Dr. Thomas Cameron will present: ROOT-FINDING ALGORITHMS FOR THE EIGENVALUE PROBLEM
Friday, September 14, 2018, 3-4pm in 103A Walker Hall Abstract: Since its inception, the theory of matrix polynomials has been strongly influenced by its applications to differential equations and vibrating systems.In this talk, we 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, we give a geometric description of the eigenvalue and discuss the polynomial eigenvalue problem, which includes as special cases computing the roots of a polynomial and the eigenvalues of a matrix. Our 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. We 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.