|x|~α(1≤α<2)在Chebyshev结点组的有理逼近

On rational approximation to |x|~α(1≤α<2) at the Chebyshev nodes

由于Newman有理算子对|x|逼近效果较好,所以考虑利用Newman-α型有理算子对|x|~α进行逼近.构造Newman-α型有理算子,讨论Newman-α算子在Chebyshev结点组下逼近|x|~α的收敛速度,最后得到精确的逼近阶为O(1/(n~αlogn)).该结果包含了α=1时的情形.

Since the Newman rational operator＇s approximation effect of ｜x｜ is better, this paper considers the Newman-atype rational operator＇s approximation to ｜x｜^a. Newman-a type rational operator is constructed and the convergence rate of the Newman-atype rational operator approximating to ｜x｜a is discussed based on Chebyshev notes. Finally, the exact order of approximation of O（1/（n^a logn） ） is obtained, which containsthe approximation result when a= 1.