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A machine method for square-root computation

R. W. Bemer
1958 Communications of the ACM  
A MACHINE METHOD FOR SQUARE-ROOT COMPUTATION R. W. BEMER I.B.M.  ...  Well-suited for computing square root on decimal ma- chines is a variation of Newton’s method which uses a linear first approximation such that convergence to the desired accuracy occurs in 2 iterations  ... 
doi:10.1145/368685.368690 fatcat:azybiyao6bfx5pgeaetjx3ygzi

Page 16 of The American Statistician Vol. 11, Issue 2 [page]

1957 The American Statistician  
The Control of Computational Error One method of controlling the computational error arising from a series of operations involving approxi- mations, such as division or square root, is to avoid the approximate  ...  A single square root, with the sign of t determined by the sign of NoSX,—N,=X> then determines t. For a_ two-tailed test the value of t?  ... 

Page 357 of Mathematics of Computation Vol. 1, Issue 9 [page]

1945 Mathematics of Computation  
In some cases when the square root is in the denominator T. 57 might prove more effective. It may be argued that no table for square root is necessary if one has a computing machine.  ...  Most computers are familiar with a square root process based on the identity 14+34+54+7+---+(2n-1) = which is well suited to some machines and which will yield the square root of an occasional number sooner  ... 

Evaluation of functions on microcomputers: square root

M. Andrews, S.F. McCormick, G.D. Taylor
1978 Computers and Mathematics with Applications  
This paper focuses on the evaluation of square roots and features a careful treatment of Newton's method with linear initialization.  ...  a more general mathematical software library or for special computation in real-time applications.  ...  In terms of square root routines, it may be measured as the range of input values for which an approximate square root is returned with a relative error near the machine precision.  ... 
doi:10.1016/0898-1221(78)90016-0 fatcat:grhyg3wy7ba7lf6fm55av4s4sa

Page 178 of Mathematics Teacher Vol. 44, Issue 3 [page]

1951 Mathematics Teacher  
Consider its ease and speed for the computation of the square root of 5, using a desk machine. The first steps may be mental.  ...  The algorithm is especially adapted to in fact, the machine computation (it is, method which the makers of desk calcu- lators publish for the extraction of any square root.)  ... 

Page 321 of Mathematics of Computation Vol. 2, Issue 20 [page]

1947 Mathematics of Computation  
Extraction of square roots by the odd number method. The ordinary method for finding on the calculating machine the square root of a number of 3 or 4 digits of the form (10x + y)? = 100x?  ...  The number a = 3586 is entered on the machine as if for square root. Then from it are subtracted as in that process the numbers 1, 3, 5, ---, each however combined with 6 = 80.  ... 

Page 302 of Mathematics Teacher Vol. 48, Issue 5 [page]

1955 Mathematics Teacher  
There is a number which we may call a, which the machine will have computed at some stage of your computa- tion, and you are going to need the square root of this number.  ...  You therefore wish the machine at the appropriate stage of the computation to find the square root of the number which will at that time be stored in cell number 100. .  ... 

The Square Root Method and its Use in Correlation and Regression

Paul S. Dwyer
1945 Journal of the American Statistical Association  
and, as a result, a tendency toward fewer errors, less computing time, and more pleasure for the computer.  ...  THE SQUARE ROOT METHOD AND ITS USE IN CORRELATION AND REGRESSION Pau. S. Dwyer.  ... 
doi:10.2307/2280218 fatcat:e2culbdkprgp5phvli7j7mebzm

Page 267 of Journal of Applied Physics Vol. 21, Issue 4 [page]

1950 Journal of Applied Physics  
Is it worth while, for example, to instruct the machine how to take square roots? The ENIAC is so instructed. On a single order, the ENIAC will take the square root of a designated num- ber.  ...  If that program is saved, it can be used over and over again whenever the major computation demands that a square root be taken. As a machine is used for extended periods, the number of 267  ... 

Page 653 of Journal of Forestry Vol. 49, Issue 9 [page]

1951 Journal of Forestry  
If these instructions were simple enough for a machine to follow, it seemed to me that here was a practical method of determining square roots to a large number of signifi- cant digits.  ...  for square roots whenever possible.  ... 

The Square Root Method and its Use in Correlation and Regression

Paul S. Dwyer
1945 Journal of the American Statistical Association  
Certainly the part un- der the square root sign (.568764) can be computed as a single machine operation.  ...  For example the value .754 may be obtained immedi- ately with use of a three place square root table. Formula (9) describes a single machine operation, too.  ... 
doi:10.1080/01621459.1945.10500749 fatcat:w3c4zzezqzfqhbbp7p6c3owdti

Square Root

Fred Gruenberger
1951 Mathematics Teacher  
The subject of square root cuts across the entire range of mathematics courses, from arithmetic to the calculus, and seems to cause trouble in every course.  ...  Consider its ease and speed for the computation of the square root of 5, using a desk machine. The first steps may be mental.  ...  The algorithm is especially adapted to in fact, the machine computation (it is, method which the makers of desk calcu- lators publish for the extraction of any square root.)  ... 
doi:10.5951/mt.44.3.0177 fatcat:rmlrkbtdardwjku3hjwkxalire

Page 13 of Mathematics of Computation Vol. 3, Issue 21 [page]

1948 Mathematics of Computation  
The Square Root Method for Solving Simultaneous Linear Equations The square root method for solving a system of linear equations was probably first developed by BANACHIEWICZ!  ...  The NBSCL has applied the square root method for solving systems of normal equations arising in least square solutions and has found the method very efficient.  ... 

Page 92 of The American Mathematical Monthly Vol. 58, Issue 2 [page]

1951 The American Mathematical Monthly  
Square roots are considered as solutions of special quadratic equations. A method is then given for finding ¢ from cos ¢, involving 4 square roots.  ...  If it were required to build a super-machine for the automatic solution of triangles, use of our method would obviate the necessity of building a set of tables into the machine.  ... 

The square root method for solving simultaneous linear equations

Jack Laderman
1948 Mathematics of Computation  
In applying the square root method, all computations should be performed on a calculating machine writing down only the final results in the following compact and systematic arrangement: It should be noted  ...  The NBSCL has applied the square root method for solving systems of normal equations arising in least square solutions and has found the method very efficient.  ... 
doi:10.1090/s0025-5718-1948-0025263-3 fatcat:zhadlyurkzhqnho6qvlnlyiv7m
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