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Endpoint formulas for interpolatory cubic splines


Authors: Thomas I. Seidman and Robert J. Korsan
Journal: Math. Comp. 26 (1972), 897-900
MSC: Primary 65D05
DOI: https://doi.org/10.1090/S0025-5718-1972-0314228-3
MathSciNet review: 0314228
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Abstract: In the absence of known endpoint derivatives, the usual procedure is to use a ``natural'' spline interpolant which Kershaw has shown to have $ \mathcal{O}({h^4})$ error except near the endpoints. This note observes that either the use of appropriate finite-difference approximations for the endpoint derivatives or a proposed modification of the interpolation algorithm leads to $ \mathcal{O}({h^4})$ error uniformly in the interval of approximation.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1972-0314228-3
Keywords: Interpolation, cubic splines, endpoint formula
Article copyright: © Copyright 1972 American Mathematical Society