Home → Magazine Archive → September 1980 (Vol. 23, No. 9) → An overrelaxation for a numerical inverse of a constant → Abstract

An overrelaxation for a numerical inverse of a constant

By Hitohisa Asai

Communications of the ACM, Vol. 23 No. 9, Pages 503-510
10.1145/359007.359011


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When division is performed by a power series implementation with additions, subtractions, digit shifts, and multiplications, the convergence rate of the power series is important in practical application. Particularly if the rate of the power series is close to one, the convergence is slow and therefore a special method to accelerate the convergence is needed. Without such an acceleration, the power series implementation is less attractive. An acceleration method is proposed for the slow convergence rate. First, the worst case convergence rate of the power series is determined for a given appropriate acceleration factor. Next, a simple way to choose the appropriate acceleration factor is presented.

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