Abstract by Natalie Larsen
Stably Constructing a Basis for Spectral Rootfinding
We have developed a multivariate numerical rootfinding algorithm that finds all real zeros in a given compact region in $\\C^n$ of a system of functions. In our algorithm, it is key to find an appropriate basis for our quotient algebra in order to construct the needed Moeller-Stetter matrix. Here we present the Telen-Van Barel Method which uses the construction of the Macaulay matrix to find this basis. This method is modified in our algorithm to better suit the Moeller-Stetter problem and allows for it to be more well-conditioned than with other bases, leading to an overall more accurate algorithm.