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ISSAC
2007
Springer
99views Mathematics» more  ISSAC 2007»
13 years 11 months ago
Computing monodromy via parallel homotopy continuation
Numerical homotopy continuation gives a powerful tool for the applied scientist who seeks solutions to a system of polynomial equations. Techniques from numerical homotopy continu...
Anton Leykin, Frank Sottile
ISSAC
2007
Springer
177views Mathematics» more  ISSAC 2007»
13 years 11 months ago
Component-level parallelization of triangular decompositions
We discuss the parallelization of algorithms for solving polynomial systems symbolically by way of triangular decompositions. We introduce a component-level parallelism for which ...
Marc Moreno Maza, Yuzhen Xie
SMA
2010
ACM
164views Solid Modeling» more  SMA 2010»
13 years 5 months ago
Topologically guaranteed univariate solutions of underconstrained polynomial systems via no-loop and single-component tests
We present an algorithm which robustly computes the intersection curve(s) of an under-constrained piecewise polynomial system consisting of n equations with n + 1 unknowns. The so...
Michael Barton, Gershon Elber, Iddo Hanniel
JSC
2006
102views more  JSC 2006»
13 years 5 months ago
Counting and locating the solutions of polynomial systems of maximum likelihood equations, I
In statistics, mixture models consisting of several component subpopulations are used widely to model data drawn from heterogeneous sources. In this paper, we consider maximum lik...
Max-Louis G. Buot, Donald St. P. Richards
COMPUTING
2006
127views more  COMPUTING 2006»
13 years 5 months ago
PHoMpara - Parallel Implementation of the Polyhedral Homotopy Continuation Method for Polynomial Systems
The polyhedral homotopy continuation method is known to be a successful method for finding all isolated solutions of a system of polynomial equations. PHoM, an implementation of t...
T. Gunji, S. Kim, K. Fujisawa, M. Kojima