# 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.

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:

14F25

Keywords: