In this work, we start from a family of iterative methods for solving nonlinear multidimensional problems, designed using the inclusion of a weight function on its iterative expression. A deep dynamical study of the family is carried out on polynomial systems by selecting different weight functions and comparing the results obtained in each case. This study shows the applicability of the multidimensional dynamical analysis in order to select the methods of the family with the best stability properties.

中文翻译：

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关于多维权函数对迭代过程稳定性的影响

在这项工作中，我们从解决非线性多维问题的一系列迭代方法开始，这些迭代方法是在迭代表达式中包含权重函数而设计的。通过选择不同的权函数并比较每种情况下获得的结果，对多项式系统进行了深入的动力学研究。这项研究表明了多维动力学分析的适用性，以便选择具有最佳稳定性的族系方法。