| In the study of Mathematical Science,multivariate interpolation has always been a crucial problem which in the numerical mathematics' study,in practical scientific research,the study of problem that multivariate interpolation will help people solve some numerical mathematics' problems.With the rapid development of science and technology,many experts and scholars pay more and more attention on the theory and method of multivariate interpolation.The related issues of triple function interpolation has been attrating the people's attention and exploration,because triple Lagrange interpolation is not only the promotion of bivariate Lagrange interpolation,but also the foundation of multivariate Lagrange interpolation.As is known to us all,compared with the interpolation function of single variable,multivariate interpolation problem is more complex,more difficult.While the methods and means to study some single variable interpolation functions cannot be extended to the problem of multivariate interpolation simply.In this paper,we study the solvability issues of triple Lagrange interpolation node group on the tetrahedral framework.On the basis,the struction of triple function interpolation on the tetrahedral framework and the way to structure the solvability node set are given.In finally,we give two examples to verify the feasibility of this theory.They aer two parts in this paper:The first part mainly introduces the preparatory knowledge of multivariate function interpolation,the basic concepts of multivariate rational interpolation and the relatival conlusion for the solutions of multivariate rational interpolation.The second part introduces the new method of constructing triple Lagrange interpolation,and then studied and discussed the solvability issues of triple Lagrange interpolation node group on the tetrahedral frameworkthe solutions of problems on tetrahedral framework by this method,finally,the effectiveness of this method is verified by some numerical examples. |
PDF Full Text Request