We present methods that provide all zeroes and extrema of a function that do not require differentiation. Using point process theory, we are able to describe the locations of zeroes or maxima, their number, as well as their distribution over a given window of observation. The algorithms in order to accomplish the theoretical development are also provided, and they are exemplified using many illustrative examples, for real and complex functions.

翻译：本文提出无需微分运算即可获取函数所有零点与极值的方法。借助点过程理论，我们能够描述零点或极大值的位置、数量及其在给定观测窗口内的分布。文中同时提供了实现理论发展的算法，并通过大量示例对实函数与复函数进行了演示说明。