The content of this paper is twofold. First, it aims to provide some new Newton-like methods for solving the root-finding problem in the complex plane. Moreover a convergence test for the resulted methods is phrased and proved. The pseudo-Newton method of Kalantari for finding the maximum modulus of complex polynomials arises as particular case of the newly proposed procedures. Secondly, a recently introduced Thakur iterative process is used in connection with the newly described methods. Its stability and data dependence is subject to analysis. Ultimately, an illustrative analysis regarding some modified Thakur iteration procedures, is obtained via polynomiographic techniques.

本文的内容是双重的。首先，它旨在提供一些类似于牛顿的新方法来解决复杂平面中的寻根问题。此外，对所得方法的收敛性测试进行了表述和证明。作为新提出的程序的特殊情况，出现了卡兰塔里（Karantari）的拟牛顿法，用于寻找复多项式的最大模量。其次，结合新近介绍的方法使用了最近引入的Thakur迭代过程。其稳定性和数据依存性有待分析。最终，通过多项式摄影技术获得了有关某些改进的Thakur迭代程序的说明性分析。