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Mathematics of Computation

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A class of cubic splines obtained through minimum conditions


Authors: D. Bini and M. Capovani
Journal: Math. Comp. 46 (1986), 191-202
MSC: Primary 41A15; Secondary 65D07
MathSciNet review: 815840
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Abstract: A class of cubic spline minimizing some special functional is investigated. This class is determined by the solution of a quadratic programming problem in which the minimizing function depends linearly on a parameter $ \alpha < 2$. For $ \alpha = 1/2$ natural splines are obtained. For $ \alpha = - 1$ the spline minimizing the mean value of the third derivative is obtained. It is shown that this spline has the best convergence order.


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DOI: https://doi.org/10.1090/S0025-5718-1986-0815840-5
Article copyright: © Copyright 1986 American Mathematical Society