Methods for Certifying Solutions to Square Systems with D-finite Functions

Student Algebraic Geometry Seminar
Friday, March 16, 2018 - 10:00am
1 hour (actually 50 minutes)
Skiles 006
Georgia Tech

Expanding the topic we discussed on last week, we consider the way to certify roots for system of equations with D-finite functions. In order to do this, we will first introduce the notion of D-finite functions, and observe the property of them. We also suggest two different ways to certify this, that is, alpha-theory and the Krawczyk method. We use the concept of majorant series for D-finite functions to apply above two methods for certification. After considering concepts about alpha-theory and the Krawczyk method, we finish the talk with suggesting some open problems about these.