避免二阶导数计算的迭代法

Newton迭代法是求非线性方程数值解的一个非常有效的方法,它只需计算一阶导数值,不必计算高阶导数值,且具有二阶收敛速度.为了进一步提高收敛速度,且不用计算高阶导数值,提出了一个新的修正的Newton迭代方法,它只需提供一阶导数值,不必计算高阶导数值,但收敛速度却更高,具有至少三阶的收敛速度,它和别的同类型的方法相比具有形式简单、计算量少等特点.最后,给出了数值试验,从数值试验可看出,方法是非常有效的.

The second-order-derivative-free interative for solving nonlinear equation

Newton interative method is a very good method for solving nonlinear equation, it is a second-order convergence rate method without employing 2-order derivatives, to make it higher convergence rate, a new interative method is given, it has at least three-order convergence rate and without calculating 2-order derivatives, compare with orther interative method, it is easier to calculate, in the end, the numerical experience is given, it shows that the method is effective.