Trivariate Grated Lagrange Interpolation

Multivariate interpolation problem is one of the important contents in mathematics,many scholars have put their eyes on the theory of multivariate interpolation.Multivariate interpolation will make outstanding contributions in spatial interpolation and the smooth curvature of vehicle or ship's shape.At the same time,due to the continuous development and improvement of algebraic geometry theory and method in recent years,it provides a strong theoretical basis and a new research method for the further study of multivariate interpolation problem.Due to the constantly progress of computer science,people can make use of the computer to analyze the problems in some practical production,which greatly reduces the manpower and material resources.We also hope that the programming about function interpolation will be refined constantly,so that it will make more contributions to the practical application.In this paper,we mainly study and discuss the theory of the trivariate grated Lagrange interpolation and the structure of its interpolation.Basic on professor Liang's Lagrange interpolation along the non repetitive components of algebraic curves,and the grated interpolation method based on this,after continuous research and exploration,we make some achievements in constructing the properly posed set of nodes for trivariate grated Lagrange interpolation on R3.This paper is composed of four chapters.The first chapter is introduction,we introduce the research meaning of multivariate polynomial interpolation,especially about the situation of domestic and foreign.Briefly introducing the main content and structure of this paper.In the second chapter,several common interpolation methods are briefly involved.We compare them simply so that it will contribute to help choosing which method according the case.In the third chapter,we recommend some basic notions of multivariate polynomial interpolation,and constructive method of the bivariate grated Lagrange interpolation.The last chapter is the main study of the trivariate grated Lagrange interpolation,we give the method for constructing its properly posed set of notes,and constructing interpolation polynomials on the hexahedron.