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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On the mean iteration $ (a,b)\leftarrow ((a+3b)/4,(\sqrt{ab}+b)/2)$


Authors: J. M. Borwein and P. B. Borwein
Journal: Math. Comp. 53 (1989), 311-326
MSC: Primary 30D05; Secondary 33A25
MathSciNet review: 968148
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Abstract | References | Similar Articles | Additional Information

Abstract: The iterative process

$\displaystyle {a_{n + 1}} = ({a_n} + 3{b_n})/4,\quad {b_{n + 1}} = (\sqrt {{a_n}{b_n}} + {b_n})/2$

is studied in detail. The limit of this quadratically converging process is explicitly identified, as are the uniformizing parameters. The role of symbolic computation, in discovering these nontrivial identifications, is highlighted.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1989-0968148-4
PII: S 0025-5718(1989)0968148-4
Article copyright: © Copyright 1989 American Mathematical Society