标题： 牛顿类求根方法的动力学 显示英文标题

标题： Dynamics of Newton-like root finding methods

摘要： 当查阅文献时，可以观察到当将\textit{类似牛顿的}根查找算法应用于二次多项式$z^2-c$时得到的算子，无论使用哪种算法，其形式都相同。 在本文中，我们解释了为什么得到这个表达式。 这是通过研究应用牛顿类似算法到次数为$d$的多项式族$p(z)=z^d-c$所得到的算子的对称性来完成的。 此外，我们提供了一个迭代过程来获得新牛顿类似算法的表达式。 我们还对给定的通用算子进行了动力学研究，并提供了此类方法的一般结论。 显示英文摘要

摘要： When exploring the literature, it can be observed that the operator obtained when applying \textit{Newton-like} root finding algorithms to the quadratic polynomials $z^2-c$ has the same form regardless of which algorithm has been used. In this paper we justify why this expression is obtained. This is done by studying the symmetries of the operators obtained after applying Newton-like algorithms to a family of degree $d$ polynomials $p(z)=z^d-c$. Moreover, we provide an iterative procedure to obtain the expression of new Newton-like algoritms. We also carry out a dynamical study of the given generic operator and provide general conclusions of this type of methods.