Abstract 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.

中文翻译：

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Bernstein 基的准插值算子

摘要 本文的目的是提出一个基于伯恩斯坦基的多项式拟插值族。更准确地说，我们将结合极坐标形式和对称多项式的强特征来推导出伯恩斯坦基表示中的准插值系数。我们还推导出了一组样条准插值器，它们可再现高达 2 次的多项式函数。数值例子支持理论结果，并表明所提出的方案简单有效。