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A machine method for square-root computation

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 ...

##
###
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

1978
*
Computers and Mathematics with Applications
*

This paper focuses on the evaluation of

doi:10.1016/0898-1221(78)90016-0
fatcat:grhyg3wy7ba7lf6fm55av4s4sa
*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. ...##
###
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*.) ...##
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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

1945
*
Journal of the American Statistical Association
*

and, as

doi:10.2307/2280218
fatcat:e2culbdkprgp5phvli7j7mebzm
*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. ...##
###
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

1945
*
Journal of the American Statistical Association
*

Certainly the part un- der the

doi:10.1080/01621459.1945.10500749
fatcat:w3c4zzezqzfqhbbp7p6c3owdti
*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. ...##
###
Square Root

1951
*
Mathematics Teacher
*

The subject of

doi:10.5951/mt.44.3.0177
fatcat:rmlrkbtdardwjku3hjwkxalire
*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*.) ...##
###
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*. ...

##
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The square root method for solving simultaneous linear equations

1948
*
Mathematics of Computation
*

In applying the

doi:10.1090/s0025-5718-1948-0025263-3
fatcat:zhadlyurkzhqnho6qvlnlyiv7m
*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. ...
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