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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Sterbenz, P. H

Authors: I. F. Ganžela and C. T. Fike
Journal: Math. Comp. 23 (1969), 313-318
MSC: Primary 65.50
MathSciNet review: 0245199
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Abstract: Various writers have dealt with the subject of optimal starting approximations for square-root calculation by Newton’s method. Three optimality criteria that have been used can be shown to lead to closely related approximations. This fact makes it surprisingly easy to choose a starting approximation of some prescribed form so that the maximum relative error after any number of Newton iterations is as small as possible.

References [Enhancements On Off] (What's this?)

    H. J. Maehly, Approximations for the CDC 1604, Control Data Corp., 1960. J. Eve, “Starting approximations for the iterative calculation of square roots,” Comput. J., v. 6, 1963, pp. 274–276. W. J. Cody, “Double-precision square root for the CDC-3600,” Comm. ACM, v. 7, 1964, pp. 715–718. C. T. Fike, “Starting approximations for square-root calculation on IBM System/360,” Comm. ACM, v. 9, 1966, pp. 297–299. D. G. Mouksund, “Optimal starting values for Newton-Raphson calculation of $\surd x$,” Comm. ACM, v. 10, 1967, pp. 430–432.
  • Richard F. King and David L. Phillips, The logarithmic error and Newton’s method for the square root, Comm. ACM 12 (1969), 87–88. MR 0285109, DOI
  • N. I. Achieseh, Theory of Approximation, OGIZ, Moscow, 1947; English transl., Ungar, New York, 1956. MR 10, 33; MR 20 #1872. C. T. Fike, “Letter to the editor,” Comm. ACM, v. 10, 1967, pp. 683–684.

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Article copyright: © Copyright 1969 American Mathematical Society