Abstract by Lukas Erekson
A Numerical Method for Multivariate Rootfinding
We have developed a multivariate numerical root-finding algorithm that finds all the real zeros in a compact region of a system of n equations in n variables. Our algorithm uses a synthesis of subdivision, approximation, and matrix methods to find the roots of the system. In particular, it utilizes the accuracy of Chebyshev interpolation on smooth functions on a compact interval, reinterpreting the general rootfinding problem as a polynomial rootfinding problem, which segues naturally into an eigenvalue problem. In practice, the algorithm appears to be fairly stable in solving two- or three-dimensional systems, seeing success in as high as ten dimensions. In my talk, I present significant results concerning our algorithm's speed and accuracy and compare them to a popular Matlab root-finding package, Chebfun.