一个无限可微函数类的最优埃尔米特插值  

OPTIMAL HERMITE INTERPOLATION OF A CLASS OF INFINITELY DIFFERENTIABLE FUNCTIONS

作　　者：马孟瑾 于晓晨 许贵桥[1] Ma Mengjin;Yu Xiaochen;Xu Guiqiao(School of Mathematical Sciences,Tianjin Normal University,Tianjin 300387)

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《高等学校计算数学学报》2022年第2期175-186,共12页Numerical Mathematics A Journal of Chinese Universities

基　　金：Supported by the National Natural Science Foundation of China:11871006。

摘　　要：This paper investigates the optimal Hermite interpolation of a class F_(∞) of infinitely differentiable functions on[-1,1]in L_(∞)[-1,1]and weighted spaces L_(p,w)[-1,1],1≤p∞[-1,1]and L_(p,w)[-1,1],1≤p<∞ with w a continuous integrable weight function in(-1,1).We proved that the Lagrange interpolation polynomials based on the ze-ros of polynomials with the leading cofficient 1 of the least deviation from zero in L_(∞)[-1,1]and L_(p,w)[-1,1],1≤p<∞are optimal for 1≤p≤∞.We also give the optimal Hermite interpolation nodes when we ask the endpoints to be included in the nodes.

关 键 词：worst case setting optimal Hermite interpolation infinitely differentiable function space 

分 类 号：O174.41[理学—数学]