structured 2D problem is proposed, analyzed and tested on hand of some examples from the literature. |
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Keywords: | Data fitting bivariate least squares approximation splines with free knots constrained separable optimization problems |
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