| 赵易,周颂平.│x│的有理插值的若干注记(英文)[J].数学研究及应用,2003,23(1):65~70 |
| │x│的有理插值的若干注记(英文) |
| Some Remarks on Rational Interpolation to |x| |
| 投稿时间：2000-05-28 |
| DOI：10.3770/j.issn:1000-341X.2003.01.011 |
| 中文关键词: |
| 英文关键词:rational approximation interpolation nodes. |
| 基金项目: |
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| 中文摘要: |
| 本文中我们构造了一个结点组,基于它定义的有理插值函数,对于任意给定的自然数k,对|x|的逼近能达到精确阶O(1/(nklogn)).更重要的是,这样的构造揭示了一个本质:当结点向(|x|的唯一奇异点)零点集中时,|x|的有理插值逼近阶也随之更佳,这或许为将来本质性的自然结点组的构造提供了一种思路. |
| 英文摘要: |
| The present paper constructs a set of nodes which can generate a rationalinterpolating function to approximate |x|at the rate of O(1/(nk log n))for any givennatural number κ.More importantly.this construction reveals the fact that the higherdensity the distribution of a set of nodes has to zero (that is the singular point of thefunction |x|!),the better the rational interpolation approximation behaves.This probablyalso provides an idea to construct more valuable sets of nodes in the future. |
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