A review of vector convergence acceleration methods, with applications to linear algebra problems

In this article, in a few pages, we will try to give an idea of convergence acceleration methods and extrapolation procedures for vector sequences, and to present some applications to linear algebra problems and to the treatment of the Gibbs phenomenon for Fourier series in order to show their effectiveness. The interested reader is referred to the literature for more details. In the bibliography, due to space limitation, we will only give the more recent items, and, for older ones, we refer to Brezinski and Redivo-Zaglia, Extrapolation methods. (Extrapolation Methods. Theory and Practice, North-Holland, 1991). This book also contains, on a magnetic support, a library (in Fortran 77 language) for convergence acceleration algorithms and extrapolation methods.