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. Associated continued fraction interpolation is a classical nonlinear interpolation. A new kind of blending rational interpolants was constructed by combining barycentric interpolation and associated continued fractions. We discussed the interpolation theorem, error estimation, numerical examples. Applications to image processing are discussed.
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