Quadratic spline interpolation with coinciding interpolation and spline grids (Q759937)

The authors consider the problem of quadratic spline interpolation of continuous functions in the case when the spline grid and the interpolation grid coincide. The main purpose of the paper is to deduce error estimations for the quadratic spline function s interpolating a given function f on a grid with width h. In order to obtain convergence procedures it is assumed that the function to be interpolated is suitably smooth or possesses a special behaviour. For example, if f' is of bounded variation then the interpolating spline s converges to f for arbitrary grid sequences. The same result is valid for functions of higher smoothness. The authors examine a best approximation property of quadratic interpolating splines. In the final part of the paper the authors find an approximation solution for a boundary value problem of first order by means of the collocation method using quadratic spline functions.