Solving Polynomial Systems using Numerical Homotopies

Abstract:

Because of its local quadratic convergence, Newton's method is often the preferred approach to numerically solve nonlinear problems. While Newton's method needs an initial guess, sufficient close to a solution, globally convergent solvers use homotopies and do not require the user to provide an initial guess for a solution. When the nonlinear system is polynomial, homotopy methods can find approximations for all isolated solutions. Examples will be given of mechanical design problems which lead to polynomial systems. Every real solution of such a polynomial system corresponds to one particular assembly of the mechanism. Parallel computers are used to solve large polynomial systems.

Graduate Colloquium at the University of Minnesota at Duluth, 9 November 2006

slides of the talk