Title: Decomposing solution sets of polynomial systems: a new parallel monodromy breakup algorithm

Authors: Anton Leykin, Jan Verschelde

Addresses: Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 South Morgan (M/C 249), Chicago, IL 60607-7045, USA. ' Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 South Morgan (M/C 249), Chicago, IL 60607-7045, USA

Abstract: Our problem is to decompose a positive dimensional solution set of a polynomial system into irreducible components. This solution set is represented by a witness set, which can be partitioned into irreducible subsets according to the action of monodromy. Our straightforward parallel version of the original monodromy breakup algorithm suffers from synchronisation issues. The new approach not only resolves these issues, but also, according to accumulated statistics, reduces the expected number of homotopy continuation paths tracked. The latter property gives a faster serial algorithm.

Keywords: homotopy; irreducible components; linear trace; monodromy; numerical algebraic geometry; parallel path tracking; polynomial systems.

DOI: 10.1504/IJCSE.2009.027001

International Journal of Computational Science and Engineering, 2009 Vol.4 No.2, pp.94 - 101

Published online: 12 Jul 2009 *

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