Summary
It is shown that the convergence of limit periodic continued fractionsK(a n /1) with lima n =a can be substantially accelerated by replacing the sequence of approximations {S n (0)} by the sequence {S n (x 1)}, where\(x_1 = - 1/2 + \sqrt {1/4 + a} \). Specific estimates of the improvement are derived.
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Thron, W.J., Waadeland, H. Accelerating convergence of limit periodic continued fractionsK(a n /1). Numer. Math. 34, 155–170 (1980). https://doi.org/10.1007/BF01396057
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DOI: https://doi.org/10.1007/BF01396057