Acceleration methods for vector sequences

AbstractThe purpose of this paper is to propose acceleration methods for certain logarithmically convergent vector sequences. These methods are obtained by extending acceleration methods for scalars: Lubkin's W transform, the θ-algorithm and the ϱ-algorithm. Applied to a system of singular equations, new methods are compared with the vector ϵ-algorithm, the minimal polynomial extrapolation, and the generalized θ-algorithm of Brezinski. Theoretical results are also given