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OALib Journal期刊
ISSN: 2333-9721
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|x|α在第二类Chebyshev结点的有理插值
DOI: 10.3969/j.issn.1001-8395.2015.06.019, PP. 889-892
Keywords: Lagrange插值,第二类Chebyshev结点,有理插值,Newman-α型有理算子,逼近阶
Abstract:
由于|x|α的Lagrange插值多项式逼近|x|α的效果很差,非光滑函数|x|的有理逼近非常有效,所以考虑|x|α的有理逼近.首先构造Newman-α型有理算子,它在(-∞,+∞)与|x|α有共单调性.然后考虑Newman-α型有理算子逼近|x|α的收敛速度,结点组X取第二类Chebyshev结点.得到确切的逼近阶仅为O(1/n).这个结果虽不及|x|的有理逼近,但优于|x|α的Lagrange插值逼近.
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