Computing the range of values of real functions using B-spline form

In this paper, we present an easy and efficient method for computing the range of a function by using spline quasi-interpolation. We exploit the close relationship between the spline function and its control polygon and use tight subdivision technique in order to obtain monotonic splines which make the range of the spline easy to compute. The proposed method is useful in case of given scattered data generated by some (unknown) function f or scientific measurements. Several numerical examples are given, for cubic and quintic quasi-interpolant approximant, to illustrate the efficiency and the performance of our method.