The improvements of modified Newton’s method

摘要

In this paper, we improve some third-order modifications of Newton’s method and obtain many new methods for solving non-linear equations. The new methods have the order of convergence five or six. Per iteration these methods require two evaluations of the function and two evaluations of its first derivative and therefore the efficiency of the new methods may also be improved. These methods can compete with Newton’s method, as we show in some examples.