MAA Treasurer
Professor of Mathematics Emeritus - Boston University
Term: July 1, 2025, to June 20, 2029

Newton’s Method: Complex Numerics and Complex Dynamics

Newton’s method is an iterative root-finding algorithm that is both simple and surprisingly efficient. We start with an initial guess for the root and apply the algorithm repeatedly until we obtain the desired approximation. Unfortunately, a random guess does not always lead to a root. In this talk, we use the theory of complex dynamics along with some computer graphics to explain the difficulties that might arise, and we suggest ways to avoid these pitfalls. As the story unfolds, we encounter both chaos and fractals

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