Finding all real solutions contained in a complex algebraic curve

Wednesday, September 20, 2006 - 9:30am - 10:20am
EE/CS 3-180
Charles Wampler (General Motors Corporation)
Using the methods of numerical algebraic geometry, one can compute a
numerical irreducible decomposition of the solution set of polynomial
systems. This decomposition describes the enitre solution set and
its breakup into irreducible pieces over complex Euclidean space.
However, in engineering or science, it is common that only the real
solutions are of interest. A single complex component may contain
multiple real components, some possibly having lower dimension in the
reals than the dimension of the complex component that contains them.
We present an algorithm for finding all real solutions inside the
pure-one-dimensional complex solution set of a polynomial system.
The algorithm finds a numerical approximation to all isolated real
solutions and a description of all real curves in a Morse-like
representation consisting of vertices with edges connecting them.

The work presented in this talk has been done in collaboration with
Ye Lu, Daniel Bates, and Andrew Sommese.
MSC Code: