Agnes Szanto - Certification of Isolated Roots of Overdetermined and Singular Polynomial Systems, and their Multiplicity Structure
11 April 2018 –
Certification of Isolated Roots of Overdetermined and Singular Polynomial Systems, and their Multiplicity Structure
Agnes Szanto (North Carolina State University, Raleigh, USA)
This talk is concerned with certifying that a given point is near an exact root of an overdetermined or singular polynomial system with rational coefficients. The difficulty lies in the fact that consistency of overdetermined systems is not a continuous property. Our certification is based on hybrid symbolic-numeric methods. In the first part of the talk we describe an algorithm to certify approximate roots of exact overdetermined systems over Q, and analyze its bit complexity. In the second part of the talk we certify points near exact singular roots, using new improved versions of the so called isosingular deflation method. Moreover, we also give a new algorithm that computes and certifies the multiplicity structure of the exact root near our given point. This is a joint work with Tulay Akoglu, Jonathan Hauenstein and Bernard Mourrain.