clarke@utcsri.UUCP (Jim Clarke) (02/23/87)
GRAPHICS SEMINAR, Tuesday, February 24, 2 pm, GB221 Dick Rubinstein and Harry Hersch Digital Equipment Corporation ``Models for Affective Human Interface Design" GRAPHICS SEMINAR, Wednesday, February 25, 2 pm, GB119 Mr. Larry Yaeger Omnibus-Abel Computer Graphics Inc. ``Cray-based Production of Computer Graphics" THEORY SEMINAR, Thursday, February 26, 3 pm, GB220 Professor Joel Friedman University of California ``On The Convergence of Newton's Method" In this talk we estimate the density of the set of points for which Newton's methods converges. Given a polynomial of degree d with complex coefficients whose roots lie in the unit ball (a condition which is easy to check and to ensure by suitable rescaling), we ask what is the measure of the set of points in the ball of radius 2 for which Newton's method con- verges. We prove that for each d this measure is bounded from below by a positive number, and d we give an estimate of this number. We may also discuss results on a related problem, an average case analysis of the set of points for which Newton's method converges ``very'' quickly (i.e. ``approximate zero'' for Newton's method). -- Jim Clarke -- Dept. of Computer Science, Univ. of Toronto, Canada M5S 1A4 (416) 978-4058 {allegra,cornell,decvax,linus,utzoo}!utcsri!clarke