wjgilbert@watmath.waterloo.edu (William J. Gilbert) (01/21/88)
UNIVERSITY OF WATERLOO
FRACTAL GEOMETRY AND DYNAMICAL SYSTEMS SEMINAR SERIES
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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.