The Study Of Methods Of Multivariate Rational Interpolation

The article mainly studied two bivariate rational interpolation problem, we know, algebraic interpolation can estimate values of the function in the other points by its values at some points which were given out by constructing polynomial or rational function That is similar to the given function.Polynomial interpolation has simple structure and can be operated conveniently, so the polynomial interpolation has a wide range of application in solving equations, numerical differentiation, numerical integration. But polynomial interpolation has difficulties in solving the nonlinear feature model, in order to deal with the nonlinear problems, the rational interpolation had been introduced in, it is flexibler and effectiver than polynomial interpolation and can achieve better results near the poles. Therefore, the research of the rational interpolation problem is very necessary, especially on multivariate rational interpolation problem.On the bivariate rational interpolation of multivariate rational interpolation problem,by learning from the obtained research findings,same new bivariate rational interpolations are given out:Barycentric-Newton type two bivariate rational interpolation has been constructed over the rectangular grid,which combined the Newton type polynomial interpolation and based on Barycentric rational interpolation, The new blending rational interpolation inherited the small calculation quantity, no poles,good numerical stability of barycentric rational interpolations and the favorite linear interpolation of Newton polynomial; By the numerical example is given to show the effectiveness of the constructed method, the advantages of no poles and good numerical stability. Based on stieltijes type branched continued fraction interpolation and conbined the thiele type rational interpolation and newton polynomial interpolation, stieltijes type bivariate blending rational interpolants function was constructed over the square grid. By defining the partial difference、the partial inverse difference and blending inverse difference the recursive algorithm was builded,.Also the error analysis was given out; Then we constructed Lagrange-Stieltijes type rational interpolation over the triangular Grid, which is combined with the Stieltijes type continued fractions based on the Lagrange polynomial, the interpolanting function that is constructed satisfies the given interpolating conditions, by defining the blending inverse difference, the recursive algorithm is given out,and the characterization theorems is carried out.