New Book on Numerical Algebraic Geometry
Dr. Dan Bates recently co-authored a new book, released by SIAM in November 2013
and titled Numerically Solving Polynomial Systems with Bertini. Bates' co-authors
include Jon Hauenstein (NC State), Andrew Sommese (Notre Dame), and Charles
Wampler (General Motors). The book is aimed at scientists and engineers, from late
undergraduates through full-time researchers, who need to solve polynomial systems in
various application areas. The methods of the book are rooted in the continuation
methods studied by Allgower and Georg here at CSU.
The book has two goals: to introduce the reader to both the basics and the latest
advances in the numerical solution of polynomial systems, and to serve as a user's
manual for the Bertini software package (developed by the authors of the book). The
book is broken into three sections, with a gentle introduction to finding isolated
solutions, a more technical introduction to finding positive-dimensional solution sets,
and synopses of several of the latest results and applications. There are numerous
examples throughout the book, and the several appendices form a complete guide to
Bertini.