Multivariate Blending Osculatory Rational Interpolants Based On Continued Fractions

The summaries of this paper are the researches on the multivariate blending osculatory rational interpolants based on continued fractions, which include bivariate blending osculatory rational interpolants of one order, bivariate blending osculatory rational interpolants of two orders and composite scheme of multivariate blending osculatory rational interpolants of two orders.By the blending of expansive Newton polynomial and Salzer osculatory continued fraction, we construct the blending osculatory rational interpaltion polynomial of one order (SNBORIs). Then, a recursive algorithm is presented by the recursive and circulating format. Numerical examples illustrate that the blending osculatory rational interpolation of one order have good approximate effects which interpolate a series of given data.We get blending osculatory rational interpaltion of two orders by extending the blending osculatory rational interpaltion of one order. We need to consider about partial derivative with respect to x, y and blending partial derivative in (x_i,y_j) which lead to complex algorithm. In this paper the multivariate blending osculatory rational interpolation formulas (NSMORIs and SNMORIs) of two orders are constructed and recursive algorithms are deduced. Furthermore, characterization theorem and error estimate are presented.Considering about the existence of the rational interpolation, a square grid can be divided into two triangular subgrids and two allocated functions are constructed which lead to composite scheme of multivariate blending osculatory rational interpolation of two orders.