Hybrid Symbolic-Numeric Methods for the Solution of Polynomial Systems [Tutorial Overview]

In this tutorial we will focus on the solution of polynomial systems given with inexact coefficients using hybrid symbolic-numeric methods. In particular, we will concentrate on systems that are over-constrained or have roots with multiplicities. These systems are considered ill-posed or ill-conditioned by traditional numerical methods and they try to avoid them. On the other hand, traditional symbolic methods are not designed to handle inexactness. Ill-conditioned polynomial equation systems arise very frequently in many important applications areas such as geometric modeling, computer vision, fluid dynamics, etc.