Research On Multivariate Interpolation Problem Defined On Parabolic Cylinder

On the basis of introducing binary Lagrange interpolation,this paper constructs a method about the regular node group of ternary Lagrange interpolation,and introduces in detail the construction theorem and determination theorem about the regular node group of ternary Lagrange interpolation.By selecing points on the parabolic cylinder and constructing the ternary quadratic interpolation polynomial and the ternary quadratic interpolation polynomial,this paper constructs the interpolation on the parabolic cylinder.Value is the only solvable node group,and relevant conclusions are drawn.We know that parabolic cylindrical surface is another kind of main quadratic algebraic surface besides spherical surface.Parabolic cylindrical surface is widely used in military,astronomy and life.This paper mainly includes the following three chapters:In Chapter 1,we first give a brief introduction to the practical application of multivariate polynomial interpolation and its basic concepts and methods.Secondly,we introduce the related theories of binary polynomial interpolation.In this part,we first introduce the properties of algebraic curves in real plane and real field,and summarize the methods of constructing suitable set of nodes for interpolation.The last part of the chapter introduces the related theories of multivariate polynomial interpolation,including the construction method of multivariate interpolation polynomial space,the polynomial quotient ring and the related concepts of Grobner basis.Chapter 2 is divided into two parts.The first part introduces the theory and general methods of constructing interpolated well-posed node groups along plane algebraic curves.The second part introduces the general methods of constructing interpolated well-posed node groups along algebraic surfaces and along space algebraic curves.In the third chapter,we mainly study the unique solvability of Lagrange interpolation in three-dimensional Euclidean space.For the parabolic cylinder on R3,we make the interpolated function f(x,y,z)=(?),the equation of parabolic cylinder is y2 = z,and select and construct the interpolation polynomial of three-dimensional quadratic and the interpolation of three-dimensional quadratic.Then the coefficients of interpolation polynomial are calculated by using the software of matlab,and plotted by the software of matlab.Finally,the error analysis is carried out and the effectiveness of the example algorithm is verified.