- Published 2012

Today, most computer algebra systems offer efficient solvers for computing the complex solutions of polynomial systems. Some of them, such as Maple, provide tools for “identifying” which of those solutions are real. These tools support many applications in areas like robotics, program verification, and dynamical system analysis, to name a few. In this thesis, we investigate parallel algorithms for isolating the real roots of univariate equations with rational number coefficients. This type of calculation is fundamental to the computation of the real solutions of polynomial systems. Our objective is to improve performance of real root isolation on multicore processors in terms of parallelism and cache complexity, such that harder problems can be tackled on these architectures. On multicores, the parallelization of real root isolation reduces to that of Taylor shift computations, which generalize the Pascal Triangle construction. With respect to previous works, we provide a more realistic analysis (in terms of work, span, burdened span, cache complexity) of the parallelization of this method. This leads us to develop poly-algorithms which can adapt the granularity of their parallelism dynamically depending on the local amount of work. Experimentation illustrates the effectiveness of this approach.

@inproceedings{Haque2012MultiT,
title={Multi - threaded real root isolation on multi - core architectures ( Spine title : Real Root Isolation for Polynomial System},
author={Zunaid Haque and Robert E. Mercer},
year={2012}
}