Polynomial Interpolation - Purdue University
www.cs.purdue.edu › homes › ren105there exists only one polynomial that interpolates a function at those points. Proof Let P(x) and Q(x) be two interpolating polynomials of degree at most n, for the same set of points x 0 < x 1 < ··· < x n. Also, let R(x) = P(x)−Q(x). Then R(x) is also a polynomial of degree at most n. Since P(x i) = Q(x i) = f i, we have, R(x i) = 0 for i = 0,1,...,n. In other words R(x) has (n + 1) roots.