Quartic spline-on-spline interpolation

This paper provides a class of quartic spline-on-spline interpolation S-[k](x) on the function f(x), k = 0(1)4. Under the end conditions selected appropriately, we show that when the knots are equally spaced, with spacing h, then the order of accuracy of the spline-on-spline S-[0](x), S-[1](x) approximations f(x), f' (x) are O(h(5)), respectively, and the order of accuracy of the spline-on-spline S-[k](x) approximations f((k))(x) are O(h(4)), k = 2, 3, 4.