Root-finding Algorithms for the Eigenvalue Problem
Dr. Thomas Cameron, Davidson College
Friday, September 14, 2018
103A Walker Hall
This talk is free and open to the public
Since its inception, the theory of matrix polynomials has been strongly influenced by its applications to differential equations and vibrating systems. In this talk, Cameron will give a brief history of matrix polynomials and motivate the definition of a matrix polynomial through an initial value problem that models a mass-spring system. Then, he gives a geometric description of the eigenvalue and discusses the polynomial eigenvalue problem, which includes as special cases computing the roots of a polynomial and the eigenvalues of a matrix.
The primary focus is to outline several recent advancements in solving for the roots of a polynomial and their application to the polynomial eigenvalue problem. This outline will include core-chasing algorithms, produced by Aurentz, Mach, Vandebril and Watkins, and a modification of Laguerre’s method, created by Cameron. He will conclude by discussing the positives and negatives of these advancements as it applies to the polynomial eigenvalue problem, current projects and directions for future research.
Sponsored by the Department of Mathematical Sciences, please contact Quinn Morris email@example.com or Travis Weiland firstname.lastname@example.org or visit our the department colloquium website at: https://mathsci.appstate.edu/activities-outreach/department-colloquia for more information and for other upcoming events.
About the Department of Mathematical Sciences
The Department of Mathematical Sciences offers undergraduate degrees in actuarial science and mathematics, with concentrations in business, computation, life sciences, physical sciences, secondary teaching and statistics, plus a general, self-designed concentration. The department also offers the Master of Arts in mathematics, with concentrations in college teaching and secondary teaching. Learn more at https://mathsci.appstate.edu.
Sept. 10, 2018