光滑区域上Hermite插补多项式同时逼近函数及其导数

Simultaneous Approximation To Function And lt's Derivative By Hermite lnterpolation Polynomials ln A Smooth Domain

设Ｄ是复平面上的Ｊｏｒｄａｎ区域，｛ｚｋ｝ｎ－１ｏ是Ｄ上的Ｆｅｊｅｒ点．考虑用Ｈｅｒｍｉｔｅ插值多项式逼近Ｄ内的函数及其导数，在某些边界条件下得出了一致逼近与平均逼近的阶．

Let D be a Jordan domain in complex plane,and {zk }n-1 be the Fejer points on r=D.In the domain D consider simultaneous approximating to function and its derivative by Hermite interpolation polpondals in Fejer points. The sharp orders of uniform approximation and approximation in the mean are obtained Under some boundary conditions respectively.