Abstract
The behaviour of four algorithms accelerating the convergence of a subset of LOG is compared (LOG is the set of logarithmic sequences). This subset, denoted LOGF ′1 , is that of fixed point sequences whose associated error sequence,e n =S n −S, verifiese n+1 =e n + α2 e 2 n + α3 e 3 n +... , where α3 ≠ α 22 , α2 < 0. The algorithms are modifications of the ɛ-algorithm and of Aitken'sΔ 2 adapted to LOGF ′1 , the iteratedθ 2-algorithm, or Lubkin's transform, and the θ-algorithm of Brezinski. All of them accelerate the convergence of sequences in LOGF ′1 , but precise results are given on their relative convergence speed. This comparison is illustrated by numerical examples.
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Communicated by C. Brezinski
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Sablonniere, P. Comparison of four algorithms accelerating the convergence of a subset of logarithmic fixed point sequences. Numer Algor 1, 177–197 (1991). https://doi.org/10.1007/BF02142320
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DOI: https://doi.org/10.1007/BF02142320