The numerical algebraic geometry of bottlenecks

Numerical Real Algebraic Geometry

Sottile’s lectures from the Oberwolfach Seminar “New trends in algorithms for real algebraic geometry”, November 23–28, 2009.

Numerical Algebraic Geometry

Numerical Algebraic Geometry and Algebraic Kinematics

In this article, the basic constructs of algebraic kinematics (links, joints, and mechanism spaces) are introduced. This provides a common schema for many kinds of problems that are of interest in kinematic studies. Once the problems are cast in this algebraic framework, they can be attacked by tools from algebraic geometry. In particular, we review the techniques of numerical algebraic geometr...

Introduction to Numerical Algebraic Geometry

In a 1996 paper, Andrew Sommese and Charles Wampler began developing a new area, “Numerical Algebraic Geometry”, which would bear the same relation to “Algebraic Geometry” that “Numerical Linear Algebra” bears to “Linear Algebra”. To approximate all isolated solutions of polynomial systems, numerical path following techniques have been proven reliable and efficient during the past two decades. ...

Numerical Algebraic Geometry for Macaulay2

Numerical algebraic geometry uses numerical data to describe algebraic varieties. It is based on numerical polynomial homotopy continuation, which is a technique alternative to the classical symbolic approaches of computational algebraic geometry. We present a package , whose primary purpose is to interlink the existing symbolic methods of Macaulay2 and the powerful engine of numerical approxim...