Are resultant methods numerically unstable for multidimensional rootfinding

16 June 2015
14:30
Alex Townsend
Abstract
A popular class of algorithms for global multidimensional rootfinding are hidden-variable resultant methods. In two dimensions, when significant care is taken, 
they are competitive practical rootfinders.  However, in higher dimensions they are known to be notoriously difficult, if not impossible, to make numerically robust.  We will show that the most popular variant based on the Cayley resultant is inherently and spectacularly numerically unstable by a factor that grows exponentially with the dimension. Disastrous. Yet, perhaps, it can be circumnavigated. 
  • Numerical Analysis Group Internal Seminar