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Positivity of cubic polynomials on intervals and positive spline interpolation. (English) Zbl 0642.41007

Summary: 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 cubic C 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.

MSC:

41A15 Spline approximation
65D07 Numerical computation using splines
41A10 Approximation by polynomials

Software:

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References:

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