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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On the mean iteration $(a,b)\leftarrow ((a+3b)/4,(\sqrt {ab}+b)/2)$
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by J. M. Borwein and P. B. Borwein PDF
Math. Comp. 53 (1989), 311-326 Request permission


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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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Math. Comp. 53 (1989), 311-326
  • MSC: Primary 30D05; Secondary 33A25
  • DOI:
  • MathSciNet review: 968148