Lagrangian Interpolation at the Chebyshev Points xn, cos ( /n), = 0(1)n; some Unnoted Advantages

Besides many applications of the Chebyshev points xnν ≡ cos(νπ/n),ν = 0(1)n, in approximation, interpolation by Chebyshev series, numerical integration and numerical differentiation, there are advantages in their use in the barycentric form of the Lagrange interpolation formula and in checking by divided differences. When n = 2m, we obtain X2m,ν with less than half the number of square roots that are required to find the other Chebyshev points X′2m,ν ≡ cos[(2ν – 1) π/2m+1], ν = 1(1)2m. Also, the barycentric interpolation formula may be applied to the solution of a near-minimax problem so as to avoid extensive calculation of auxiliary polynomials, and in a numerical differentiation procedure that conveniently by-passes direct differentiation of the interpolation polynomial.