An optimal interpolation problem with hermite information in the sobolev class $W^{n}_{1}([-1,1])$

In this paper, we study the optimal interpolation problem in the Sobolev class $W^{n}_{1}([-1,1])$, $n\in\mathbb N$, with Hermite information. By some properties of spline functions, we proved that the Lagrange interpolation based on the extreme points of Chebyshev polynomials is optimal for $W^{n}_{1}([-1,1])$, and we obtained the approximation error for the optimal interpolation problem.