Acceleration of convergence of a family of logarithmically convergent sequences

Van Tuyl, Andrew H.

doi:10.1090/S0025-5718-1994-1234428-2

Acceleration of convergence of a family of logarithmically convergent sequences
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Math. Comp. 63 (1994), 229-246 Request permission

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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