Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1109/ICPPW.2005.31 | ICPP Workshops |
Keywords | Field | DocType |
solution set,high degree,numerical algebraic geometry,parallel implementation,. linear trace,numerical irreducible decomposition,monodromy,homotopy continuation,factoring solution sets,paral- lel computation,original algorithm,positive dimensional solution set,different homotopies,path following,polynomial systems,polynomial systems.,numerical homotopy al- gorithms,servant parallel programming paradigm,good speedup,recent algorithm,parallel computation,computational geometry,statistics,parallel algorithms,computer science,mathematics,polynomials,parallel programming,concurrent computing | Polynomial,Computer science,Parallel algorithm,Monodromy,Solution set,Probabilistic logic,Homotopy continuation,Factoring,Speedup,Distributed computing | Conference |
ISSN | ISBN | Citations |
1530-2016 | 0-7695-2381-1 | 10 |
PageRank | References | Authors |
0.62 | 15 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Anton Leykin | 1 | 173 | 18.99 |
| Jan Verschelde | 2 | 676 | 64.84 |