Accelerating infinite products

Alan M. Cohen, David Levin

Research output: Contribution to journalArticlepeer-review

Abstract

Slowly convergent infinite products Πn=1 bn are considered, where {bn} is a sequence of numbers, or a sequence of linear operators. Using an asymptotic expansion for the "remainder" of the infinite product a method for convergence acceleration is suggested. The method is in the spirit of the d-transformation for series. It is very simple and efficient for some classes of sequences {bn}. For complicated sequences {bn} it involves the solution of some linear systems, but it is still effective.

Original languageEnglish
Pages (from-to)157-165
Number of pages9
JournalNumerical Algorithms
Volume22
Issue number2
DOIs
StatePublished - 1999

Keywords

  • Convergence acceleration
  • Infinite products

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