| 摘要: |
| 本文研究了Newman-α型有理算子逼近|x|α（1 ≤ α < 2）收敛速度的问题，取插值结点组为X={xi=bi，b=m（-1）/√n}i=1n，其中e < m < n.利用基本不等式以及放缩法，获得了逼近阶为3e（-α√n）/（logm）. |
| 关键词: 有理插值 Newman-α型有理算子 逼近阶 |
| DOI： |
| 分类号:O174.41 |
| 基金项目:国家自然科学基金资助项目（11601110）. |
|
| ON RATIONAL INTERPOLATION TO |x|α |
|
XU Jiang-hai1, ZHAO Yi2
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1.School of Science, Hangzhou Dianzi University, Hangzhou 310018, China;2.School of Science, Hangzhou Normal University, Hangzhou 311121, China
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| Abstract: |
| In this paper, we study the problem of the convergence rate of Newman-α rational operator approximation to|x|α(1 ≤ α < 2), and take the interpolation node group as X={xi=bi, b=m(-1)/√n}i=1n, where e < m < n. By using the basic inequality and the scaling method, we obtain that the approximation order is 3e(-α√n)/(logm). |
| Key words: rational interpolation Newman-α type rational operators order of approximation |
