Factoring Solution Sets of Polynomial Systems in Parallel

We report on a £rst 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 modi£cations to the method which will also improve the serial version of the original algorithm. 2000 Mathematics Subject Classi£cation. Primary 65H10. Secondary 14Q99, 68W30. Key words and phrases. Linear trace, monodromy, numerical algebraic geometry, numerical homotopy algorithms, numerical irreducible decomposition, parallel computation, path following, polynomial systems.

• Type: Conference
• Year: 2005
• Where: ICPPW
• Authors: Anton Leykin, Jan Verschelde
• Keywords: Distributed And Parallel Computing, ICPPW 2005, Polynomial Systems, Solution Sets, £rst Parallel Implementation