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 …

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 …

Smale's α-theory uses estimates related to the convergence of Newton's method to certify
that Newton iterations will converge quadratically to solutions to a square polynomial …

A standard question in real algebraic geometry is to compute the number of connected
components of a real algebraic variety in affine space. This manuscript provides algorithms …

This article introduces the concept of isosingular sets, which are irreducible algebraic
subsets of the set of solutions to a system of polynomial equations constructed by taking the …

Elimination is a basic algebraic operation which geometrically corresponds to projections.
This article describes using the numerical algebraic geometric concept of witness sets to …

Parameterized systems of polynomial equations arise in many applications in science and
engineering with the real solutions describing, for example, equilibria of a dynamical system …

We study the geometry underlying the difference between non-negative polynomials and
sums of squares (SOS). The hypersurfaces that discriminate these two cones for ternary …

Maximum likelihood estimation is a fundamental optimization problem in statistics. We study
this problem on manifolds of matrices with bounded rank. These represent mixtures of …

We introduce numerical algebraic geometry methods for computing lower bounds on the
reach, local feature size, and weak feature size of the real part of an equidimensional and …