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Mathematics of Computation

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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: The iterative process \[ {a_{n + 1}} = ({a_n} + 3{b_n})/4,\quad {b_{n + 1}} = (\sqrt {{a_n}{b_n}} + {b_n})/2\] 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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Article copyright: © Copyright 1989 American Mathematical Society