Symbolic Computation Group
David R. Cheriton School of Computer Science


Friday, October 9, 2009, at Maplesoft.
Abstract:
In the last two decades, the homotopy continuation method has been
established in the U.S. for finding the full set of isolated solutions to a
polynomial system numerically. The method involves first solving a trivial
system, and then deforming these solutions along smooth paths to the
solutions of the target system. Recently, modeling the sparse structure of a
polynomial system by its Newton polytopes leads to a major computational
breakthrough in solving polynomial systems by the homotopy continuation
methods. Based on an elegant formula for computing the mixed volume, the new
polyhedral homotopy can find all isolated zeros of a polynomial system by
following much fewer solution paths. The method has been successfully
implemented and proved to be very powerful in many occasions, especially
when the systems are sparse. In this talk we will elaborate the polyhedral
homotopy continuation method and its resulting code HOM4PS2.0 which leads
the existing codes PHC and PHoM for the same purpose by a big margin in
speed.

Last modified on Sunday, 04 November 2012, at 20:42 hours.