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 …

Systems of polynomial equations are a common occurrence in problem formulations in
engineering, science, and mathematics. Solution sets of such systems, ie, algebraic sets, are …

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 …

Though numerical methods to find all the isolated solutions of nonlinear systems of
multivariate polynomials go back 30 years, it is only over the last decade that numerical …

Solving polynomial systems by homotopy continuation methods Page 29 18 Computer
Mathematics Proc. of the Special Program at Nankai Institute of Mathematics January 1991-June …

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 …

In engineering and applied mathematics, polynomial systems arise whose solution sets
contain components of different dimensions and multiplicities. In this article we present …

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

We present a new probabilistic method for solving systems of polynomial equations and
inequations. Our algorithm computes the equidimensional decomposition of the Zariski …

Given a polynomial system f, a fundamental question is to determine if f has real roots. Many
algorithms involving the use of infinitesimal deformations have been proposed to answer …