一个无限可微函数类的最优埃尔米特插值CSCD

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.