Research On Interpolation Of Multivariate Quasi Double N Degree Polynomial Function

Multivariate function interpolation is a very classical mathematical problem in computational mathematics and has a high status in the field of mathematics.Among them,the study of multivariate graded interpolation is an important content in many scientific research,practical production and other fields(such as digital image processing,surface stitching technology,body design,finite element method,etc.).This makes the study of such problems even more important.Therefore,this thesis studies a special case of the multivariate graded interpolation problem: multivariate quasi double n degree polynomial interpolation.This thesis consists of three parts,the specific contents are as follows:The first chapter introduces the research status of multivariate polynomial interpolation at home and abroad in recent years,and summarizes the relevant knowledge and research situation of binary and ternary polynomial interpolation by summarizing the research results of previous scholars.In the second chapter,on the basis of the existing research on multivariate interpolation problems,further research the geometric structure of the multivariate quasi double n degree interpolation regular node group.Meanwhile we've got a superposition method to construct multivariate quasi double n degree polynomial space and a method to construct a set of interpolated regular nodes along multivariate quasi double n degree algebraic hyper-surface,and the feasibility of the method is proved through the rigorous reasoning process;Then,three experimental examples are given to illustrate the above construction method.At the same time,the image of the interpolation function and the interpolated function in the same coordinate system is drawn through Matlab software,so that the effect of interpolation,approximation and the influence of interpolation polynomials of different degrees on the interpolation results can be seen more clearly.The third chapter is based on the construction method of binary double n degree polynomial interpolation format defined in triangle and rectangle fields,we analyze the interpolation format of ternary quasi double n degree polynomial functions,and give a method for constructing interpolation format of ternary quasi double n degree polynomial functions defined on tetrahedron and cube in space respectively.