Fair upper bounds for the curvature in univariate convex interpolation |
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Authors: | Jochen W Schmidt Walter hess |
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Institution: | (1) Institute of Numerical Mathematics, Technical University of Dresden, D-01062 Dresden, Germany |
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Abstract: | In convex interpolation the curvature of the interpolants should be as small as possible. We attack this problem by treating
interpolation subject to bounds on the curvature. In view of the concexity the lower bound is equal to zero while the upper
bound is assumed to be piecewise constant. The upper bounds are called fair with respect to a function class if the interpolation
problem becomes solvable for all data sets in strictly convex position. We derive fair a priori bounds for classes of quadraticC
1, cubicC
2, and quarticC
3 splines on refined grids. |
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Keywords: | 65D07 41A15 |
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