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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?)

  • [1] H. J. Maehly, Approximations for the CDC 1604, Control Data Corp., 1960.
  • [2] J. Eve, ``Starting approximations for the iterative calculation of square roots,'' Comput. J., v. 6, 1963, pp. 274-276.
  • [3] W. J. Cody, ``Double-precision square root for the CDC-3600,'' Comm. ACM, v. 7, 1964, pp. 715-718.
  • [4] C. T. Fike, ``Starting approximations for square-root calculation on IBM System/360,'' Comm. ACM, v. 9, 1966, pp. 297-299.
  • [5] D. G. Mouksund, ``Optimal starting values for Newton-Raphson calculation of $ \surd x$,'' Comm. ACM, v. 10, 1967, pp. 430-432.
  • [6] 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,
  • [7] N. I. Achieseh, Theory of Approximation, OGIZ, Moscow, 1947; English transl., Ungar, New York, 1956. MR 10, 33; MR 20 #1872.
  • [8] 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

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