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» Homogeneous Decomposition of Polynomials
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ISSAC
2007
Springer
177views Mathematics» more  ISSAC 2007»
16 years 14 hour 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
CORR
2007
Springer
105views Education» more  CORR 2007»
15 years 5 months ago
Relative-Error CUR Matrix Decompositions
Many data analysis applications deal with large matrices and involve approximating the matrix using a small number of “components.” Typically, these components are linear combi...
Petros Drineas, Michael W. Mahoney, S. Muthukrishn...
LICS
2010
IEEE
15 years 3 months ago
Fixed-Point Definability and Polynomial Time on Graphs with Excluded Minors
We prove that fixed-point logic with counting captures polynomial time on all classes of graphs with excluded minors. That is, for every class C of graphs such that some graph H is...
Martin Grohe
ISSAC
2009
Springer
169views Mathematics» more  ISSAC 2009»
16 years 13 days ago
Computations modulo regular chains
The computation of triangular decompositions involves two fundamental operations: polynomial GCDs modulo regular chains and regularity test modulo saturated ideals. We propose new...
Xin Li, Marc Moreno Maza, Wei Pan
ICPPW
2005
IEEE
15 years 11 months ago
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,...
Anton Leykin, Jan Verschelde