On the choice of β in the u - transformation for convergence acceleration

Javad Abdalkhani, David Levin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish
Pages (from-to)205-213
Number of pages9
JournalNumerical Algorithms
Issue number1
StatePublished - 28 Sep 2015


  • Convergence
  • Nonlinear sequence transformations
  • Parameter optimization
  • u- transformation


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