Lebesgue Constant Minimizing Bivariate Barycentric Rational Interpolation

The barycentric form is the most stable formula for a rational interpolant on a finite interval. The choice of the barycentric weights can ensure the absence of poles on the real line, so how to choose the optimal weights becomes a key question for bivariate barycentric rational interpolation. A new optimization algorithm is proposed for the best interpolation weights based on the Lebesgue constant minimizing. Several numerical examples are given to show the effectiveness of the new method