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 occur in a wide variety of application domains. Homotopy continuation
methods are reliable and powerful methods to compute numerically approximations to all …

Given a finitely generated algebra A, it is a fundamental question whether A has a full rank
discrete (Krull) valuation v with finitely generated value semigroup. We give a necessary and …

The subject of this book is the solution of polynomial equations, that is, systems of
(generally) non-linear algebraic equations. This study is at the heart of several areas of …

We study vector space interference alignment for the multiple-input multiple-output
interference channel with no time or frequency diversity, and no symbol extensions. We …

Understanding, finding, or even deciding on the existence of real solutions to a system of
equations is a difficult problem with many applications outside of mathematics. While it is …

We describe a geometric Littlewood-Richardson rule, interpreted as deforming the
intersection of two Schubert varieties into the union of Schubert varieties. There are no …

Numerical nonlinear algebra is a computational paradigm that uses numerical analysis to
study polynomial equations. Its origins were methods to solve systems of polynomial …

The positive steady states of chemical reaction systems modeled by mass action kinetics are
investigated. This sparse polynomial system is given by a weighted directed graph and a …

We develop a new eigenvalue method for solving structured polynomial equations over any
field. The equations are defined on a projective algebraic variety which admits a rational …