We develop a sixth order Steffensen-type method with one parameter in order to solve systems of equations. Our study’s novelty lies in the fact that two types of local convergence are established under weak conditions, including computable error bounds and uniqueness of the results. The performance of our methods is discussed and compared to other schemes using similar information. Finally, very large systems of equations ($100\times 100$ and $200\times 200$) are solved in order to test the theoretical results and compare them favorably to earlier works.

中文翻译：

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源自现实生活问题的非线性模型的一些高阶迭代方法

我们开发具有一个参数的六阶Steffensen型方法，以求解方程组。我们研究的新颖之处在于，在弱条件下建立了两种类型的局部收敛，包括可计算的误差范围和结果的唯一性。我们讨论了我们方法的性能，并将其与使用类似信息的其他方案进行了比较。最后，非常大的方程组（$100\times 100$ 和 $200\times 200$解决）以测试理论结果并将其与早期工作进行比较。