# 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.

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.