HOM4PS-2.0para: Parallelization of HOM4PS-2.0 for solving polynomial systems
Parallel Computing
Polynomial homotopies on multicore workstations
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
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Homotopy continuation methods to compute numerical approximations to all isolated solutions of a polynomial system are known as "pleasingly parallel", i.e.: because of their low communication overhead, these methods scale very well for a large number of processors. Because so many important problems remain unsolved mainly due to their intrinsic computational complexity, it would be embarrassing not to develop parallel implementations of polynomial homotopy continuation methods."Parallel PHCpack", is a project which started a couple of years ago developed by my advisor Jan Verschelde and his student Yusong Wang (parallel pieri homotopy), and which continues with Anton Leykin (parallel irreducible decomposition).The focus of this thesis is the development of "parallel PHCpack". For sparse polynomial systems, polyhedral methods give efficient homotopy algorithms. The polyhedral homotopy methods run in three stages: (1) compute the mixed volume; (2) solve a random coefficient start system; (3) track solution paths to solve the target system.