A highly parallel algorithm for root extraction

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