Abstract by Erik Parkinson
Polynomial Rootfinding using the Division Matrix
We have developed a multivariate numerical rootfinding algorithm that finds all real zeros in a given compact region in Cn of a system of functions. Currently, a common rootfinding method is to construct a multiplication-by-x Moeller-Stetter matrix, and use the eigenvalues and/or eigenvectors to find the roots. However, construction of this matrix can be numerically unstable in certain cases. In order to fix this, we instead develop a method to construct a division-by-x matrix. This improvement allows us to create a fast, stable, numerical rootfinding algorithm.