Optimal starting values for Newton-Raphson calculation of x1 2
Communications of the ACM
Double-precision square root for the CDC-3600
Communications of the ACM
Proceedings of the 1999 ACM symposium on Applied computing
A note on best one-sided approximations
Communications of the ACM
Optimal starting approximations for generating square root for slow or no divide
Communications of the ACM
Communications of the ACM
Evaluation of the square root function on microprocessors
ACM '76 Proceedings of the 1976 annual conference
Establishing lower bounds on algorithms: a survey
AFIPS '72 (Spring) Proceedings of the May 16-18, 1972, spring joint computer conference
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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 inital 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.