Successive polynomial spline function approximation

Abstract

Abstract.The use of successive pol~momiat spline approximation is established as a method of improving the accuracy of estimates of derivatives of periodic functions approximated by interpolating odd order splines defined on a uniformly spaced set of data points. For the various configurations possible with this multipleapproximation method, bounds for the leading error terms are explicitly given. In particular, for the quintic spline, the variety of approximation sequences is described in detail.