Convergence acceleration of continued fractions of poincaré's type

A method of convergence acceleration of some continued fractions II

“…In the case of one-variant CFs ∈ C kl , this is close to the method of Hautot [4]; he used several values of initial coefficients τ j in order to get modifying factors ω m . Then, a standard sequence transformation, such as Brezinki's θ or u-Levin algorithm, was applied to {S m (ω m )}.…”

“…[4,5,7,8,[10][11][12]. For example, the good approximations of the tails of CF in (1) can be obtained using so-called 'improvement machine'-the method of Lorentzen and Waadeland, since its can be transformed equivalently into a limit periodic CF of loxodromic type; see [7] or [9, p. 227] for more details.…”