A bivariate rational interpolation and the properties

In this paper a bivariate rational interpolation is constructed using both function values and partial derivatives of the function being interpolated as the interpolation data. The interpolation function has a simple and explicit rational mathematical representation with parameters, and it can be expressed by the symmetric bases. It is proved that the interpolation is stable. The concept of integral weights coefficients of the interpolation is given, which describes the “weight” of the interpolation points and the quantity as the interpolation data in the local interpolating region.