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Parallel polynomial root extraction on a ring of processors

Sarbazi Azad, H ; Sharif University of Technology | 2005

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  1. Type of Document: Article
  2. DOI: 10.1109/IPDPS.2005.328
  3. Publisher: 2005
  4. Abstract:
  5. 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: 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
  6. Keywords:
  7. Approximated roots ; Durand-Kerner's method ; Parallel polynomials ; Root extraction ; Approximation theory ; Data mining ; Iterative methods ; Parallel algorithms ; Polynomials ; Program processors ; Parallel processing systems
  8. Source: 19th IEEE International Parallel and Distributed Processing Symposium, IPDPS 2005, Denver, CO, 4 April 2005 through 8 April 2005 ; Volume 2005 , 2005 ; 0769523129 (ISBN); 0769523129 (ISBN); 9780769523125 (ISBN)
  9. URL: https://ieeexplore.ieee.org/document/1420234