Quadratic/linear rational spline interpolation - Ideon, Erge; Oja, Peeter (Mathematical Modelling and Analysis, 2013)
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 + 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 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.