Old and new multidimensional convergence accelerators
Faculty of Sciences. Mathematics and Computer Science
Applied numerical mathematics. - Amsterdam
, p. 169-185
University of Antwerp
In the past some multidimensional convergence accelerators have been studied by Levin , by Albertsen, Jacobsen and SØrensen  and by the author . 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.