Certified numerical polynomial homotopy continuation

Series: 
Algebra Seminar
Monday, November 23, 2009 - 15:30
1 hour (actually 50 minutes)
Location: 
Skiles 255
,  
Georgia Tech
Organizer: 
This talk will start with an introduction to the area of numerical algebraic geometry. The homotopy continuation algorithms that it currently utilizes are based on heuristics: in general their results are not certified. Jointly with Carlos Beltran, using recent developments in theoretical complexity analysis of numerical computation, we have implemented a practical homotopy tracking algorithm that provides the status of a mathematical proof to its approximate numerical output.