A New Approach to Trivariate Blending Rational Interpolation

The advantages of barycentric interpolation formulations in computation are small number of floating points operations and good numerical stability. Adding a new data pair, the barycentric interpolation formula don’t require to renew computation of all basis functions. Thiele-type continued fractions interpolation and Newton interpolation may be the favoured nonlinear and linear interpolation. A new kind of trivariate blending rational interpolants were constructed by combining barycentric interpolation, Thiele continued fractions and Newton interpolation. We discussed the interpolation theorem, dual interpolation, no poles of the property and error estimation.