论文标题
Schröder方法的多项式方法的动力学表征
A characterization of the dynamics of Schröder's method for polynomials with two roots
论文作者
论文摘要
这项工作的目的是为Schröder方法的动态行为提供第一种方法，Schröder方法是解决非线性方程的众所周知的迭代过程。在这种情况下，我们考虑在复杂平面中定义的方程式。通过使用拓扑结合，我们表征了Schröder方法吸引的盆地，该方法应用于具有两个根和不同多重性的多项式。实际上，我们表明这些盆地是半平台或圆圈，具体取决于根的多重性。我们通过图形库完成了研究，该图库使我们能够比较牛顿和Schröoder方法的吸引力，并应用于某些给定的多项式。 关键：Schröder的方法；吸引力的盆地；非线性方程。
The purpose of this work is to give a first approach to the dynamical behavior of Schröder's method, a well known iterative process for solving nonlinear equations. In this context we consider equations defined in the complex plane. By using topological conjugations, we characterize the basins of attraction of Schröder's method applied to polynomials with two roots and different multiplicities. Actually, we show that these basins are half-planes or circles, depending on the multiplicities of the roots. We finish our study with a graphical gallery that allow us to compare the basins of attraction of Newton's and Schröoder's method applied to some given polynomials. Key: Schröder's method; basin of attraction; nonlinear equation.
