In this paper, we introduce seventh- and sixth-order methods for solving the systems of nonlinear equations. The convergence analysis of the proposed methods is provided. The computational efficiency for these methods is $$ 6^{1/(3n+2n^2)} $$ 6 1 / ( 3 n + 2 n 2 ) and $$ 7^{1/(4n+2n^2)} $$ 7 1 / ( 4 n + 2 n 2 ) . Computational efficiency of new methods is compared with Newton’s method and some other recently published methods. Numerical examples are included to demonstrate the validity and applicability of the methods and comparison is made with the existing results.

中文翻译：

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非线性方程组数值解的三步迭代法

在本文中，我们介绍了求解非线性方程组的七阶和六阶方法。提供了所提出方法的收敛性分析。这些方法的计算效率为 $$ 6^{1/(3n+2n^2)} $$ 6 1 / ( 3 n + 2 n 2 ) 和 $$ 7^{1/(4n+2n^2) } $$ 7 1 / ( 4 n + 2 n 2 ) 。新方法的计算效率与牛顿方法和其他一些最近发表的方法进行了比较。包括数值例子来证明方法的有效性和适用性，并与现有结果进行比较。