RESUMEN

A convergence acceleration method with one parameter for a sequence {Sn} satisfying

Sn ~  S + n^θ (c₀ +c₁/n + c₂/ n₂ + ... ) as n → ∞,

is proposed. When the parameter is equal to - 1, the method agrees with Wynn’s ρ -algorithm. Hence the method is designated as a generalized ρ –algorithm. When Sn is the nth partial sum of a series whose nth term is asymptotic to An^{0 - 1}, where θ is negative, the generalized ρ –algorithm with parameter θ agrees essentially with the modified Wynn’s ρ –algorithm taken up by Drummond. Error estimates and numerical examples of the generalized ρ –algorithm with parameter θ are given.

The exponent θ in the expansion above can be estimated using the generalized ρ –algorithm with parameter -2. In practice, by estimating the exponent θ , the generalized ρ –algorithm can be automatically applied to the sequence. This scheme is illustrated by numerical examples.