Convergence acceleration algorithms related to a generalized E-transformation and its particular cases

Abstract

In this paper, a generalized E-transformation arising from the study of a generalization of sequence transformations and triangular recursion schemes is proposed. Three new algorithms, namely, the generalized E-algorithm, the generalized FS-algorithm and the generalized hungry type E-algorithm, are constructed for implementing the generalization of the E-transformation. Some convergence results of the generalized E-algorithm are obtained. In addition, some particular cases of the generalized E-transformation and the recursive algorithms for their computation are also studied.