Abstract by Tyler Moncur
Interval Checks in Rootfinding
We have developed a multivariate numerical rootfinding algorithm that finds all real zeros in a given compact region of a system of functions. As part of our rootfinding algorithm, we implement several techniques to speed up computation. Our method finds real roots by first subdividing the original search region and approximating the functions with Chebyshev polynomials. We find the roots within a specific subinterval using a modified version of the Telen Van Barel method, which is the most expensive aspect of our algorithm. So we have achieved a significant speed improvement by developing multiple methods for checking whether a given Chebyshev polynomial contains any zeros within a subinterval.