Polynomial Interpolation Problem In R~S Space

Approximations of Multivariate Functions is the development of Unary function approximation, which is the approaches the tool and the object aspect of the multi-dimensional promotion. The multi-dimensional approximation theory's research has become one of hot spots in the approximation and computing science research now, which receives mathematics, the computer science, physical and the project domain expert and scientific and technical worker's value day by day.This paper describes the concepts, theories related to the issues , and has done a thorough study and elaborated of polynomial interpolation problem. In the fully absorb and digest foreign scholars on Polynomial Interpolation Problem in R~S Space. Several conclusions are Drawn , which based on the results of research . This paper contains the following three parts of the main elements:The first part describes of interpolation one variable and algebra basis of multivariate polynomial interpolation . This part is detailed in the essential knowledge of multiple interpolation problem.The second part describes the existing space on multi-polynomial interpolation of the node set of questions posed and the construction of polynomial interpolation problem.The third part is the main part of this paper. Some conclusions Are described about the spatial construction of Lagrange interpolation polynomial in R~2 space, while others are described about the network of rectangular and triangular Lagrange polynomial interpolation Lagrange interpolation polynomial in R~2 space. Then, we generalize it to R~S space. Furthermore, we study field size outlets on the Lagrange interpolation polynomial and the remaining items in R~S space, and then prove them. these theorems and their proof are the main contributions of this paper.Through the above theories, the paper identified a lot of work to do in multivariate interpolation problem in interpolation nodes group, polynomial interpolation and polynomial interpolation over items, etc.