Low-degree spline quasi-interpolants in the Bernstein basis

In this paper we propose the construction of univariate low-degree quasi-interpolating splines in the Bernstein basis, considering C 1 and C 2 smoothness, specific polynomial re-production properties and different sets of evaluation points. The splines are directly de-termined by setting their Bernstein-Bezier coefficients to appropriate combinations of the given data values. Moreover, we get quasi-interpolating splines with special properties, im-posing particular requirements in case of free parameters. Finally, we provide numerical tests showing the performances of the proposed methods. & COPY; 2023 Elsevier Inc. All rights reserved.