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Author Phillips, David L. ♦ King, Richard F.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Language English
Subject Keyword Square root ♦ Logarithmic error ♦ Recurrence relation ♦ Best fit ♦ Integer root ♦ Error curve ♦ Newton's method ♦ Maximal error ♦ Optimal approximation ♦ Relative error
Abstract The problem of obtaining optimal starting values for the calculation of the square root using Newton's method is considered. It has been pointed out elsewhere that if relative error is used as the measure of goodness of fit, optimal results are not obtained when the inital approximation is a best fit. It is shown here that if, instead, the so-called logarithmic error is used, then a best initial fit is optimal for both types of error. Moreover, use of the logarithmic error appears to simplify the problem of determining the optimal initial approximation.
Description Affiliation: Argonne National Lab., Argonne, IL (King, Richard F.) || Argonne National Lab., IL (Phillips, David L.)
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2005-08-01
Publisher Place New York
Journal Communications of the ACM (CACM)
Volume Number 12
Issue Number 2
Page Count 2
Starting Page 87
Ending Page 88


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Source: ACM Digital Library