一类求解非线性方程的3阶收敛迭代格式

One Class of Third-Order Iteration Methods for Solving Non-Linear Equations

该文提出了求非线性方程根的3阶收敛的牛顿类迭代方法,并对收敛性进行了证明.该牛顿类迭代方法有效地克服了传统的牛顿迭代方法在目标函数的1阶导数等于0或者接近于0时失效的缺点.通过数值例子来验证该类迭代格式的有效性.

In this paper,one class of modified Newton methods for solving non-linear equations is presented.Analysis of convergence shows that the new method is cubically convergent.The main advantage of this method is that it can overcome the shortcoming of Newton′s method which the derivative of the function is either zero or very small of the required root.The effectiveness of the present method is demonstrated by some numerical examples.