Computing monodromy via parallel homotopy continuation
Proceedings of the 2007 international workshop on Parallel symbolic computation
Decomposing solution sets of polynomial systems: a new parallel monodromy breakup algorithm
International Journal of Computational Science and Engineering
Polynomial homotopies on multicore workstations
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Parallel homotopy algorithms to solve polynomial systems
ICMS'06 Proceedings of the Second international conference on Mathematical Software
Interfacing with the numerical homotopy algorithms in PHCpack
ICMS'06 Proceedings of the Second international conference on Mathematical Software
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We report on a first parallel implementation of a recent algorithm to factor positive dimensional solution sets of polynomial systems. As the algorithm uses homotopy continuation, we observe a good speedup of the path tracking jobs. However, for solution sets of high degree, the overhead of managing different homotopies and large lists of solutions exposes the limits of the master/servant parallel programming paradigm for this type of problem. A probabilistic complexity study suggests modifications to the method which will also improve the serial version of the original algorithm.