Abstract by Hayden Ringer

Personal Infomation

Presenter's Name

Hayden Ringer

Degree Level



Tyler Jarvis
Sue Stephenson
Natalie Larsen
Erik Parkinson
Daniel Christensen
Lukas Erekson

Abstract Infomation



Faculty Advisor

Tyler Jarvis


Multivariate Rootfinding Using Chebyshev Approximation and Möller-Stetter Matrices


Root-finding algorithms are key kernels in many areas of scientific computing. However, there are few robust methods for finding all, or even several, roots of multivariate systems. We present a method for finding all the common roots of a system of multivariate smooth functions lying within a compact set in R^n . Our method utilizes multivariate Chebyshev polynomials to approximate smooth functions to high precision, and then uses a generalized form of the companion matrix, known as a Möller-Stetter matrix, to find the roots of the approximate polynomial system. We explore the numerical properties that the algorithm exploits in order to avoid a number of obstacles. We compare our method to other popular multivariate root-finding methods, including Chebfun2 and Bertini.