摘要
本文研究以Jacobi多项式的J_n(x)=sin(2n+1)/2θ/sinθ/2(x=cosθ,0≤θ≤π)的零点为基点的Hermite-Fejer插值过程H_(2n-1)(f,x).对于Lipα(0<α<1)类中函数,改进了[1]的结果:得到了H_(2n-1)(f,x)逼近有界变差函数的阶估计. 设函数f(x)∈C〔-1,1〕,x=cosθ(0≤θ≤π),J_n(x)是n阶Jacobi多项式,x_k=x_k^(n)=cosθk=cos(2kπ)/(2n+1)(k=1,2,…,n)是J_n(x)的零点,以{x_1,x_2,…,x_n}为基点的Hermite-Fejer插值算子是(见文〔1〕(4))
Let H_(2n-1) (f,x) be polynomial of Hermite-Fejer interpolation,which is based on the zeros of the Jacobi polynomial J_n(x)=sin(2n+1)θ/2 /sinθ/2(x=cosθ,0≤θ≤π), In this paper we improved the result of article [1] and proved the following.Theorem 1: Let f(x)??Lipα,Then |H_(2n-1)(f,x)-f(x)|≤C_α,x·1/n~α,0<α<1 Theorem 2 Let f(x) be bounded variation function, that is f(x)??[-1,1],Then we have.|H_(2n-1)(f,x)-f(x)|??Here C is an abstract constant,
出处
《淮北煤师院学报（自然科学版）》
1989年第1期15-21,26,共8页
Journal of Huaibei Teachers College(Natural Sciences Edition)
