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cs.DC2014★ 1 cited
GPU acceleration of Newton's method for large systems of polynomial equations in double double and quad double arithmetic
Jan Verschelde, Xiangcheng Yu
In order to compensate for the higher cost of double double and quad double arithmetic when solving large polynomial systems, we investigate the application of NVIDIA Tesla K20C ge…
cs.DC2011★ 4 cited
Quality Up in Polynomial Homotopy Continuation by Multithreaded Path Tracking
Jan Verschelde, Genady Yoffe
Speedup measures how much faster we can solve the same problem using many cores. If we can afford to keep the execution time fixed, then quality up measures how much better the sol…
cs.DC2005
Decomposing Solution Sets of Polynomial Systems: A New Parallel Monodromy Breakup Algorithm
Anton Leykin, Jan Verschelde
We consider the numerical irreducible decomposition of a positive dimensional solution set of a polynomial system into irreducible factors. Path tracking techniques computing loops…