On Current Methods for Certifying System of Equations

Student Algebraic Geometry Seminar
Friday, March 9, 2018 - 10:00
1 hour (actually 50 minutes)
Skiles 006
Georgia Tech
This is an intoductory talk for the currently using methods for certifying roots for system of equations. First we discuss about alpha-theory which was constructed by Smale and Shub, and explain how this theory could be modified in order to apply in actual problems. In this step, we point out that alpha theory is still restricted only into polynomial systems and polynomial-exponential systems. After that as a remedy for this problem, we will introduce an interval arithmetic, and the Krawczyk method. We will end the talk with a discussion about how these current methods could be used in more general setting.