Interconnection networks for large-scale parallel processing: theory and case studies
Interconnection networks for large-scale parallel processing: theory and case studies
Introduction to numerical analysis: 2nd edition
Introduction to numerical analysis: 2nd edition
Resultant Procedure and the Mechanization of the Graeffe Process
Journal of the ACM (JACM)
Algorithm 493: Zeros of a Real Polynomial [C2]
ACM Transactions on Mathematical Software (TOMS)
Parallel numerical methods for the solution of equations
Communications of the ACM
Analysis of Asynchronous Polynomial Root Finding Methods on a Distributed Memory Multicomputer
IEEE Transactions on Parallel and Distributed Systems
Family of simultaneous methods of Hansen-Patrick's type
Applied Numerical Mathematics
Polynomial interpolation and polynomial root finding on OTIS-mesh
Parallel Computing
A posteriori error bound methods for the inclusion of polynomial zeros
Journal of Computational and Applied Mathematics
Parallel algorithms for finding polynomial Roots on OTIS-torus
The Journal of Supercomputing
| Hi-index | 14.98 |
A parallel algorithm for extracting the roots of a polynomial is presented. The algorithm is based on Graeffe's method, which is rarely used in serial implementations, because it is slower than many common serial algorithms, but is particularly well suited to parallel implementation. Graeffe's method is an iterative technique, and parallelism is used to reduce the execution time per iteration. A high degree of parallelism is possible, and only simple interprocessor communication is required. For a degree-n polynomial executed on an (n+1)-processor SIMD machine, each iteration in the parallel algorithm has arithmetic complexity of approximately 2n and a communications overhead n. In general, arithmetic speedup is on the order of p/2 for a p-processor implementation.