Abstract: Based on the new recursive algorithms of bivariate non-tensor-product-typed inverse divided differences,the scattered data interpolating schemes via bivariate continued fractions were established in the case of odd and even interpolating nodes,respectively.Then two equivalent identities of the interpolated function were obtained.Moreover,by means of the three-term recurrence relations,the degrees of the numerators and denominators were determined,i.e.,the characterization theorem,so do the corresponding recursive algorithms.Meanwhile,compared with the degrees of the numerators and denominators of the well-known bivariate Thiele-typed interpolating continued fractions,those of the presented bivariate rational interpolating functions are much lower respectively,due to the reduction of redundant interpolating nodes.Furthermore,the operation count for the rational function interpolation is smaller than that of radial basis function interpolation from the aspect of complexity of the operations.Finally,some numerical examples show that it’s valid for the recursive continued fraction interpolation,and imply that these interpolating continued fractions change as the order of the interpolating nodes change,although the node collection is invariant.

Key words: Scattered data interpolation,Bivariate continued fraction,Radial basis function,Non-tensor product type,Characterization theorem