Approximating singular solutions of polynomial systems

Wednesday, September 27, 2006 - 11:15am - 12:15pm
Lind 305
Anton Leykin (University of Minnesota, Twin Cities)
In the assumption of regularity, the existing tools of numerical algebraic geometry provide an effective way to deal with solution sets of systems of polynomials both 0- and positive-dimensional. Should a solution be singular, Newton's method involved in tracking the corresponding homotopy continuation path loses its quadratic convergence.

This talk concerns a symbolic-numerical method called deflation that restores this convergence by considering an augmented system in more variables. Time permitting, we will discuss the higher-order deflation related to the topic of computation of the multiplicities of singular solution component