Overconvergence properties of quintic interpolatory splines (Q1113258)

This work generalizes the results of the authors [BIT 19, 19-26 (1979; Zbl 0407.65006)], concerning the superconvergence properties of a cubic interpolatory spline to the case of quintic spline interpolation. Let Q be a quintic spline with equally spaced knots interpolating a given function y at the knots. The parameters which determine Q are used to construct a piecewise defined polynomial P of degree six. The polynomial P gives better orders of approximation to y and its derivatives than those obtained from Q and the authors show that the superconvergence properties of Q are consequences of the properties of P. A numerical example illustrates the improvement in accuracy obtained when P is used instead of Q.