BYU

Abstract by Erik Parkinson

Personal Infomation


Presenter's Name

Erik Parkinson

Co-Presenters

None

Degree Level

Undergraduate

Co-Authors

None

Abstract Infomation


Department

Mathematics

Faculty Advisor

Tyler Jarvis

Title

Root-finding Techniques in Multiple Dimensions

Abstract

We developed a new method for finding the roots of systems of multivariate functions. A common method for root finding is using chebyshev polynomails to approximate the functions and then finding the roots of them. One of the best known methods for finding roots of polynomials uses a companion matrix, which is unstable with chebyshev interpolated polynomials due to the high degree coefficients being small. We fix this problem using the inverse of the companion matrix, which is succesfully able to find roots. This leads to a a fast and stable root-finding method that can solve problems unapproachable to other techniques.