Sterbenz, P. H

Authors:
I. F. Ganžela and C. T. Fike

Journal:
Math. Comp. **23** (1969), 313-318

MSC:
Primary 65.50

DOI:
https://doi.org/10.1090/S0025-5718-1969-0245199-6

MathSciNet review:
0245199

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Abstract | References | Similar Articles | Additional Information

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.

**[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 ,''*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**, https://doi.org/10.1145/362848.362861**[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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DOI:
https://doi.org/10.1090/S0025-5718-1969-0245199-6

Article copyright:
© Copyright 1969
American Mathematical Society