The new bivariate rational interpolation over the triangular grids

Barycentric rational interpolation possesses various advantages in comparision with Thiele-type continued fraction, such as small amount of calculation, good numerical stability, no poles, no unattainable points and arbitrarily high approximation order regardless of the distribution of the points. In this paper, two new bivariate rational interpolation over triangular grids are presented, the first one is bivariate barycentric rational interpolation; the second one is a blending interpolation based on Newton interpolation and barycentric rational interpolation. One numerical example is given to show the effectiveness of the new approach.