  Homotopy methods to solve polynomial systems are well suited for parallel
computing because the solution paths defined by the homotopy can be tracked
independently. Both the static and dynamic load balancing models are
implemented in C with MPI, adapting PHCpack written in Ada using gcc, and
tested on academic benchmarks and mechanical applications. We studied the
parallelization of Pieri homotopies to compute all feedback laws to control
linear systems. To distribute the workload, we mapped the poset onto a tree. As
the dimensions of the Pieri homotopies grow incrementally from the root to the
leaves in the tree, we found the Pieri homotopies well suited for parallel
computing.
