A dual algorithm for convex-concave data smoothing by cubicC 2-splines |
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Authors: | Jochen W. Schmidt Isa Scholz |
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Affiliation: | (1) Sektion Mathematik, Technische Universität, Mommsenstrasse 13, DDR-8027 Dresden, German Democratic Republic;(2) Sektion Mathematik, Pädagogische Hochschule, Wigardstrasse 17, DDR-8060 Dresden, German Democratic Republic |
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Abstract: | Summary In this paper the problem of smoothing a given data set by cubicC2-splines is discussed. The spline may required to be convex in some parts of the domain and concave in other parts. Application of splines has the advantage that the smoothing problem is easily discretized. Moreover, the special structure of the arising finite dimensional convex program allows a dualization such that the resulting concave dual program is unconstrained. Therefore the latter program is treated numerically much more easier than the original program. Further, the validity of a return-formula is of importance by which a minimizer of the orginal program is obtained from a maximizer of the dual program.The theoretical background of this general approach is discussed and, above all, the details for applying the strategy to the present smoothing problem are elaborated. Also some numerical tests are presented. |
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Keywords: | AMS(MOS): 65D10, 41A15, 90C25 CR: G1.6 |
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