Theoretical Results on Polynomial Root-Finding,   Bahman Kalantari,   Rutgers University,  Fri, 20 March, 2009,   3:00 p.m. C-236


The talk will focus on several results inspired by, or related to the historic problem of polynomial root finding

Newton's method and its complexity; determinantal generalizations of Taylor's theorem and Newton's method; Iteration functions; dynamical systems; bounds on zeros; continued fractions; homogeneous linear recurrence relations; Voronoi region; Gauss Lucas theorem; Maximum modulus; principle; computational geometry; formulas for approximation of pi;and lastly "polinomiography" a term I have coined for the visualization of the process of root finding via iteration functions. Our theoretical results in particular drastically improve Smale's bound on zeros, give a novel lower bound on determinants, new iterative functions and their connections with homogeneous linear recurrence relations.