Visualization of Homotopy's and their Properties
Paul Vrbik, University of Western Ontario.
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!