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Positivity of cubic polynomials on intervals and positive spline interpolation

by: Jochen W Schmidt, Walter Heß
BIT Numerical Mathematics, Vol. 28, No. 2. (1 June 1988), pp. 340-352.

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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 cubicC1-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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