by Andrew J Sommese (University of Notre Dame du Lac, USA) & Charles W Wampler (General Motors Research & Development, USA)

Table of Contents (193k)
Preface (197k)
Chapter 1: Polynomial Systems (414k)

Written by the founders of the new and expanding field of numerical algebraic geometry, this is the first book that uses an algebraic-geometric approach to the numerical solution of polynomial systems and also the first one to treat numerical methods for finding positive dimensional solution sets. The text covers the full theory from methods developed for isolated solutions in the 1980's to the most recent research on positive dimensional sets.

• Background:
  • Polynomial Systems
  • Homotopy Continuation
  • Projective Spaces
  • Genericity and Probability One
  • Polynomials of One Variable
  • Other Methods
• Isolated Solutions:
  • Coefficient-Parameter Homotopy
  • Polynomial Structures
  • Case Studies
  • Endpoint Estimation
  • Checking Results and Other Implementation Tips
• Positive Dimensional Solutions:
  • Basic Algebraic Geometry
  • Basic Numerical Algebraic Geometry
  • A Cascade Algorithm for Witness Supersets
  • The Numerical Irreducible Decomposition
  • The Intersection of Algebraic Sets
• Appendices:
  • Algebraic Geometry
  • Software for Polynomial Continuation
  • HomLab User's Guide