The Further Study Of Rational Interpolation

Rational interpolation problem is natural generalization of polynomial interpolation. In the paper, by making use of Lagrange primary function, the interpolation nodes will be divided into pieces regularly (for univariate condition, it is piecewise), then by applying polynomial interpolation formula to combine them properly, it gives rational interpolation formula of bivariate function in rectangular domain and the methods of constructing univariate and bivariate vector valued rational interpolation function. The methods are simple and easy. Compared with other methods, the degree of constructed rational interpolation function is lower, it is easy for practical application. The specific arrangements is as follows:In chapter 1, it briefly introduces the basic theory and methods of rational interpolation, and the work to be done in the paper.In chapter 2, on the basis of analyzing the existing research work, it gives interpolation formula which is similar to polynomial interpolation for rational interpolation problem in rectangular domain.In chapter 3, it analyzes the vector valued rational interpolation problem briefly,and gives simple methods of constructing univariate and bivariate vector valued rational interpolation function.In chapter 4, for the questions which was to be researched, it gives brief summary and presents some questions which is worthwhile to explore and research.