1 research outputs found
Decomposing Solution Sets of Polynomial Systems: A New Parallel Monodromy Breakup Algorithm
We consider the numerical irreducible decomposition of a positive dimensional
solution set of a polynomial system into irreducible factors. Path tracking
techniques computing loops around singularities connect points on the same
irreducible components. The computation of a linear trace for each factor
certifies the decomposition. This factorization method exhibits a good
practical performance on solution sets of relative high degrees.
Using the same concepts of monodromy and linear trace, we present a new
monodromy breakup algorithm. It shows a better performance than the old method
which requires construction of permutations of witness points in order to break
up the solution set. In contrast, the new algorithm assumes a finer approach
allowing us to avoid tracking unnecessary homotopy paths.
As we designed the serial algorithm keeping in mind distributed computing, an
additional advantage is that its parallel version can be easily built.
Synchronization issues resulted in a performance loss of the straightforward
parallel version of the old algorithm. Our parallel implementation of the new
approach bypasses these issues, therefore, exhibiting a better performance,
especially on solution sets of larger degree.Comment: 15 page