Research Progress on Newton’s Iterative Methods for Nonlinear Equation

Reviewed the research progress of Newton’s iterative methods for nonlinear equation. Convergence with second order, third order, fourth order, fifth order, sixth order, seventh order, eighth order and ninth order Newton’s iterative methods are given in turn, and the efficiency index of these iterative methods are analyzed. Numerical experiments show that the convergence process of the three Newton iterative methods, and the results indicate that the convergence of the higher-order Newton’s method can be well demonstrated only when the initial point is close to the root.