Seminar series
Date
Tue, 16 Jun 2015
Time
14:30 -
15:00
Location
L3
Speaker
Alex Townsend
Organisation
MIT
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.
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.