单纯形上Bernstein多项式的一些性质

Some Properties of Bernstein Polynomials on a Simples

设Ｂ＿ｍ（ｆ，·）为函数ｆ在ｄ维单纯形σ上的ｎ阶Ｂｅｒｎｓｔｅｉｎ多项式，本文对ｆ∈Ｃ￣ｒ（σ）及ｆ∈Ｃｒ＋２（σ）给出了ｆ的各阶编导数用Ｂ＿ｎ（ｆ，·）相应偏导数逼近的误差估计．

Let B_n(f,) be the Bernstein polynomial of degree n for a continuous functionf with respect to a d-dimensional simplex σ. In this paperi the approximiation error ofpartial derivatives of f by the partial derivatives of B_n(f,) for f ∈ C￣r(σ) and for f ∈C￣r+2(σ) are obtained. Also, the approximation, in L_p- norm, by the partial derivativesof Bernstein polynomials with integral coefficients on the simplex is considered.