| 矩形域上Bernstein—Bezier多项式的正性和凸性条件 |
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| 引用本文： | 丁友东,冯玉瑜.矩形域上Bernstein—Bezier多项式的正性和凸性条件[J].中国科学技术大学学报,1993,23(4):391-397. |
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| 作者姓名： | 丁友东 冯玉瑜 |
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| 作者单位： | 中国科学技术大学数学系
(丁友东)，中国科学技术大学数学系(冯玉瑜) |
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| 基金项目： | The projet supported by NNSF of China and SF of Chinese Educational Committee |
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| 摘 要： | 本文给出了矩形域上Bernstein-Bezier多项式的一般升阶公式,并证明了它的升阶系数的极限逼近性质。在此基础上,得到了多项式为正和(强)凸的充分必要条件。
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| 关 键 词： | 升阶公式 Bernstein-Bezier多项式 正性 凸性 |
Positivity and Convexity Conditions for Bernstein-Bezier Polynomials Over Rectangles |
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| Ding Youdong Feng Yuyu.Positivity and Convexity Conditions for Bernstein-Bezier Polynomials Over Rectangles[J].Journal of University of Science and Technology of China,1993,23(4):391-397. |
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| Authors: | Ding Youdong Feng Yuyu |
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| Institution: | Department of Mathematics |
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| Abstract: | The degree elevation formula for the Bernstein-Bezier polynomial over rectangles is presented, and the limit approximating property of the coefficients (Farin Theorem) is proved. Based on the formula, this paper obtains the conditions (necessary and sufficient) for the positivity and (strong) convexity of the Bernstein-Bezier polynomial over rectangles. |
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| Keywords: | degree elevation the Bernstein-Bezier polynomial positivity convexity |
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