Newton's Method for Finding Roots of Complex Polynomials: Complex Dynamics Between Combinatorics and Numerical Analysis

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• Dierk Schleicher (Jacobs University, Bremen)
• Thursday 28 January 2010, 14:30-15:30
• MR12.

If you have a question about this talk, please contact Andrew Thomason.

We shall discuss Newton’s root-finding method for the case of complex polynomials in a single variable. This method has been known to approximate roots extremely efficiently, once good approximate solutions are known, but its global properties are known to be difficult to describe. We shall discuss recent results towards turning Newton’s method into an efficient algorithm for finding all roots of given complex polynomials, and give a classification of all “bad cases” in combinatorial terms using “Newton graphs”. This also answers a question raised by Smale.

This talk is part of the Combinatorics Seminar series.

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