Kisun Lee, Numerical Certification and Certified Homotopy Tracking

A certified algorithm produces a solution and a certificate of correctness to a problem. Numerical certification studies certified algorithms for results obtained from numerical methods in algebraic geometry. In this talk, we discuss why numerical certification is needed in numerical algebraic geometry and introduce the Krawczyk homotopy as one of its methods. The Krawczyk homotopy exploits interval arithmetic to track the homotopy solution path without path jumping so that the correctness of its output is guaranteed. This is joint work with Timothy Duff.