Quasi-interpolant operators in Bernstein basis

The aim of this paper is to present a family of polynomial quasi-interpolants in Bernstein basis. More precisely, we will combine the strong features of the polar forms and the symmetric polynomials to derive the coefficients of the quasi-interpolant in the Bernstein basis representation. We also derive a collection of spline quasi-interpolants that reproduce polynomial functions up to degree 2. Numerical examples support the theoretical results and show that the proposed scheme is simple and effective.