Application Of Aitken Extension Algorithm In 3D Space Interpolation

Based on the research results of multivariate polynomial interpolation problems on algebraic surfaces and spatial algebraic curves,the focus is on the in-depth study of the well-posed set of nodes for bivariate and Lagrange multivariate interpolation,and on this basis,a well-posed set of nodes for interpolation defined on tetrahedrons is studied.In this thesis,a new Aitken method is proposed and proved.Finally,two examples are given to test the conclusions of this thesis.The interpolation of binary and multivariate polynomials has always been an important research field in computational mathematics.Due to the continuous progress and development of computational science,the manpower and material resources have been greatly reduced.At the same time,we also hope that the program of function interpolation in the computer can be continuously improved.Multivariate function interpolation will also play a greater role in practical applications.The first chapter is the introduction,which mainly introduces the background and significance of this thesis.The research status of Lagrange multivariate interpolation problem and Aitken algorithm problem at home and abroad is sorted out in detail.The main research contents,research methods and research framework of this thesis are discussed.The second chapter introduces and discusses how the multivariate interpolation problem is proposed and discusses its research and development process.Then it describes the specific definition theorems of binary Lagrange interpolation and ternary Lagrange interpolation and the application of Lagrange interpolation in curve interpolation and surface interpolation.The third chapter focuses on the research results of Lagrange interpolation along the plane algebraic curve and along the space algebraic surface,and makes an in-depth study on the well-posed node group of multivariate Lagrange interpolation.The fourth chapter analyzes the problem of Lagrange interpolation well-posed set of nodes on the tetrahedral framework,and describes in detail how to take points on the tetrahedron and the principle of determining the number of points.From easy to difficult,an experimental example of binary Lagrange interpolation on the plane and the experimental example of ternary Lagrange interpolation on two spatial tetrahedrons are given respectively,which verifies the rationality of the problem of constructing the interpolation well-posed set of nodes defined on the tetrahedron.