A Newton's Method for Best Uniform Polynomial Approximation

We present a novel algorithm, inspired by the recent BRASIL algorithm [10] for rational approximation, for best uniform polynomial approximation based on a formulation of the problem as a nonlinear system of equations and barycentric interpolation. We use results on derivatives of interpolating polynomials with respect to interpolation nodes to compute the Jacobian matrix. The resulting method is fast and stable, can deal with singularities and exhibits superlinear convergence in a neighborhood of the solution.