On the Condition Number of the Newton Interpolation on the Unit Disk

The stability of representations of univariate Lagrange interpolation polynomials in the complex plane is measured through a condition number. We study the growth of the condition number of the Newton formula for Lagrange interpolation. We prove that the condition number of Newton’s formula at the first n points of a Leja sequence for the closed unit disk 𝔻 is bounded by (n^3+2n-3)/3 from above and by n /2 from below. We also point out that the condition number corresponding to any n+1 distinct points on the unit circle is greater than n^c , where 0更多