Mathematics · Numerical Analysis

Let f be an infinitely differentiable real-valued function on a bounded interval I. Take n ≥ 1 interpolation points {x 0 , x 1 , ..., x n-1 } and n additional points x n+j = x j + ε (j = 0, 1, ..., n-1) where ε > 0 is such that all 2n points are distinct. Let p 2n-1 be the Lagrange interpolation polynomial of degree 2n-1 for f on these 2n points, and q 2n-1 be the Hermite interpolation polynomial of degree 2n-1 on the first n points. In the limit ε → 0, the quantity sup x∈I |p 2n-1 (x) - q 2n-1 (x)|: