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Mathematics of Computation

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Computation of continued fractions without input values

Author: P. Shiu
Journal: Math. Comp. 64 (1995), 1307-1317
MSC: Primary 11Y65; Secondary 11A55, 11K50
MathSciNet review: 1297479
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Abstract: An algorithm for the computation of the continued fraction expansions of numbers which are zeros of differentiable functions is given. The method is direct in the sense that it requires function evaluations at appropriate steps, rather than the value of the number as input in order to deliver the expansion. Statistical data on the first 10000 partial quotients for various real numbers are also given.

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Keywords: Direct algorithm, partial quotients, Khintchine’s constant
Article copyright: © Copyright 1995 American Mathematical Society