wjgilbert@watmath.waterloo.edu (William J. Gilbert) (01/21/88)
UNIVERSITY OF WATERLOO FRACTAL GEOMETRY AND DYNAMICAL SYSTEMS SEMINAR SERIES ===================================================== TITLE: Newton's Method and Complex Analytic Dynamics SPEAKER: Prof. Paul Blanchard, Boston University DATE: Thursday, January 28, 1988 [Note change of date from the December posting] TIME: 3:30 p.m. ROOM: MC 1056 ABSTRACT: We shall start the lecture with a general overview of complex analytic dynamical systems including a discussion of the classical Fatou-Julia theory. This beautiful theory will then be applied to Newton's method - a numerical algorithm for solving nonlinear equations. In theory, the method is flawed because one can start with a poor approximation to a solution and, as a result, the method does not converge. However, in practice, Newton's method works very well, and we shall discuss this dichotomy in light of the Fatou-Julia theory.