关于修正型的Hermite插值过程的平方收敛

The Average Convergence Order of Interpolation Process by the Modified Hermite Polynomials

1. 设U_n(X)=sinNθ/sinθ(X=cosθ,0≤θ≤π,N=n+1)是第二类chebyshev多项式。以R(x)=(1-x^2)U_n(x)的零点X_k(X_k=cosθ_k=cos(Kπ/N),K=0,1,…,N)

We considered that the average convergence order of interpolation process by the modified Hermite polynomials with zeros of Chebyshev polynomials of second kind and proved the average convergence order was the best if f(x)∈C^2[-1,1].