Visualization of Homotopy's and their Properties

Paul Vrbik, University of Western Ontario.

Monday June 1st, 2:30pm, in K9509.

Abstract: 

Much attention has been given to the development of local methods for  
polynomial system solving. However, less work has been done on the  
study of globally convergent methods. We investigate the behavior of  
one such method: homotopy continuation.  That method applies a  
succession of Newton's and an Euler's approximations to travel along a  
path connecting roots of a "easy" system to those of an "hard" one. By  
plotting these paths and corresponding basins of attraction on Riemann  
spheres we get insight into the behavior of this method when  
convergence is not achieved.

A note from the speaker:
I will be using no mathematics beyond basic vector calculus. I hope  
this acts as some additional incentive to come see this talk!