Research On The Only Solution Of Multivariate Interpolation Problems

Interpolation problem has always been a priority direction of computationalmathematics mathematical content, which is the basis for many research andproduction problems, due to the diverse list of functions, surface shape designand finite element method, and many other areas of practice will be applied to it,therefore, interpolation depth study of the problem becomes very necessary.Through the efforts of many mathematical predecessors, spent a lot of time andeffort of a dollar of basic theory and method of interpolation has to fill the gap.Later, we put eyeing the multivariate interpolation problem, multiple polynomialinterpolation problem has gradually become a new hotspot, because multivariateinterpolation is more suitable for practical applications, this study is amulti-purpose interpolation. Associated on multivariate interpolationinterpolation nodes for the solvability of the sole have been put forward.However, to one dollar from the theory of polynomial interpolation is a directanalogy to the multivariate case is difficult, from one to a pluralistic, not onlyquantitative, there are many theories for a dollar does not apply to binary, andtherefore the study is not pretty easy. Through exploration and research,multivariate polynomial interpolation in the course of the study related issues, weare the first to discuss the analysis of interpolation nodes on the set, in otherwords, how to find the polynomial space can exist, and is the only aninterpolation polynomial exists, you can make a collection of these nodes areinterpolated in any one of you has been given interpolation function, I will startfrom the beginning of my thesis topic.This article is divided into four parts, the first part is the introduction,describes the focus of writing text and writing purposes; second part describeswhat is multivariate polynomials, and research methods; third part explains thedefinition of high-dimensional interpolation and related some of the operator; thelast part is my own findings, multiple sub-views are given proper interpolationset of nodes defined by the multiple graded structure suitable set of nodes forinterpolation methods and so on related issues.In general, that is, starting from the direction of algebraic geometry, fromone dollar to the yuan expansion, increased from one-dimensionaltwo-dimensional, multiple points of views in order to apply interpolation uniqueset of nodes to the theoretical foundation Interpolation.