Abstract by Erik Parkinson
Root-finding Techniques in Multiple Dimensions
We developed a new method for finding the roots of systems of multivariate functions. A common method for root finding is using chebyshev polynomails to approximate the functions and then finding the roots of them. One of the best known methods for finding roots of polynomials uses a companion matrix, which is unstable with chebyshev interpolated polynomials due to the high degree coefficients being small. We fix this problem using the inverse of the companion matrix, which is succesfully able to find roots. This leads to a a fast and stable root-finding method that can solve problems unapproachable to other techniques.