Linear/linear rational spline interpolation

Abstract

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 ¦S(x_i ) − y(x_i )¦8 = O(h ⁴) on uniform mesh x_i = a + ih, i = 0,…, n. We prove also the superconvergence of order h³ for the first derivative and of order h² for 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.

First published online: 10 Feb 2011