| 吴顺唐,洪东.单纯形上Bernstein多项式的一些性质[J].数学研究及应用,1994,14(3):355~366 |
| 单纯形上Bernstein多项式的一些性质 |
| Some Properties of Bernstein Polynomials on a Simples |
| 投稿时间：1992-06-20 |
| DOI：10.3770/j.issn:1000-341X.1994.03.007 |
| 中文关键词: |
| 英文关键词:Bernstein polynomial integral coefficient derivative approximation |
| 基金项目: |
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| 摘要点击次数: 2486 |
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| 中文摘要: |
| 设Ｂm（ｆ，·）为函数ｆ在ｄ维单纯形σ上的ｎ阶Ｂｅｒｎｓｔｅｉｎ多项式，本文对ｆ∈Ｃｒ（σ）及ｆ∈Ｃr+2（σ）给出了ｆ的各阶编导数用Ｂn（ｆ，·）相应偏导数逼近的误差估计．同时也考虑了整系数Ｂｅｒｎｓｔｅｉｎ多项式的Ｌp模估计 |
| 英文摘要: |
| Let Bn(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 Bn(f,) for f ∈ Cr(σ) and for f ∈Cr+2(σ) are obtained. Also, the approximation, in Lp- norm, by the partial derivativesof Bernstein polynomials with integral coefficients on the simplex is considered. |
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