Research On Posedness Graded Interpolation Problem Of Ternary Polynomial Function

As far as it is known,the study of the interpolation problem of multivariate functions is more complicated than the already developed single-variable function interpolation problem,and the variable factors are also considered more common.At the same time,some methods and methods commonly used in the interpolation of univariate functions can not be directly and directly extended to the multivariate interpolation problem.If you want to construct a multidimensional interpolation format,the problem of appropriateness must be solved first.In computational mathematics,the interpolation and approximation of multivariate functions have been around the development of trunk knowledge,and the status within the relevant disciplines can not be underestimated..It is one of the core of the research on the approximation of function at home and abroad,and it is the basic theory of computational mathematics research.The study of multivariate fractional interpolation is an important research content involved in many practical scientific research,experiment and production,such as securities investment analysis,algebraic coding theory,hull lofting,3D stereoscopic design,human organ(or lesion Organization)reconstruction technology.The content of this article is presented in three chapters.In the first chapter,the basic concepts,background information and current development of multivariate polynomial interpolation are described,and we compared it with the interpolation methods commonly used in basic research and engineering technology.In particular,the problem of the interpolation function space and the node group's well-posedness is expounded,and the existing results of multivariate Lagrange interpolation and multivariate Hermite interpolation are briefly described.This paper gives a comprehensive review on interpolation of the binary polynomials and the graded binary polynomials,then explains the construction process of arc-shaped,vertical-shaped properly node group.In the second chapter,the preliminary knowledge of the paper is introduced.First,the problem of the whole number of ternary polynomial interpolation is analyzed and discussed.The geometrical structure and basic characteristics of the interpolation node are expounded,especially their topology.The basic knowledge of algebraic cluster and ideal is given,and the binary polynomial graded interpolation is given as the starting point.The recursive construction principle of multi-element and graded interpolation node is realized.The third chapter is the main part of this article,but also the core lies.The method of constructing a suitable set of nodes in the ternary graded interpolation space is proposed from two ideas.Firstly,the ternary graded interpolation space is defined by the basis of the definition of the properly node group on plane.The new method is to add the orthogonal plane method,and the node group is the mesh node group.The second method makes the recursive construction principle concrete on ternary fractional space,gives two new interpolation methods-adding oblique plane method and adding quadratic surface method,and some examples are given to verify.