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SUMMARY:Newton's Method for Finding Roots of Complex Polynomials: Complex 
 Dynamics Between Combinatorics and Numerical Analysis - Dierk Schleicher (
 Jacobs University\, Bremen)
DTSTART:20100128T143000Z
DTEND:20100128T153000Z
UID:TALK21928@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:We shall discuss Newton's root-finding method for the case of 
 complex polynomials in a single variable. This method has been known to ap
 proximate roots extremely efficiently\, once good approximate solutions ar
 e known\, but its global properties are known to be difficult to\ndescribe
 . We shall discuss recent results towards turning Newton's method into an 
 efficient algorithm for finding all roots of given complex polynomials\, a
 nd give a classification of all "bad cases" in combinatorial\nterms using 
 "Newton graphs". This also answers a question raised by Smale.\n
LOCATION:MR12
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