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Acceleration of Convergence of a Family of Logarithmically Convergent Sequences

Andrew H. Van Tuyl
Mathematics of Computation
Vol. 63, No. 207 (Jul., 1994), pp. 229-246
DOI: 10.2307/2153571
Stable URL: http://www.jstor.org/stable/2153571
Page Count: 18
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Acceleration of Convergence of a Family of Logarithmically Convergent Sequences
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Abstract

The asymptotic behavior of several sequence transformations is investigated as n → ∞ when applied to a certain family of logarithmically convergent sequences. The transformations considered are the iterations of the transformations e(s)1 (An) of Shanks and Wn of Lubkin, the θ-algorithm of Brezinski, the Levin u- and v-transforms, and generalizations of the ρ-algorithm and the Neville table. Computational results are give for both real and complex sequences.

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