A COMPARISON OF THE E(3) AND NOT-A-KNOT CUBIC-SPLINES

The algorithms and schemes of the cubic spline interpolation with two end conditions which do not require the derivative information at the end points are of great practical importance and have been included in several general purpose software libraries. The cubic spline with not-a-knot end conditions is one of them and it is implemented in the widely used IMSL and NAG software libraries. In this paper we compare the E(3) cubic spline with the not-a-knot cubic spline and we will show that the E(3) cubic spline is more accurate than the second one, and also, it has superconvergence properties which the not-a-knot cubic spline does not have. These superconvergence properties of the E(3) cubic spline can be used in different fields for better approximation.