Sterbenz, P. H
Authors:
I. F. Ganžela and C. T. Fike
Journal:
Math. Comp. 23 (1969), 313318
MSC:
Primary 65.50
MathSciNet review:
0245199
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Abstract: Various writers have dealt with the subject of optimal starting approximations for squareroot 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. 274276.
 [3]
W. J. Cody, ``Doubleprecision square root for the CDC3600,'' Comm. ACM, v. 7, 1964, pp. 715718.
 [4]
C. T. Fike, ``Starting approximations for squareroot calculation on IBM System/360,'' Comm. ACM, v. 9, 1966, pp. 297299.
 [5]
D. G. Mouksund, ``Optimal starting values for NewtonRaphson calculation of ,'' Comm. ACM, v. 10, 1967, pp. 430432.
 [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
(44 #2333)
 [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. 683684.
 [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. 274276.
 [3]
 W. J. Cody, ``Doubleprecision square root for the CDC3600,'' Comm. ACM, v. 7, 1964, pp. 715718.
 [4]
 C. T. Fike, ``Starting approximations for squareroot calculation on IBM System/360,'' Comm. ACM, v. 9, 1966, pp. 297299.
 [5]
 D. G. Mouksund, ``Optimal starting values for NewtonRaphson calculation of ,'' Comm. ACM, v. 10, 1967, pp. 430432.
 [6]
 R. F. King & D. L. Phillips, ``The logarithmic error and Newton's method for the square root,'' Comm. ACM, v. 12, 1969, pp. 8788. MR 0285109 (44:2333)
 [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. 683684.
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DOI:
http://dx.doi.org/10.1090/S00255718196902451996
PII:
S 00255718(1969)02451996
Article copyright:
© Copyright 1969
American Mathematical Society
