基于单位根的(0,1,…,q)Hermite-Fejer插值多项式的一致收敛性  

On Uniform Convergence of(0, 1,…,q)Hermite-Fejer Interpolating Polynomials at Roots of Unity

作　　者：朱长青[1] 

机构地区：[1]郑州测绘学院

出　　处：《工程数学学报》1992年第4期85-92,共8页Chinese Journal of Engineering Mathematics

摘　　要：设f(z)在|z|<1解析,在|z|≤1连续,在|z|=1有界变差,本文得到了复平面上f(z)的基于单位根的(0,1,…,q)Hermitc—Fcjcr插值多项式在|z|≤1上一致收敛于f(z)的结论。对于(0,1,…,q)Hcrmitc插值多项式,也有类似的结论。Let f(z) be analytie in |z|<1, continous on |z|≤1 and of bounded variation on |z|=1.In this paper, we obtain that the(0,1,…q) Hermite-Fejer interpolating polynomials with nodes at roots of unity of f(z) converge to f(z) uniformly on |z|≤1. Similar convergence of (0,1,…,q) Hermite interpolating polynomials are obtained also.

关 键 词：H-F插值 多项式 一致收敛 单位根 

分 类 号：O241.3[理学—计算数学]