Low-degree spline quasi-interpolants in the Bernstein basis

Abstract

In this paper we propose the construction of univariate low-degree quasi-interpolating splines in the Bernstein basis, considering C1 and C2 smoothness, specific polynomial reproduction properties and different sets of evaluation points. The splines are directly determined by setting their Bernstein–Bézier coefficients to appropriate combinations of the given data values. Moreover, we get quasi-interpolating splines with special properties, imposing particular requirements in case of free parameters. Finally, we provide numerical tests showing the performances of the proposed methods.