Newton-Barycentric-Associated Continued Fractions Type Blending Rational Interpolation

Associated continued fractions interpolation and Newton interpolation may be the favoured nonlinear and linear interpolation. Barycentric interpolation formulation has many advantages. A new kind of trivariate blending rational interpolants is constructed by combining Newton interpolation, associated continued fractions and barycentric interpolation. We discussed the interpolation theorem, no poles of the property and error estimation. We also give some remark about the methods.