Abstract by Natalie Larsen
Checking Existence of Roots in Numerical Root-finding
We have developed a multivariate numerical rootfinding algorithm that finds all real zeros in a given compact region of a system of functions, using a mix of subdivision and eigenvalue methods. As part of the root-finding algorithm, we look to throw out intervals that surely have no roots in them. Using the properties of Chebyshev polynomials we have developed some quick checks for that purpose. We discuss potential additional checks and how this affects the overall algorithm.