In this article, we propose a new family of methods, such as Jarratt, with the fifth and sixth order. This includes some popular methods as special cases. We propose four different selection for parameter matrix $T_k$. The main advantage of the proposed methods is that they work well for any value of parameter “$a$” in the first stage of iterations, while the existing methods work only for some $a$ $(2/3\text{or}1/2)$. Thus, we extend essentially the domain of applicability of the original ones. Based on the computational efficiency analysis, we also made a selection of some high-efficiency ones among the families.

中文翻译：

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求解非线性方程组的高阶类Jarratt迭代

在本文中，我们提出了一种新的方法系列，例如Jarratt，具有第五和第六个顺序。这包括一些流行的方法作为特殊情况。我们为参数矩阵提出了四种不同的选择${Ť}_{ķ}$。提出的方法的主要优点是，它们对于参数“$\mathrm{一种}$在迭代的第一阶段，而现有方法仅适用于某些 $\mathrm{一种}$ $（2/3\text{要么}\mathrm{1个}/2）$。因此，我们实质上扩展了原始方法的适用范围。在计算效率分析的基础上，我们还选择了一些高效率的家庭。