Abstract
In the past some multidimensional convergence accelerators have been studied by Levin [13], by Albertsen, Jacobsen and SØrensen [1] and by the author [5]. We show here that all these multidimensional convergence accelerators are particular cases of a whole class of multidimensional convergence accelerators. The common underlying principle is that they can be considered as multivariate Padé approximants for a multivariate function that is different for different algorithms. Since we work in a very general framework, we are able to introduce a number of new multidimensional convergence accelerators and generalize them by using multivariate rational Hermite interpolants instead of multivariate Padé approximants.
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