摘要
由于｜x｜^α的Lagrange插值多项式逼近｜x｜^α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有理逼近.首先构造Newman-α型有理算子,它在（-∞,＋∞）与｜x｜6α有共单调性.然后考虑Newman-α型有理算子逼近｜x｜^α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（1n）.这个结果虽不及｜x｜的有理逼近,但优于｜x｜^αLagrange插值逼近.
Due to the Lagrange interpolation of ｜x｜^α approximation properties is poor, rational approximation of nonsmooth function I xl is very effective, this paper considers the rational approximation of ｜x｜^α The Newman-α type rational operator is constructed, it has eomonotone properties with ｜x｜^α on （ -∞,＋∞ ）. Then the convergence rate of the Newman-α type rational operator to ｜x｜^α is considered based on Chebyshev notes of second kind. The exact order of approximation is only O（1n）. The result is worse than ration- n al approximation of ｜x｜, but better than the Lagrange interpolation approximation of ｜x｜^α
出处
《四川师范大学学报（自然科学版）》
CAS
北大核心
2015年第6期889-892,共4页
Journal of Sichuan Normal University（Natural Science）
基金
河北省高等学校科学技术研究青年基金(QN2014018)
