Continued Fractions-Barycentric Type Blending Rational Interpolation

The advantages of barycentric interpolation of mulations in computation are small number of floating poin operations and good numerical stability. Adding a new data pair, the barycentric interpolation formula don't require to renew computation all basis functions. Thiele-type continued fraction interpolation may be the favoured nonlinear interpolation. new kind of blending rational interpolants was constructed b combining Thiele continued fractions and associated continue fractions. We discussed the interpolation theorem, dual interpolation, the properties of no poles and error estimation, numerical example is given to show the the validity of the new method.