论文标题
在单位圆上的高阶Hermite-Fejer插值
Higher order Hermite-Fejer Interpolation on the unit circle
论文作者
论文摘要
本文的目的是使用单位圆上的高阶Hermite-Fejer插值过程研究功能的近似。节点系统由Jacobi多项式的垂直投影的零组成，其边界点为$ \ pm1 $。多项式及其前四个衍生物的值是通过节点处的插值条件固定的。对于合适域上的分析功能，获得了该过程的收敛性，并估计了收敛速率。
The aim of this paper is to study the approximation of functions using a higher order Hermite-Fejer interpolation process on the unit circle. The system of nodes is composed of vertically projected zeros of Jacobi polynomials onto the unit circle with boundary points at $ \pm1 $. Values of the polynomial and its first four derivatives are fixed by the interpolation conditions at the nodes. Convergence of the process is obtained for analytic functions on a suitable domain, and the rate of convergence is estimated.
