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Quadratic/linear rational spline interpolation

Abstract

We describe the construction of an interpolating quadratic/linear rational spline S of smoothness class C 2 for a strictly convex (or strictly concave) function y on [a, b]. On uniform mesh x i a + ihi = 0,..., n, in the case of sufficiently smooth function y the expansions of S and its derivatives are obtained. They give the superconvergence of order h 4 for the first derivative, of order h 3 for the second derivative and of order h 2for the third derivative of S in certain points. Corresponding numerical examples are given.

Keyword : rational spline, interpolation, superconvergence

How to Cite
Ideon, E., & Oja, P. (2013). Quadratic/linear rational spline interpolation. Mathematical Modelling and Analysis, 18(2), 250-259. https://doi.org/10.3846/13926292.2013.781071
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Apr 1, 2013
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