| 多元Stancu多项式与连续模 |
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| 引用本文： | 曹飞龙.多元Stancu多项式与连续模[J].数学学报,2005,48(1):51-62. |
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| 作者姓名： | 曹飞龙 |
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| 作者单位： | 中国计量学院理学院信息与数学科学系 |
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| 基金项目： | 国家自然科学基金(60473034)
博士后基金(20040350225)
浙江省自然科学基金(102002)
高校中青年学科带头人基金资助项目 |
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| 摘 要： | 本文研究单纯形上多元Stancu多项式与连续模之间的关系,证明了Stancu多项式具有保持连续模的性质,推广了一元Bernstein多项式的相应结果.同时,利用多元函数的Ditzian-Totik连续模估计Stancu多项式逼近多元连续函数速度的上界和下界,得到一个使得逼近速度为O(n-a)(0
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| 关 键 词： | 单纯形 Stancu多项式 连续模 |
Multivariate Stancu Polynomials and Modulus of Continuity |
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| Fei Long CAO.Multivariate Stancu Polynomials and Modulus of Continuity[J].Acta Mathematica Sinica,2005,48(1):51-62. |
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| Authors: | Fei Long CAO |
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| Institution: | Fei Long CAODepartment of Information and Mathematical Sciences, Faculty of Science, China Jiliang University,Hangzhou 310018, P. R. China |
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| Abstract: | This paper investigates the relationship between the multivariate Stancu polynomials and the modulus of continuity. First, it is shown that the property of modulus of continuity is preserved by the multivariate Stancu polynomials and hence a corresponding one to univariate Bernstein polynomials is generalized. Then, by means of the Ditzian-Totik's modulus of continuity, the estimates of upper and lower bounds of rate for the polynomials approximating the continuous function are given. A necessary and sufficient condition on the smoothness of function is also obtained from the estimates so that the rate of approximation is O(n-a) (0 < a < 1). |
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| Keywords: | Simplex Stancu polynomials Modulus of continuity |
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