Univariate Thiele Type Continued Fractions Rational Interpolation with Parameters.

Thiele-type continued fractions interpolation may be the classical rational interpolation and plays critical role in image interpolation and numerical analysis. Different from the traditional method, a new Thiele type continued fractions rational interpolation method with parameters was presented to address the interpolation problem efficiently. Firstly, in order to gain neat expressions in terms of inverse differences, we chose the multiplicity of the points strategically. Secondly, we constructed a univariate Thiele type continued fractions rational interpolation with parameters, which can satisfy the interpolation condition. We also discussed the interpolation algorithm, interpolation theorem. Numerical examples were given to show that the presented method achieves state-of-the-art performance.