Local smoothing splines with a regularizing parameter (Q1814526)

This paper presents a contribution to the following problem: incorrect values of a function are given and a good approximation of this function and its derivatives must be found. The problem is solved by using a quasi-interpolating formula, in which I. J. Schoenberg's variation- diminishing quasi-interpolant is linearly combined with a special polynomial spline with simple knots constructed by the author. In the combination there is a free parameter and its suitable choice leads to good numerical results. This is shown in the case of functions of one and two variables.