For a strictly monotone function y on [a, b] we describe the construction of an interpolating linear/linear rational spline S of smoothness class C1. We show that for the linear/linear rational splines we obtain ¦S(xi) − y(xi)¦8 = O(h4) on uniform mesh xi = a + ih, i = 0,…, n. We prove also the superconvergence of order h3for the first derivative and of order h2for the second derivative of S in certain points. Numerical examples support the obtained theoretical results.
This work was supported by the Estonian Science Foundation grant 8313.
Ideon, E., & Oja, P. (2010). Linear/linear rational spline interpolation. Mathematical Modelling and Analysis, 15(4), 447-455. https://doi.org/10.3846/1392-6292.2010.15.447-455
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