Zeroes and Extrema of Functions via Random Measures

TL;DR

This paper introduces a novel approach using random measures and point process theory to identify all zeros and extrema of functions without differentiation, applicable to real and complex functions.

Contribution

It develops new methods for locating zeros and extrema of functions through probabilistic models, avoiding traditional derivative-based techniques.

Findings

Effective algorithms for zero and extrema detection

Applicable to both real and complex functions

Demonstrated with multiple illustrative examples

Abstract

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.