We describe the construction of an interpolating quadratic/linear rational spline S of smoothness class C2 for a strictly convex (or strictly concave) function y on [a, b]. On uniform mesh xi= a + ih, i = 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 h4 for the first derivative, of order h3 for the second derivative and of order h2for the third derivative of S in certain points. Corresponding numerical examples are given.
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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