Abstract
AbstractThis paper investigates the optimal Hermite interpolation of Sobolev spaces$W_{\infty }^{n}[a,b]$W∞n[a,b],$n\in \mathbb{N}$n∈Nin space$L_{\infty }[a,b]$L∞[a,b]and weighted spaces$L_{p,\omega }[a,b]$Lp,ω[a,b],$1\le p< \infty $1≤p<∞withωa continuous-integrable weight function in$(a,b)$(a,b)when the amount of Hermite data isn. We proved that the Lagrange interpolation algorithms based on the zeros of polynomial of degreenwith the leading coefficient 1 of the least deviation from zero in$L_{\infty }$L∞(or$L_{p,\omega }[a,b]$Lp,ω[a,b],$1\le p<\infty $1≤p<∞) are optimal for$W_{\infty }^{n}[a,b]$W∞n[a,b]in$L_{\infty }[a,b]$L∞[a,b](or$L_{p,\omega }[a,b]$Lp,ω[a,b],$1\le p<\infty $1≤p<∞). We also give the optimal Hermite interpolation algorithms when we assume the endpoints are included in the interpolation systems.
Funder
National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis