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Parallel Iteration Methods

  • Shmuel Winograd
Part of the The IBM Research Symposia Series book series (IRSS)

Abstract

One of the problems which arise from the increasing use of multiprocessing is the efficient utilization of all the processors. If the solution of a problem requires T units of time when only one processor is used, it is hoped that using k processor will require only T/k units of time. Dorn (1962A) considered the problem of evaluating a polynomial, and showed that for k small compared with the degree n of the polynomial, a modification of Horner’s method requires about n/k additions and n/k multiplications. Munro and Paterson (1971A) proved that for any k and n, a bound on the number of operations required to evaluate an n degree polynomial is about 2n/k + log2k, and showed a method which approaches this bound. Thus, for polynomial evaluation, one can achieve a good utilization of all the processes when their number is much smaller than the degree of the polynomial.

Keywords

Iterative Method Iteration Step Iterative Scheme Degree Polynomial Iteration Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Press, New York 1972

Authors and Affiliations

  • Shmuel Winograd
    • 1
  1. 1.Mathematical Sciences DepartmentIBM Thomas J. Watson Research CenterYorktown HeightsUSA

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