关于Lagrange平均插值过程的逼近阶估计

The Estimation of Approximation Order on a Average of Lagrange Interpolation Process

本文以多项式（１＋ｘ）Ｖｎ（ｘ）Ｖｎ（ｘ）＝ｃｏｓ２ｎ＋１２θｃｏｓθ２，ｘ＝ｃｏｓθ的零点作为插值的节点，构造了一个Ｌａｇｒａｎｇｅ插值多项式算子过程Ｃｎ（ｆ，ｘ），给出了其逼近阶估计．同时证明Ｃｎ（ｆ，ｘ）亦满足Ｄｉｔｚｉａｎ－Ｔｏｔｉｋ定理．

In this paper the average interpolation Process of Lagrange C n(f,x) with zeros of (1+x)V n(x) is constructed and its approximation order is given meanwhile C n(f,x) also satisfies the Ditzian Totik theorem.