Numerical methods for solving polynomial equations

Jonathan Hauenstein

University of Notre Dame
Barton Lectures in Computational Mathematics


Date: Wednesday, February 19, 2020
Time: 4:00 pm - 5:00 pm
Location: Petty 136

Reception ∙ Petty 116∙3:30 – 4:00 PM

Nonlinear polynomial equations have been solved for several millennia such as those documented on Babylonian clay tablets involving the relationship between perimeter and area of rectangles. The Abel-Ruffini theorem and the development of Galois theory two centuries ago showed that solutions to most systems of polynomial equations could not be expressed in terms of radicals necessitating development of numerical computational methods to approximate solutions. This talk will explore various numerical methods for computing and analyzing solutions to systems of polynomial equations, collectively called numerical algebraic geometry. Some recent results for polynomial systems arising in science and engineering applications along with current computational challenges associated with solving polynomial systems will be discussed.