  Polynomial systems occur in many areas of science and engineering. Unlike
general nonlinear systems, the algebraic structure enables to compute all
solutions of a polynomial system. We describe our massive parallel
predictor-corrector algorithms to track many solution paths of a polynomial
homotopy. The data parallelism that provides the speedups stems from the
evaluation and differentiation of the monomials in the same polynomial system
at different data points, which are the points on the solution paths.
Polynomial homotopies that have tens of thousands of solution paths can keep a
sufficiently large amount of threads occupied. Our accelerated code combines
the reverse mode of algorithmic differentiation with double double and quad
double precision to compute more accurate results faster.
