A new class of C1 piecewise-cubic interpolatory polynomials is defined, by generalizing the definition of cubic X-splines given recently by Clenshaw & Negus (1978). It is shown that this new class contains a number of ...

A class of end conditions is derived for cubic spline interpolation at unequally spaced knots. These conditions are in terms of function values at the knots and lead to 0 (h4) convergence uniformly on the interval of ...

Let s be a cubic spline, with equally spaced knots on [a, b] interpolating a given function y at the knots. The parameters which determine s are used to construct a piecewise defined polynomial P of degree four. It is shown ...