Linear/Linear Rational Spline Interpolation

For a strictly monotone function y on [a, b] we describe the construction of an interpolating linear/linear rational spline S of smoothness class C-1. We show that for the linear/linear rational splines we obtain parallel to S(x(i)) - y(x(i))parallel to(infinity) = O(h(4)) on uniform mesh x(i) = a + ih, i = 0, ... , n. We prove also the superconvergence of order h(3) for the first derivative and of order h(2) for the second derivative of S in certain points. Numerical examples support the obtained theoretical results.