Parallel Iteration Methods
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.
KeywordsIterative Method Iteration Step Iterative Scheme Degree Polynomial Iteration Scheme
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