OPTIMAL INITIAL APPROXIMATIONS FOR THE NEWTON-RAPHSON DIVISION ALGORITHM

Newton-Raphson iteration provides a high-speed method for performing d ivision. The Newton-Raphson division algorithm begins with an initial approximation to the reciprocal of the divisor. This value is iterativ ely refined until a specified accuracy is achieved. In this paper, we develop methods for selecting constant and linear approximations which minimize the maximum absolute error of the final result. These approx imations are compared with previous methods which minimize the maximum relative error in the final result or the maximum absolute error in t he initial value.