1932	 The Logarithmic Error and Newton s Method for the Square Root	 The problem of obtaining optimal starting values for the calculation of the square root using Newton s method is considered. It has been pointed out elsewhere that if relative error is used as the measure of goodness of fit optimal results are not obtained when the initial approximation is a best fit. It is shown here that if instead the so-called logarithmic error is used then a best initial fit is optimal for both types of error. Moreover use of the logarithmic error appears to simplify the problem of determining the optimal initial approximation. square root Newton s method relative error logarithmic error best fit optimal approximation maximal error recurrence relation integer root error curve
