Some applications of nonlinear convergence accelerators

Abstract

A number of established nonlinear convergence acceleration methods are presented. It is discussed how these methods, and also some new algorithms, can be applied successfully to Fourier series. Some of the new accelerators are tailored for these‐series. Others are also useful for other types of series and sequences, and not only for convergence acceleration, but also for extrapolation or summation problems. Applications to the numerical inversion of the Laplace transform and to a Fourier series arising in the Matsubara formalism are presented. © 1993 John Wiley & Sons, Inc. Copyright © 1993 John Wiley & Sons, Inc.