Research On Local Lagrangian Numerical Differentiation

In this dissertation, the following critical theoretical problems on local La-grangian numerical differentiation are studied: explicit formulas, local estimate for the remainder, and the highest order of approximation in the case that the values of the function at these interpolation nodes have perturbationsLagrangian numerical differentiation is a method that the Lagrange interpolation polynomialis differentiated to approximate the derivative, where Tn = {t₀,t₁,...... ,t_n} is a group of distinct nodes, andHowever, experts in approximation theory and computational mathematics have different views on the Lagrange interpolation: the former think the convergence of interpolation as a process as the order n of interpolation approaches to infity, but the latter think the convergence of interpolation as a process as the distance h between interpolation nodes approaches to 0. Hence, the former can be called the global Lagrange interpolation, and the latter can be called the local Lagrange interpolation.In this dissertation, Lagrangian numerical differentiation formula L^k is expressed explicitly by means of cycle indicator polynomials of symmetric group. As a method based on the Lagrange interpolation, numerical differentiation also has the difference between "global" and "local". As far as global Lagrangian...