| 关于分形插值函数的连续性和可微性 |
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| 引用本文： | 李红达,叶正麟,高行山. 关于分形插值函数的连续性和可微性[J]. 应用数学和力学, 2002, 23(4): 422-428 |
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| 作者姓名： | 李红达 叶正麟 高行山 |
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| 作者单位： | 1.中国科学院, 研究生院, 信息安全国家重点实验室, 北京, 100039; |
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| 基金项目： | 国家自然科学基金资助项目 (10 0 710 6 0 ) |
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| 摘 要： | 获得了由迭代函数系统(IFS)定义的两类分形插值函数具有Hlder连续性的充分条件,给出了这两类分形插值函数连续可微的充要条件,并证明了可微分形插值函数的导函数是由关联IFS生成的分形插值函数.
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| 关 键 词： | 分形 插值函数 Hlder连续 可微性 |
| 文章编号： | 1000-0887(2002)04-0422-07 |
| 收稿时间： | 2000-08-30 |
| 修稿时间： | 2000-08-30 |
On the Continuity and Differentiability of a Kind of Fractal Interpolation Function |
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| LI Hong-da ,YE Zheng-lin ,GAO Hang-shan. On the Continuity and Differentiability of a Kind of Fractal Interpolation Function[J]. Applied Mathematics and Mechanics, 2002, 23(4): 422-428 |
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| Authors: | LI Hong-da YE Zheng-lin GAO Hang-shan |
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| Affiliation: | 1.State Key Laboratry of Information, Security Graduate School, Chinese Academy of Sciences, Beijing 100039, P. R. China;2.Department of Mathematics and Information, Northwestern Polytechnical University, Xi'an 710072, P. R. China;3.Department of Engineering Mechanics, Northwestern Polytechnical University, Xi'an 710072, P. R. China |
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| Abstract: | The sufficient conditions of H*ilder continuity of two kinds of fractal interpolation functions defined by IFS were obtained. The sufficient and necessary condition for its differentiability was proved. Its derivative was a fractal interpolation function generated by the associated IFS, if it is differentiable. |
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| Keywords: | fractal interpolation function H*ilder continuity differentiability |
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