145
reads

Tsung-Lin Lee

2010-03-25
13:30:00 - 14:20:00

Solving polynomial systems by homotopy continuation method

405 , Mathematics Research Center Building (ori. New Math. Bldg.)

While the classical linear homotopy continuation method was developed for solving polynomial systems in 1980's, the polyhedral homotopies were established in 1995, which yields a drastic improvement over the classical linear homotopies. HOM4PS-2.0 is a software package which implements the polyhedral homotopy continuation method for solving polynomial systems. With several sophisticatedly designed algorithms in mixed cell computation and curve tracing, it surpasses the existing packages in finding all isolated zeros of polynomial systems, such as PHCpack, PHoM, and Bertini, in speed by big margins. The marvelous efficiency of HOM4PS-2.0 makes it possible now to solve some very large systems that can not be solved before, such as 5-body problem.