Parallel Polynomial Real Root Isolation

Traditional numerical methods for polynomial root computation are fast but they sometimes return wrong results. Algorithms from computer algebra, on the other hand, guarantee correctness but tend to require long computing times. The computing time can, however, be dramatically reduced if exact arithmetic is carefully replaced by floating point arithmetic and if, moreover, ways are found to employ parallel computation. We applied this dual strategy to an algorithm for real root computation that is based on Descartes’ rule of signs [5]. We obtained an efficient infallible method to compute real roots of polynomials with degrees in the thousands. Such computations are needed to solve certain problems in high-energy physics.