Study On Lagrange Interpolation Problem On Quadric Surfaces

Multivariate interpolation occupied the important position in computational mathematics research area,multivariate polynomial interpolation more widely applied in the actual life.Some time we need to set up simulate of surface to solve practical problem,such as the joining together of curved contour surface of industrial products and discrete data approximation of image processing,etc.This means that the research of multivariate Lagrange interpolation is of great significance.In this master thesis,we mainly discuss the multivariate interpolation on quadric surfaces and its unique solution node group of construction method.Using the MATLAB software image processing and analysis of the error.This master thesis mainly divides into three chapters to present the content of the thesis.First of all,the first chapter mainly introduces the basic theory and method of multivariate polynomial interpolation,and explains the previous research results of binary Lagrange interpolation.In particular,the construction principle of the unique solution node group for binary Lagrange interpolation is expounded and introduce methods that adding straight line method and adding conic curve method to construct plane algebraic curve interpolation.I also introduce adding the arbitrary number of algebraic curve method which is to construct the unique solution node group of binary polynomial spatial interpolation.The second chapter is based on the research results of binary Lagrange interpolation to study the problem of solving the problem of ternary Lagrange interpolation node.we introduce the basic theory of the unique solution node group for the interpolation of algebraic curved surface and algebraic curve and introduce adding algebraic surface method of the unique solution node group of ternary Lagrange interpolation.The third chapter is the main content of this paper.This chapter mainly deals with Lagrange interpolation problems on quadric surfaces.The Lagrange interpolation problem was studied with hyperboloid of one sheet and hyperboloid of two sheets.Proposing the method of adding hyperboloid of one sheet method and adding hyperboloid of two sheets method to construct the unique solution node groups of cubic polynomial spatial interpolation and give proof.Finally,the experiment was carried out with MATLAB software,and the error analysis was carried out.