Approximation of double integrals using bivariate rational interpolation

In this paper a bivariate rational interpolation is developed to create a spacesurface using both function values and the first order partial derivatives of thefunction being interpolated as the interpolation data. This method has some characteristicscomparing with present interpolation methods. First, the interpolationfunction has a simple and explicit mathematical representation. Secondly, the interpolationfunction can be expressed by symmetric bases. We use this methodto estimate the value of double integrals. Presented examples show the pertinentfeatures of the method.