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Mathematics of Computation

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Acceleration of convergence of a family of logarithmically convergent sequences


Author: Andrew H. Van Tuyl
Journal: Math. Comp. 63 (1994), 229-246
MSC: Primary 40A25; Secondary 65B05
DOI: https://doi.org/10.1090/S0025-5718-1994-1234428-2
MathSciNet review: 1234428
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Abstract: The asymptotic behavior of several sequence transformations is investigated as $n \to \infty$ when applied to a certain family of logarithmically convergent sequences. The transformations considered are the iterations of the transformations $e_1^{(s)}({A_n})$ of Shanks and ${W_n}$ of Lubkin, the $\theta$-algorithm of Brezinski, the Levin u-and v-transforms, and generalizations of the $\rho$-algorithm and the Neville table. Computational results are given for both real and complex sequences.


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Keywords: Acceleration of convergence, logarithmic convergence, Levin <I>u</I>-transform, <IMG WIDTH="16" HEIGHT="19" ALIGN="BOTTOM" BORDER="0" SRC="images/img11.gif" ALT="$\theta$">-algorithm, <IMG WIDTH="16" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$\rho$">-algorithm, slowly convergent series, slowly convergent sequences, transformations of sequences
Article copyright: © Copyright 1994 American Mathematical Society