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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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

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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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Math. Comp. 53 (1989), 311-326
  • MSC: Primary 30D05; Secondary 33A25
  • DOI: https://doi.org/10.1090/S0025-5718-1989-0968148-4
  • MathSciNet review: 968148