Computing feedback laws for linear systems with a parallel pieri homotopy
Jan Verschelde, Yusong Wang · 2004
Homotopy methods to solve polynomial systems are well suited for parallel computing because the solution paths de-fined by the homotopy can be tracked independently. Both the static and dynamic load balancing models are imple-mented in C with MPI, adapting PHCpack written in Ada using gcc, and tested on academic benchmarks and me-chanical 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 homo-topies grow incrementally from the root to the leaves in the tree, we found the Pieri homotopies well suited for parallel computing.