The generation of square roots on a computer with rapid multiplication compared with division

Abstract

The number of iterations of (1.1) necessary to achieve a prescribed accuracy will depend on the closeness of the initial approximation used and as the range of A is decreased, increasingly accurate initial approximations become possible. A way of reducing the infinite range (0, oo ) of A to a convenient finite interval consists in expressing A in the form a2e, l S a < 1, and using A2 = a'122b. Still more accurate initial approximations are possible if the reduced range is itself split up.