Quality Up in Polynomial Homotopy Continuation
by Multithreaded Path Tracking
Jan Verschelde and
Genady Yoffe
Abstract:
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 solution will be computed
using many cores. In this paper we describe our multithreaded
implementation to track one solution path defined by a polynomial homotopy.
Limiting quality to accuracy and confusing accuracy with precision,
we strive to offset the cost of multiprecision arithmetic running
multithreaded code on many cores.