On the numerical computation of bivariate Lagrange polynomials

Abstract

In this paper we propose a simple procedure for numerically computing the Lagrange interpolation polynomial on a unisolvent set of points in the plane. We suggest the use of the canonical polynomial basis centered at the barycenter of the set of points and the PA=LU decomposition for solving the associated Vandermonde system to compute the coefficients of the Taylor polynomial. We show that the 1-norm condition number of the Vandermonde matrix is an upper bound for the Lebesgue constant of the interpolation node set in the unit disk. Therefore, the analysis of the condition number can be useful to select the unisolvent set of nodes in a set of scattered nodes. Numerical experiments show the efficiency and accuracy of the proposed method.