Zeroes and Extrema of Functions via Random Measures

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.

arXiv commentFunction extrema and zeroes; Optimization; Poisson point process; Random counting measures; Riemann's zeta function