ERROR BOUNDS FOR INTERPOLATION IN THE MEAN INTEGRO QUADRATIC SPLINES AND SUPERCONVERGENCE POINTS

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