Bivariate Barycentric Rational Interpolation

摘要

Barycentric rational interpolants possess various advantages in comparison with classical continued fraction rational interpolants, for example, barycentric rational interpolants have small amount of calculation, good numerical stability, no poles and no unattainable points, regardless of the distribution of the points. New bivariate barycentric rational interpolation is presented based on univariate barycentric rational interpolation. Barycentric rational interpolation is determined while weights are given. The new bivariate barycentric rational interpolants with proper weights have no poles and no unattainable points. It is the key issue how to choose weights so that the interpolant with the minimum error is obtained. The optimal interpolation weights are obtained based on an optimization model. At last, numerical examples are given to show the effectiveness of the new method.