The convergence region of Traub’s method for solving equations is small in general. This fact limits its applicability. We locate a more precise region containing the Traub iterations leading to at least as tight Lipschitz constants as before. Our convergence analysis is finer, and obtained without additional conditions. The new theoretical results are tested on numerical examples that illustrate their superiority over earlier results.

中文翻译：

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关于Traub方法扩展收敛区域的复杂性

特劳布求解方程的方法的收敛范围通常很小。这个事实限制了它的适用性。我们找到了一个更精确的区域，其中包含导致至少与以前一样紧密的Lipschitz常数的Traub迭代。我们的收敛分析更加精细，无需附加条件即可获得。新的理论结果在数值示例上进行了测试，这些示例说明了它们比早期结果优越的优势。