Error Bounds for Integro Quadratic Spline Interpolation in the Mean and Superconvergence Points

Abstract

The problem of interpolation in the mean of a function by an integro quadratic spline given integrally averaged function values is considered. It is shown that an integro quadratic spline can be defined via a cubic interpolation spline. Since cubic interpolation splines have been studied quite well, well-known error bounds for them and some of their properties can be transferred to integro quadratic splines. Points of superconvergence of integro splines are found, i.e., points at which a spline or its derivatives provide a higher order of approximation.