This paper is devoted to a family of Newton-like methods with frozen derivatives used to approximate a locally unique solution of an equation. We perform a convergence study and an analysis of the efficiency. This analysis gives us the opportunity to select the most efficient method in the family without the necessity of their implementation. The method can be applied to many type of problems, including the discretization of ordinary differential equations, integral equations, integro-differential equations or partial differential equations. Moreover, multi-step iterative methods are computationally attractive.

中文翻译：

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关于参数化多步牛顿法的局部和半局部收敛性

本文致力于一系列类似于牛顿法的方法，其中冻结导数用于近似方程的局部唯一解。我们进行了收敛研究和效率分析。这种分析使我们有机会选择家族中最有效的方法，而无需实施它们。该方法可以应用于许多类型的问题，包括常微分方程，积分方程，积分微分方程或偏微分方程的离散化。此外，多步迭代方法在计算上很有吸引力。