Abstract
Many problems in mathematics could be summarized as a linear or nonlinear function equation:. Iterative method is one of the most efficient methods for solving the equation. In this paper, we study the convergent rate and computational efficiency of some familiar iterative methods, such as Newton method、secant method and Steffensen method, and some numerical experiments as well. By comparing their advantages and shortcomings, we could choose a more suitable method to solve the equation. Among others, Steffensen method is a very good method of solving nonlinear equations, which has the same computational efficiency as Newton method and avoids computing derivative. Through the study, we could know the conditions and efficiency of the three iterative methods better and apply these methods efficiently.
