The existence of an asymptotic expansion is proved for the Lebesgue constants associated with the polynomial interpolation at the "extended Chebyshev nodes." This series is quite different from the ...

J. Shohat, On the Convergence Properties of Lagrange Interpolation Based on the Zeros of Orthogonal Tchebycheff Polynomials, Annals of Mathematics, Vol. 38, No. 4 (Oct., 1937), pp. 758-769 ...

Finite difference stencils are also constructed, using Lagrange interpolation polynomials, based on either three or five grid points. With these choices, second-order and fourth-order convergence with ...