Parallel algorithms for finding polynomial Roots on OTIS-torus

Abstract

We present two parallel algorithms for finding all the roots of an N-degree polynomial equation on an efficient model of Optoelectronic Transpose Interconnection System (OTIS), called OTIS-2D torus. The parallel algorithms are based on the iterative schemes of Durand---Kerner and Ehrlich methods. We show that the algorithm for the Durand---Kerner method requires (N 0.75+0.5N 0.25?1) electronic moves + 2(N 0.5?1) OTIS moves using N processors. The parallel algorithm for Ehrlich method is shown to run in (N 0.75+0.5N 0.25?1) electronic moves + 2(N 0.5?1) OTIS moves with the same number of processors. The algorithms have lower AT cost than the algorithms presented in Jana (Parallel Comput 32:301---312, 2006). The scalability of the algorithms is also discussed.