Multivariate Blending Osculatory Rational Interpolants

The summaries of this thesis are the researches on the multivariate blending osculatory rational interpolants, which include bivariate branched continued fraction osculatory rational interpolation, Newton-Hermite-Thiele's osculatory rational interpolation and Thiele-Werner's osculatory rational interpolation.By the methods of branched continued fraction and univariate Thiele-type osculatory rational interpolation, we generalize the Thiele-type branched continued fraction to the bivariate osculatory rational interpolation. We construct the Thiele-Thiele type bivariate branched continued fraction osculatory rational interpolation formula over rectangular grids. The coefficient algorithm for the construced formula has been presented. The rational and duality properties of the constructed formula are discussed.Newton-Hermite's interpolation polynomials and Thiele's osculatory rational interpolating continued fractions are incorporated to construct a kind of bivariate blending osculatory rational interpolation on the basis of the multivariate blending continued fraction rational interpolation. The coefficient recursion algorithm for the constructed formula is given in details. Furthermore, the table of divided differences and the error estimation are presented. Numerical example illustrates that the blending osculatory rational interpolation have good approximate effects which interpolate a series of given data.Both the expansive Newton's interpolation polynomials and the Thiele-Werner type rational interpolation are used to construct a kind of bivariate blending Thiele-Werner type osculatory rational interpolation over rectangular grids. A recursive algorithm and characteristic theorem are given. Furthermore, the error estimation is obtained and numerical example is illustrated.