Over the past fifteen years two new techniques have yielded extremely important
contributions toward the numerical solution of nonlinear systems of equations. This book …

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 …

This book was intended as an introduction to the topic of numerical continuation which
would be accessible to a readership of widely varying mathematical backgrounds. Realizing …

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 …

This is an introduction to “polynomial continuation,” which is used to compute the solutions
to systems of polynomial equations. The book shows how to solve practical problems but …

This paper proposes a new perspective for solving systems of complex nonlinear equations
by simply viewing them as a multiobjective optimization problem. Every equation in the …

This paper presents\tt Newton, a branch and prune algorithm used to find all isolated
solutions of a system of polynomial constraints.\tt Newton can be characterized as a global …

Let P (x)= 0 be a system of n polynomial equations in n unknowns. Denoting P=(p1,…, pn),
we want to find all isolated solutions offor x=(x1,…, xn). This problem is very common in …

Many science and engineering applications require the user to find solutions to systems of
nonlinear constraints or to optimize a nonlinear function subject to nonlinear constraints. The …