A contour integral representation of linear extrapolation methods (Q1109474)

Extrapolation methods are well-known to be very efficient tools for the acceleration of the convergence of certain sequences of numbers or functions. In this note we present a representation of linear extrapolation procedures in terms of complex contour integrals. For the proof we make use of a complete characterization of these procedures as linear functionals, which is itself of some interest and can be found, for example, by \textit{R. Bulirsch} and \textit{J. Stoer} [ibid. 6, 413--427 (1964; Zbl 0123.321)].