Construction of new bivariate blending rational interpolation over the triangular grids

Laid foundation on the advantages of the simple expressions, easy to calculate of continued fractions interpolation and polynomial interpolation; small calculation quantity, no poles, good numerical stability of barycentric rational interpolation, then two kind of new bivariate blending rational interpolation are constructed over the triangular grids. The first one is based on Thiele's interpolating continued fraction and barycentric rational interpolation; second one is based on barycentric rational interpolation and polynomial interpolation. The new blending rational interpolation inherited the advantages of continued fraction interpolation, polynomial interpolation and barycentric rational interpolation, and the error estimation is given. Numerical example is given to demonstrate the accuracy and robustness of the new approach.