Sommese A.J., Wampler C.W. (II.) The Numerical Solution of Systems of Polynomials Arising in Engineering and Science

World Scientific, 2005. — 425 p.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.Preface
Conventions
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
Appendix A. Algebraic Geometry
Appendix B. Software for Polynomial Continuation
Appendix C. HomLab User's Guide
Bibliography
Index