A Multivariate Function Interpolation Schemes Are Constructed For The Problem

This article first to the problem of multivariate interpolation (including the basicdefinition of multivariate interpolation function, the existence of multivariate interpolationpolynomial) are discussed, because on the one dimensional space, its interpolation polynomialis there must be, but in high dimensional space (n) is changed. On this basis, from the point ofview of algebraic geometry of bivariate polynomial interpolation problem has carried on thedeep discussion and research, the application of computer software MATLAB to realize itsdifferent number of interpolation, and then get us the results of this paper.This paper mainly includes the following several parts:The first part of system, expounds the multivariate interpolation basic problems, mainlyintroduces the necessary theorems and their proofs, well-posed node group selection (both arereviewed briefly the basic ways of selecting well-posed node group: add the straight-linemethod, add curve method).The second part introduces the multiple contact Hermite interpolation problem inmultivariate polynomial interpolation.More than in the third part based on the theory of application of computer softwareMATLAB is relatively straightforward to make corresponding different times (specificexample of a second) and three interpolation polynomial interpolation image, get theconclusion in this paper. The first selected binary function=this typical binary polynomialinterpolation examples. Then using MATLAB software, respectively, for a binary polynomial=quadratic interpolation, three times with the MATLAB software to draw the correspondinginterpolation polynomial and be inserted function image, facilitate everybody observedvisually polynomial interpolation function of abstract through images to see directly to thecharacteristics of a number of different interpolation corresponding impact. Results throughalgebra level and finally integrated image and value of this article conclusion: binarypolynomial using the MATLAB software in computer to draw the corresponding three timesin a quadratic interpolation image interpolation polynomial and be inserted function, visuallyobserved the different influence on the corresponding interpolation results the number ofinterpolation, the precision of interpolation with the changes in the number of its, in general, increase the number of interpolation can make the interpolation result more accurate, thecorresponding interpolation for image will be closer to the original function.