一类新的牛顿迭代法的变形

The Deformation of a New Newton Iteration Method

提出了求解非线性方程f(x)=0根的一类牛顿迭代法的变形方法。与许多特殊类型的方法相比,该方法更具有一般性。同时,在证明了其收敛阶的基础上给出了一种构造该方法的可行性方案。最后,通过数值实验进一步验证了方法的有效性,而且方法(10)还移除了目标函数在根x*附近f'(x)≠0的限制性条件。

This paper proposes a new class variants of Newton’s method to solve f(x)=0. The new method is more general compared with many special types of methods. Meanwhile, on the basis of proving the convergence order, a feasible scheme is given to construct the method. Finally, the effectiveness of the method is further verified by numerical experiments, and the restriction conditions of f'(x) ≠0 in the neighborhood of root x* are also removed in the method(10).