Newton-Barycentric-Thiele Trivariate Blending Rational Interpolation on Rectangular Parallelepiped Grid

The advantages of barycentric interpolation for mulations in computation are small number of floating point operations and good numerical stability. Adding a new data pair, the barycentric interpolation formula don´t require new computation all of basis functions. Thiele-type continued fractions interpolation and Newton interpolation may be the favoured nonlinear and linear interpolations, A new kind of Tri-variate blending rational interpolants was constructed by combining of barycentric interpolation, Thiele continued fractions and Newton interpolation. We discussed the interpolation theorem with no poles and error estimation.