A fast parallel algorithm for determining all roots of a polynomial with real roots
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Speedup Versus Efficiency in Parallel Systems
IEEE Transactions on Computers
Individual and simultaneous determination of the zeros of algebraic polynomials
Computational Mathematics and Mathematical Physics
Design issues in high performance floating point arithmetic units
Design issues in high performance floating point arithmetic units
Interconnection Networks: An Engineering Approach
Interconnection Networks: An Engineering Approach
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
Parallel Polynomial Root Extraction on A Ring of Processors
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 15 - Volume 16
Parallel algorithms for finding polynomial Roots on OTIS-torus
The Journal of Supercomputing
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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: initialisation, and iteration. In the initialisation phase all the necessary preparation steps are realised to start the parallel computation. It includes register initialisation and initial approximation of roots requiring 3n驴2 communications, 2 exponentiation, one multiplications, 6 divisions, and 4n驴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.