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| Paper IPM / Computer Science / 11110 |
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| Abstract: | |
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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-Kerners 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.
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