Some Properties of Iterative Square-Rooting Methods Using High-Speed Multiplication

With the increasing availability of high-speed multiplication units in large computers it is attractive to develop an iterative procedure to compute division and square root, using multiplication as the primary operation. In this paper, we present three new methods of performing square rooting rapidly which utilize multiplication and no division. Each algorithm is considered for convergence rate, efficiency, and implementation. The most typical and efficient one of the already-known algorithms which utilizes multiplication, here called the N algorithm, is introduced for the purpose of comparison with the new algorithms. The effect and importance of the initial approximation is considered. (One of the algorithms, here called the G algorithm, is described in detail with the emphasis on its high efficiency.)