Optimal Absolute Error Starting Values for Newton-Raphson Calculation of Square Root

The problem of obtaining optimal starting values for the calculation of square root using Newton-Raphson's Method is considered. This paper presents the best starting values theory in order to optimize the maximum absolute error after a given number of iterations. Two different methods are shown, and a third, which can be considered as a mixture of the previous two, is briefly discussed. The approach combines analytical and numerical methodologies, which gives more interesting results on the main characteristics of the behavior of the absolute error for different initializations. A comparison table between the traditional optimal relative error results and the absolute error ones is provided.