| Lipschitz常数缩减的散乱数据插值 |
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| 引用本文： | 吴宗敏,陈亚亚.Lipschitz常数缩减的散乱数据插值[J].高校应用数学学报(A辑),1998(Z1). |
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| 作者姓名： | 吴宗敏 陈亚亚 |
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| 作者单位： | 复旦大学数学研究所(吴宗敏)，上海复旦大学数学系(陈亚亚) |
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| 摘 要： | 在计算机辅助设计几何中，变差缩减是一个非常重要的概念，本文分析了函数的变差和Ｌｉｐｓｃｈｉｔｚ常数的关系，指出可以用Ｌｉｐｓｃｈｉｔｚ常数来控制变差，由于变差的概念只限于一维的情形，而Ｌｉｐｓｃｈｉｔｚ常数适用于任意维，这样在高维时就可用Ｌｉｐｓｃｈｉｔｚ常数缩减的概念来代替变差缩减的概念，文中构造性地证明了Ｌｉｐｓｃｈｉｔｚ常数缩减的散乱数据插值函数的存在性，并且对这类函数的性质及光滑性条件进行了讨论．
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| 关 键 词： | 变差缩减，Lipschitz常数，插值 |
LIPSCHITZ CONSTANT DIMINISHING INTERPOLATION FOR SCATTERED DATA |
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| Wu Zongmin\ Chen Yaya.LIPSCHITZ CONSTANT DIMINISHING INTERPOLATION FOR SCATTERED DATA[J].Applied Mathematics A Journal of Chinese Universities,1998(Z1). |
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| Authors: | Wu Zongmin\ Chen Yaya |
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| Abstract: | Variation diminishing plays an important pole in CAGD.In this paper, the connection between variation and Lipschitz constant is analysed. It is found that Lipschitz constant can be used to control variation.Because variation is limited for one dimension,Lipschitz constant is for any dimension.So this paper similarly presents the conception of Lipschitz constant diminishing for high dimensions.The main results obtained here is as follows:for any scattered data,Lipschitz constant diminishing interpolation exists.The approach of the proof is constructional.At last,the properties of this kind of functions and conditions of their continuity are discussed. |
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| Keywords: | Variation Diminishing Lipschitz Constant Interpolation |
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