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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Further results on convergence acceleration for continued fractions $ K(a\sb{n}/1)$


Author: Lisa Jacobsen
Journal: Trans. Amer. Math. Soc. 281 (1984), 129-146
MSC: Primary 40A15; Secondary 30B70, 65B99
MathSciNet review: 719662
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Abstract: If $ K(a_n^{\prime}/1)$ is a convergent continued fraction with known tails, it can be used to construct modified approximants $ f_n^{\ast}$ for other continued fractions $ K({a_n}/1)$ with unknown values. These modified approximants may converge faster to the value $ f$ of $ K({a_n}/1)$ than the ordinary approximants $ {f_n}$ do. In particular, if $ {a_n} - a_n^{\prime} \to 0$ fast enough, we obtain $ \vert f - f_n^{\ast}\vert/\vert f - {f_n}\vert \to 0$; i.e. convergence acceleration. the present paper also gives bounds for this ratio of the two truncation errors, in many cases.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0719662-X
PII: S 0002-9947(1984)0719662-X
Keywords: Continued fractions, convergence acceleration, modified approximants, auxiliary continued fractions
Article copyright: © Copyright 1984 American Mathematical Society