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Mathematics of Computation

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The orders of approximation of the first derivative of cubic splines at the knots


Author: D. Kershaw
Journal: Math. Comp. 26 (1972), 191-198
MSC: Primary 65D10
MathSciNet review: 0300403
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Abstract: The order of approximation of the first derivative of four types of interpolating cubic splines are found. The splines are defined by a variety of endpoint conditions and include the natural cubic spline and the periodic cubic spline. It is found that for two types there is an increase in the order of approximation when equal intervals are used, and that for a special distribution of knots the same order can be realized for the natural spline.


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DOI: https://doi.org/10.1090/S0025-5718-1972-0300403-0
Keywords: Interpolation, cubic splines
Article copyright: © Copyright 1972 American Mathematical Society