Abstract:

In view of the higher computational complexity of the osculatory rational interpolation method of higher derivative mostly based on the idea of generalized vandermonde matrix, by means of basis function of polynomial interpolation and error nature of polynomial interpolation, we proposed an osculatory rational interpolation algorithm that not only satisfies different interpolation order but also makes the toppest of interpolation order equal 2, and it also meets the vectorvalued osculatory rational interpolation. It solves the problem of the existence of osculatory rational interpolation function and complexity of algorithm. In the end, we illustrated the effectiveness of the algorithm with a numerical example.

Key words: osculatory rational interpolation, higher order derivative, Hermite interpolation, basis function