ESTIMATE OF THE ASYMPTOTIC VALUE OF THE RESULTS OF AN ITERATIVE PROCEDURE

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP80B01138A000100050058-6
• Release Decision: RIPPUB
• Original Classification: K
• Document Page Count: 1
• Document Creation Date: December 9, 2016
• Document Release Date: May 30, 2001
• Sequence Number: 58
• Publication Date: January 17, 1968
• Content Type: MFR

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' II 17 January 1968
MEMORANDUM FOR THE RECORD
SUBJECT: Estimate of the Asymptotic Value of the
Results of an Iterative Procedure
It often happens in carrying out an iterative procedure that the
first few steps of the iterative will provide answers which fluctuate
widely, but that, as the procedure continues, the changes from one
iteration to the next are small and relatively well behaved. Further-
more? the approach to the final value is likely to slide in asymptotically.
In this circumstance it is often possible to estimate the asymptotic
value reasonably well, without going through the very large number of
variations.to arrive at it. The estimate of this asymptote is
2
A N-1 - GN GN- 2
G =
2GN-1 - GN - GN- 2
where 6 is the desired asymptote, and GN, GN-1 and GN-2 are the
estimates at the end of the N-th, (N-l)st, and (N-2)nd iterations,
respectively.
In order to use this estimate it has been assumed that all of the G's
are positive, that the denominator of the estimating equation is positive,
G is a function being maximized, and
GN 7 GN-1 7GN- 2
One use of this asymptotic estimate is as a means for deciding
when it is not worthwhile to continue the iteration procedure. The
cutoff criterion can be of the form
A
G G
Approved For Release 2001/08/31 : CIA-RDP80B01138A000100050058-6