The Several Problems In Blending Continued Fraction Research

The interpolation problem is an important problem in computational mathematics.The continued fraction interpolation is an important form of rational interpolation andone of the important methods in the nonlinear interpolation methods.In recentlyyears,use like the tensor product of rational interpolation method constructed a lot ofdifferent forms of blending rational interpolation based on continued fraction andused in many fields.This thesis mainly discusses the sevearl problems of blending continue fraction.Its content mainly includes reseach the general structure, the inverse differencequotient is zero or does not exist, inaccessible, pole, etc. problems. By introducing anew method to promote and improve the general framework, make it can be used todeal with inaccessible and inverse difference does not exist and promote them todiverse situations and block-based blending rational interpolation.This thesis mixed a symmetrical continued fraction and Lagrange rationalpolynomial interpolation to construct a new bivariate rational interpolation function.The recursive algorithm is given out by defining the blending inverse difference, andthe characterization theorem is carried out. Then we prove that the interpolationfunction satisfy the given interpolation conditions. At last, a numerical example ispresented to illustrate the effectiveness of the interpolating algorithms.