最佳多项式逼近与多元Bernstein算子的加权逼近阶

The best polynomial approximation and degree of weighted approximation of multivariate Bernstein operators

以加权最佳多项式逼近度为度量工具,建立单纯形上Bernstein算子加Jacobi权逼近的正逆定理,进而刻画逼近阶的特征.

With the best polynomial approximation as a metric tool, we have established the direct and inverse theorems of approximation with the Jacobi weight for multivariate Bernstein operators defined on simplex, and the behavior of the weighted approximation degree is characterized.