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Starting approximations for square root calculation on IBM system /360
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Communications of the ACM archive
Volume 9 ,  Issue 4  (April 1966) table of contents
Pages: 297 - 299  
Year of Publication: 1966
ISSN:0001-0782
Author
C. T. Fike  IBM Systems Research Institute, New York, NY
Publisher
ACM  New York, NY, USA
Bibliometrics
Downloads (6 Weeks): 6,   Downloads (12 Months): 23,   Citation Count: 7
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ABSTRACT

Several starting approximations for square root calculation by Newton's method are presented in a form to facilitate their use in IBM System/360 square root routines. These approximations include several for the range [1/16, 1], which is the interval of primary interest on IBM System/360.


REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

 
1
EVE, J. Starting approximations for the iterativc calculation of square roots. Comput. J. 6 (Oct. 1963), 274-276.
2
W. J. Cody, Double-precision square root for the CDC-3600, Communications of the ACM, v.7 n.12, p.715-718, Dec. 1964  [doi>10.1145/355588.365122]
 
3
MEINARDUS, C. Approximation yon Funktionen und ihre numerische Behandlung. Springer, Berlin, 1964.
4
W. Fraser , J. F. Hart, On the computation of rational approximations to continuous functions, Communications of the ACM, v.5 n.7, p.401-403, July 1962  [doi>10.1145/368273.368578]

CITED BY  7
Nabil Rousan , Hani Abu-Salem, Computation of √x, Proceedings of the 1999 ACM symposium on Applied computing, p.74-77, February 28-March 02, 1999, San Antonio, Texas, United States
David G. Moursund, Optimal starting values for Newton-Raphson calculation of x1 2 , Communications of the ACM, v.10 n.7, p.430-432, July 1967
Artenio De Matteis, Improvements based on computed errors, Communications of the ACM, v.10 n.11, p.683, Nov. 1967
M. Andrews , S. F. McCormick , G. D. Taylor, Evaluation of the square root function on microprocessors, Proceedings of the annual conference, p.185-191, October 20-22, 1976, Houston, Texas, United States
Eric M. Schwarz , Michael J. Flynn, Hardware Starting Approximation Method and Its Application to the Square Root Operation, IEEE Transactions on Computers, v.45 n.12, p.1356-1369, December 1996
Peter Kornerup , Jean-Michel Muller, Choosing starting values for certain Newton-Raphson iterations, Theoretical Computer Science, v.351 n.1, p.101-110, 14 February 2006
C. T. Fike, A rational approximation optimal by Moursund's criterion, Communications of the ACM, v.10 n.11, p.683-684, Nov. 1967

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