Remarks to a definition of convergence acceleration illustrated by means of continued fractions K(an1) where an → 0

摘要

Let {cn} and {c∗n} be two sequences of complex numbers converging to the finite limit c. We say that {c∗n} converges faster to c than {cn} if (c∗n−c)(cn−c)→0. Convergence acceleration is based on this definition. In this paper we draw attention to some of its deficiencies. As an example we consider the case where {cn} is the sequence of approximants of a continued fraction K(an1) where an → 0.