Abstract
The influence of the shift parameter β upon the convergence of the u-transformation may be crucial. It is shown, through a specific example, that a clever choice of β can improve the convergence acceleration rate of the u-transformation, while a wrong choice may even imply divergence of the method. A constructive approach for choosing an optimal shift parameter β is presented, based upon the exactness class (model) of the u-transformation. The parameter β which defines the best fitted model to a specific sequence is chosen for the acceleration of that sequence.
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The first author Javad Abdalkhani dedicates his work to his wife Mahshid Pirouznia
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Abdalkhani, J., Levin, D. On the choice of β in the u - transformation for convergence acceleration. Numer Algor 70, 205–213 (2015). https://doi.org/10.1007/s11075-014-9942-9
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DOI: https://doi.org/10.1007/s11075-014-9942-9