扩展的Hermite算子的逼近阶

Convergence order of interpolation process by Hermite polynomial of muliplier enlargement

考虑以第一类Ｃｈｅｂｙｓｈｅｖ多项式的零点为插值结点的扩展的Ｈｅｒｍｉｔｅ算子，在实轴上逼近无界函数，得到收敛阶为Ｏ（Ω￣（－１）（ｌｎｎ）ｌｎｎ／ｎ）；同时考虑了该算子的导数在实轴上逼近无界函数的导数，得到收敛阶为Ｏ（Ω￣（－１）（ｌｎｎ）（ｌｎｎ）￣２／ｎ）．

The extended Hermite interpolation operator,based on the nodes which are the zeros of first Chebyshev polynomial,is considered.This operator approxi-mates the unbounded function in the real axis,its convergence order is O(Ω￣(-1)(lnn)lnn/n);the derivative of this operator approximates the deriva-tive of unbounded function in the real axis, its convergence order is O(Ω￣(-1)(lnn)(lnn)￣2/n)