Ball convergence results are very important, since they demonstrate the complexity in choosing initial points for iterative methods. One of the most important problems in the study of iterative methods is to determine the convergence ball. This ball is small in general restricting the choice of initial points. We address this problem in the case of Wang’s method utilized to determine a zero of a derivative. Finding such a zero has many applications in computational fields, especially in function optimization. In particular, we find the convergence ball of Wang’s method using hypotheses up to the second derivative in contrast to earlier studies using hypotheses up to the fourth derivative. This way, we also extend the applicability of Wang’s method. Numerical experiments used to test the convergence criteria complete this study.

球收敛结果非常重要，因为它们证明了为迭代方法选择初始点的复杂性。迭代方法研究中最重要的问题之一是确定收敛球。该球通常很小，限制了初始点的选择。在Wang用来确定导数为零的方法的情况下，我们解决了这个问题。找到这样的零在计算领域，尤其是在函数优化中具有许多应用。特别是，我们发现了使用直到第二阶导数的假设的Wang方法的收敛球，这与使用高达第四阶导数的假设的早期研究形成了鲜明的对比。这样，我们也扩展了Wang方法的适用性。用于测试收敛准则的数值实验完成了本研究。