Speedup Versus Efficiency in Parallel Systems
IEEE Transactions on Computers
Design issues in high performance floating point arithmetic units
Design issues in high performance floating point arithmetic units
A parallel algorithm for Lagrange interpolation on the star graph
Journal of Parallel and Distributed Computing
Analysis of Asynchronous Polynomial Root Finding Methods on a Distributed Memory Multicomputer
IEEE Transactions on Parallel and Distributed Systems
Iterative Algorithms on Heterogeneous Network Computing: Parallel Polynomial Root Extracting
HiPC '02 Proceedings of the 9th International Conference on High Performance Computing
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In this paper, a parallel algorithm for computing the roots of a given polynomial of degree n on a ring of processors is proposed. The algorithm implements Durand-Kerner's method and consists of two phases: initialization, and iteration. In the initialization phase all the necessary preparation steps are realized to start the parallel computation. It includes register initialization and initial approximation of roots requiring 3n-2 communications, 2 exponentiation, one multiplications, 6 divisions, and 4n-3 additions. In the iteration phase, these initial approximated roots are corrected repeatedly and converge to their accurate values. The iteration phase is composed of some iteration steps, each consisting of 3n communications, 4n+3 additions, 3n+1 multiplications, and one division.