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Speedup measures how much faster we can solve the same problem using manycores. If we can afford to keep the execution time fixed, then quality upmeasures how much better the solution will be computed using many cores. Inthis paper we describe our multithreaded implementation to track one solutionpath defined by a polynomial homotopy. Limiting quality to accuracy andconfusing accuracy with precision, we strive to offset the cost ofmultiprecision arithmetic running multithreaded code on many cores.

Quality Up in Polynomial Homotopy Continuation by Multithreaded Path Tracking