Barycentric-Thiele Type Blending Rational Interpolation ⋆

In this paper, we construct Barycentric-Thiele type rational interpolation, which is based on Thiele continued fraction interpolation and Barycentric rational interpolation. Compared with Thiele continued fraction interpolation, Barycentric-Thiele type rational interpolation is more accuracy, better numerical stability and smaller calculation cost. While constructing the corresponding Thiele continued fraction interpolation, we can choose the appropriate number of nodes to avoid poles. Finally, the numerical examples are given to verify the correctness and validity of our method.