Positivity of cubic polynomials on intervals and positive spline interpolation |
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Authors: | Jochen W Schmidt Walter Heß |
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Institution: | (1) Department of Mathematics, Technical University of Dresden, Mommsenstraße 13, 8027 Dresden, German Democratic Republic |
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Abstract: | A criterion for the positivity of a cubic polynomial on a given interval is derived. By means of this result a necessary and sufficient condition is given under which cubicC
1-spline interpolants are nonnegative. Further, since such interpolants are not uniquely determined, for selecting one of them the geometric curvature is minimized. The arising optimization problem is solved numerically via dualization. |
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Keywords: | 65D17 41A15 90C20 |
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