| 基于修正的第二类Chebyshev结点的Newman型有理插值函数对|x|的逼近 |
| |
| 引用本文： | 朱来义,赵迎迎. 基于修正的第二类Chebyshev结点的Newman型有理插值函数对|x|的逼近[J]. 数学研究及应用, 2011, 31(2): 202-208. DOI: 10.3770/j.issn:1000-341X.2011.02.002 |
| |
| 作者姓名： | 朱来义 赵迎迎 |
| |
| 作者单位： | 中国人民大学信息学院, 北京 100872;中国人民大学信息学院, 北京 100872 |
| |
| 基金项目： | 国家自然科学基金(Grant No.10601065). |
| |
| 摘 要： | Recently Brutman and Passow considered Newman-type rational interpolation to ｜x｜ induced by arbitrary sets of symmetric nodes in [-1,1] and gave the general estimation of the approximation error.By their methods,one could establish the exact order of approximation for some special nodes.In the present note we consider the sets of interpolation nodes obtained by adjusting the Chebyshev roots of the second kind on the interval [0,1] and then extending this set to [-1,1] in a symmetric way.We show that in this case the exact order of approximation is O（ 1 n 2 ）.
|
| 关 键 词： | Newman-type rational interpolation adjusting the Chebyshev roots of the second kind exact order of approximation |
| 收稿时间： | 2009-04-10 |
| 修稿时间： | 2009-10-14 |
On Newman-Type Rational Interpolation to |x| at the Adjusted Chebyshev Nodes of the Second Kind |
| |
| Lai Yi ZHU and Ying Ying ZHAO. On Newman-Type Rational Interpolation to |x| at the Adjusted Chebyshev Nodes of the Second Kind[J]. Journal of Mathematical Research with Applications, 2011, 31(2): 202-208. DOI: 10.3770/j.issn:1000-341X.2011.02.002 |
| |
| Authors: | Lai Yi ZHU and Ying Ying ZHAO |
| |
| Affiliation: | School of Information, People's University of China, Beijing 100872, P. R. China |
| |
| Abstract: | Recently Brutman and Passow considered Newman-type rational interpolation to $|x|$ induced by arbitrary sets of symmetric nodes in $[-1,1]$ and gave the general estimation of the approximation error. By their methods, one could establish the exact order of approximation for some special nodes. In the present note we consider the sets of interpolation nodes obtained by adjusting the Chebyshev roots of the second kind on the interval $[0,1]$ and then extending this set to $[-1,1]$ in a symmetric way. We show that in this case the exact order of approximation is $O(frac{1}{n^2})$. |
| |
| Keywords: | Newman-type rational interpolation adjusting the Chebyshev roots of the second kind exact order of approximation. |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
| 点击此处可从《数学研究及应用》浏览原始摘要信息 |
|
点击此处可从《数学研究及应用》下载全文 |
