Summary
It is proved that the sequences formed by the columns and the diagonals of the array of the ɛ-algorithm converge faster than the initial sequence when it is either a non logarithmic totally monotonic sequence or a converging totally oscillating sequence.
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Brezinski, C. Convergence acceleration of some sequences by the ɛ-algorithm. Numer. Math. 29, 173–177 (1978). https://doi.org/10.1007/BF01390336
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DOI: https://doi.org/10.1007/BF01390336