Method Of Constructing Vector-Valued Rational Interpolation Functions

This paper is mainly about a structure of bivariate vector-value rational Interpo-lation on a rectangular grid, so the framework of the article is from the following aspects :Chapter 1: a brief account of the background and significance of vector-value rational functions;the main tool of researching vector-valued rational interpolation is and approximation is vector continued fractions, so chapter 2 introduces the usage of this tool : univariate Thiele vector-rational interpolation and rectangular grid vector-values rational interpolation; Through this chapter, a preliminary understanding of the basic method of constructing vector-valued rational interpolation functions .Chapter 3: It will mainly introduce the method of structuring vector interpolation,which gets rid of the repeated Samelson inverse calculations. And it has its own supe--riority which we will use some examples to explain;Chapter 4: I will extend the univariate situation to bivariate situation, and discuss the value of this approach with the existing method, then through specific examples to explore its effectiveness.Finally concluding remarks, summing up the work done and put forward the questions, which should be improved or be further explored in the future.