The Analysis of the Advantages and Disadvantages of Construction Method of Lagrange Interpolated Polynomial and Newton Interpolated Polynomial

To build a relationship between a function and a variable from a given table of n+1 interpolation nodes (x_k,y_k ),k=0..n, in Mathematics, if using numerical methods then people often build interpolated polynomials such as Lagrange interpolated polynomial, Newton interpolated polynomial, Hermit interpolated polynomial... or least squares method. However, each method has certain advantages and disadvantages. This paper will show some advantages and disadvantages of the method of constructing Lagrange interpolated polynomials and Newton interpolated polynomials.