Zeroes and Extrema of Functions via Random Measures
Methodology
2025-12-01 v3 Optimization and Control
Computation
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.
Cite
@article{arxiv.2511.10293,
title = {Zeroes and Extrema of Functions via Random Measures},
author = {Athanasios Christou Micheas},
journal= {arXiv preprint arXiv:2511.10293},
year = {2025}
}
Comments
Function extrema and zeroes; Optimization; Poisson point process; Random counting measures; Riemann's zeta function