Convergence acceleration for continued fractions $K(a_{n}/1)$
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- by Lisa Jacobsen
- Trans. Amer. Math. Soc. 275 (1983), 265-285
- DOI: https://doi.org/10.1090/S0002-9947-1983-0678349-1
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Abstract:
A known method for convergence acceleration of limit periodic continued fractions $K({a_n}/1),{a_n} \to a$, is to replace the approximants ${S_n}(0)$ by "modified approximants" ${S_n}({f^{\ast }})$, where $f^{\ast } = K(a/1)$. The present paper extends this idea to a larger class of converging continued fractions. The "modified approximants" will then be ${S_n}({f^{(n)’}})$, where $K({a’_n}/1)$ is a converging continued fraction whose tails ${f^{(n)\prime }}$ are all known, and where ${a_n} - a_n^\prime \to 0$. As a measure for the improvement obtained by this method, upper bounds for the ratio of the two truncation errors are found.References
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Bibliographic Information
- © Copyright 1983 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 275 (1983), 265-285
- MSC: Primary 40A15; Secondary 30B70
- DOI: https://doi.org/10.1090/S0002-9947-1983-0678349-1
- MathSciNet review: 678349