Mechanisms and Robot Kinematics: Numerical Algebraic Geometry

Saturday, September 16, 2006 - 1:30pm - 2:20pm
EE/CS 3-180
Charles Wampler (General Motors Company)
This talk will discuss how numerical polynomial continuation can be
used to solve the problems formulated in the first lecture. In doing
so, we will describe the basic constructs and algorithms of Numerical
Algebraic Geometry. Foremost among these is the notion of a witness
set, a numerical approximation to a linear section of an algebraic
set. We will describe how witness sets are computed, how they are
used in finding numerical irreducible decompositions, and how the
witness set for the intersection of two algebraic sets, say A and B,
can be found from the witness sets for A and B, via a diagonal
homotopy. Some recent avenues of research, such as how to find the
real solutions inside a complex curve, will be mentioned briefly.

Suggested reading: A.J. Sommese and C.W. Wampler, The numerical
solution of systems of polynomials arising in engineering and science,
World Scientific, 2005.