Homotopy continuation methods to solve polynomial systems scale very well on parallel machines. We examine its parallel implementation on multiprocessor multicore workstations using threads. With more cores we speed up pleasingly parallel path tracking jobs. In addition, we compute solutions more accurately in about the same amount of time with threads, and thus achieve quality up. Focusing on polynomial evaluation and linear system solving (key ingredients of Newton's method) we can double the accuracy of the results with the quad doubles of QD-2.3.9 in less than double the time, if all available eight cores are used.
['Jan Verschelde', 'Genady Yoffe']
Polynomial homotopies on multicore workstations