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. >

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