This paper dealt with the local convergence study of the parameter based sixth and eighth order iterative method. This analysis discuss under assumption that the first order Fréchet derivative satisfied the Lipschitz continuity condition. In this way, we also proposed the theoretical radius of convergence of these methods. Finally, some numerical examples demonstrate that our results apply to compute the radius of convergence ball of iterative method to solve nonlinear equations. We compare the results with the method in Kumar et al. (J Comput Appl Math 330:676–694, 2018) and observe that by our approach we get much larger balls as existing ones.

中文翻译：

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具有六阶和八阶收敛的基于参数的方法的局部收敛

本文研究了基于参数的六阶和八阶迭代方法的局部收敛性研究。该分析假设一阶 Fréchet 导数满足 Lipschitz 连续性条件。这样，我们也提出了这些方法的理论收敛半径。最后，一些数值例子表明我们的结果适用于计算迭代法求解非线性方程的收敛球半径。我们将结果与 Kumar 等人的方法进行比较。（J Comput Appl Math 330:676–694, 2018）并观察到，通过我们的方法，我们得到了比现有球大得多的球。