一种15阶收敛的牛顿迭代修正格式

Modification of Newton's method with fifteenth-order convergence

给出非线性方程求根的一种迭代方法,该方法是一种牛顿迭代修正格式,证明了此迭代格式是15阶收敛到单根的。通过数值实验,把所给方法与牛顿迭代法以及其它几种牛顿迭代法的变形法进行了比较,试验数据表明,本文方法有较好的效果。

An iterative method for nonlinear equations is presented. The method is the modification of Newton＇ s method based on a fifth-order method and a modified Simpson method. The numerical experiments showed that the new method with fif- teenth-order convergence is more efficient and performs better than classical Newton＇ s method and other methods.