On the conditioning of the Newton formula for Lagrange interpolation

Abstract

The stability property of representations of interpolation polynomials is measured through a condition number. We analyze the conditioning of the Newton formula for the interpolation polynomial. We show that the conditioning associated to the Newton representation of the interpolant at the first n points of an ℜ-Leja sequence grows at most like n5(5log⁡n−1). The main application is the construction of explicit multivariate points in [−1,1]d whose conditioning also grows like a polynomial.