Abstract by Catherine Kellar
Random Polynomial Interpolation from Known Roots in the Multivariate Case
Optimization problems often appear as root finding problems, and occur widely across medicine, business, economics, finance, and biology, among other fields. Because of their wide application, many algorithms exist to find the roots of polynomials. Choosing the appropriate algorithm (for instance, focusing on speed over accuracy, or visa versa) can mean the difference between the success or failure of a process. However, as new algorithms are developed, there is no standard way to benchmark those algorithms against existing ones. Though a closed-form formula exists for univariate polynomial interpolation from known roots, multivariate polynomial interpolation is an interesting problem with many unknowns that remains largely unexplored until this point. The current project explores the creation of a data set of multivariate polynomials with known roots for the purpose of benchmarking these most popular algorithms against new ones currently under development by our research group.