Certified numerical polynomial homotopy continuation

Algebra Seminar
Monday, November 23, 2009 - 15:30
1 hour (actually 50 minutes)
Skiles 255
Georgia Tech
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.