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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
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 u-transform, $ \theta $-algorithm, $ \rho $-algorithm, slowly convergent series, slowly convergent sequences, transformations of sequences
Article copyright: © Copyright 1994 American Mathematical Society

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