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| 摘要: |
| 本文研究了|x|α在改进的正切结点组的有理逼近的问题.利用改变结点的方法，获得其逼近阶为O（1/n4α）的结果.推广了一些学者在正切结点组下的研究的逼近阶，而且优于等距结点组、第一和第二类Chebyshev结点组的结果. |
| 关键词: Newman-α有理算子 逼近阶 有理插值逼近 |
| DOI： |
| 分类号:O174.41 |
| 基金项目:国家自然科学基金（61573326）；安徽省高校青年人才支持项目基金（gxyq2019082）；巢湖学院校级科研项目基金（XLY-201903）. |
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| ON RATIONAL APPROXIMATION TO |x|α(1 ≤ α < 2) AT THE IMPROVED TANGENT NODES |
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CHENG Yi-yuan,ZHA Xing-xing,ZHANG Yong-quan
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| Abstract: |
| In this paper, we study the problem of rational approximation of|x|α in the rational approximation of the improved tangent nodes. By using the method of changing nodes we obtain its approximationorder as O(1/n4α). The result not only improves the degree of approximation of the results of relevant scholars' study at tangent nodes, but also is better than which of the nodes taking for quidistant nodes, the Chebyshev nodes of the first kind and the Chebyshev nodes of the second kind. |
| Key words: the improved tangent nodes Newman type rational operator rational approximation |
