BYU

Abstract by Erik Parkinson

Personal Infomation


Presenter's Name

Erik Parkinson

Degree Level

Undergraduate

Abstract Infomation


Department

Mathematics

Faculty Advisor

Tyler Jarvis

Title

Polynomial Rootfinding using the Division Matrix

Abstract

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.