摘要
对于单纯形上的多元 Stancu 多项式M_n(f,x)(它是多元 Bernstein 多项式的广义形式),我们给出其对连续函数的最优逼近阶及其特征刻画,即我们将依据某一 K-泛函确定满足||M_nf-f||=O(n^(-1))的函数类。同时,得到了逼近的正定理和逆定理。
For the multivariate Stancu polynomials M_n(f, x), which are generalization of
the Bernstein polynomials defined on the simplex, the optimal approximation order and its
characterization of these polynomials approximating the continuous functions will be given.
That is, we will find the class of functions for which ||M_nf-f||=O(n^(-1)) in term of the
behavior of a certain K-functional. Moreover, we also give the direct and converse theorems
of approximation.
出处
《应用数学学报》
CSCD
北大核心
2004年第2期218-229,共12页
Acta Mathematicae Applicatae Sinica
基金
教育部科学技术研究重点基金(03142)
浙江省自然科学基金(102002)
