The Study Of Methods Of Multiple Barycentric Blending Rational Interpolation

This thesis mainly studies the multiple barycentric blending rational interpolation problem combined with multiple barycentric rational interpolation and the Stieltijes type continued fraction interpolation. We know that the essence of the interpolation problem is building a relatively simple function through a given discrete data values which is relatively simple and makes all the given discrete points are on the function of the constructed image.That is using values of limited point to estimate the approximated values of function at the other points. Polynomial interpolation although has the advantages of simple structure, convenient operation, but there are some inconvenience in dealing with nonlinear problems, may also appear the phenomenon of Runge, and the rational interpolation can solve nonlinear feature model, still can’t avoid the deficit business does not exist, there may be problems of unattainable points and poles.Barycentric rational interpolation not only meets the given interpolation conditions, but also has small computation, good numerical stability and avoid the emergence of the pole.This thesis briefly introduces several kinds of bivariate blending rational interpolation.From the Stieltijes type continued fraction interpolation, and combined with barycentric interpolation, we constructed Stieltijes barycentric rational interpolation function in triangular mesh, through the definition of blending inverse differences, building the recursive algorithm, so that the constructed rational interpolation function satisfies all the conditions, in addition, also gives the characteristics theorem of this interpolation algorithm and its proof.We construct the Triple barycentric Stieltijes blending rational interpolation on rectangular grids based on Stieltjies rational interpolation and barycentric rational interpolation.By defining the partial differences and partial inverse differences we get a recursive algorithm.Prove that this kind of interpolation can be avoided by variable causes the poles. In the end, by numerical examples, we get the expression of triple barycentric Stieltijes blending rational interpolation, and give the characteristic theorem for this class of interpolation, verify the correctness and effectiveness of this method.