| 多元StancU多项式的最优逼近阶及其特征刻画 |
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| 引用本文： | 曹飞龙,杨汝月.多元StancU多项式的最优逼近阶及其特征刻画[J].应用数学学报,2004,27(2):218-229. |
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| 作者姓名： | 曹飞龙 杨汝月 |
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| 作者单位： | 1. 绍兴文理学院数学系,浙江,绍兴,312000
2. 中国计量学院理学院,杭州,310034 |
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| 基金项目： | 教育部科学技术研究重点基金(03142)，浙江省自然科学基金(102002) |
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| 摘 要： | 对于单纯形上的多元Stancu多项式Mn(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-K-泛函确定满足‖Mnf-f‖=O(n^-1)的函数类．同时，得到了逼近的正定理和逆定理．
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| 关 键 词： | 单纯形 多元Stancu多项式 最优逼近阶 连续函数 |
OPTIMAL APPROXIMATION ORDER AND ITS CHARACTERIZATION FOR MULTIVARIATE STANCU POLYNOMIALS |
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| CAO FEILONG.OPTIMAL APPROXIMATION ORDER AND ITS CHARACTERIZATION FOR MULTIVARIATE STANCU POLYNOMIALS[J].Acta Mathematicae Applicatae Sinica,2004,27(2):218-229. |
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| Authors: | CAO FEILONG |
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| Institution: | CAO FEILONG Department of Mathematics,Shaoxing College of Arts and Sciences,Shaoxing 312000 YANG RUYUE Faculty Science,China Institute of Metrology,Hangzhou 310034 |
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| Abstract: | 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. |
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| Keywords: | Simplex stancu polynomials direct theorem inverse tneorem saturation |
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