Quadratic/Linear Rational Spline Interpolation

We describe the construction of an interpolating quadratic/linearrational 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(2) for the third derivative of S in certain points. Corresponding numerical examples are given.