Numerical Algorithms

, Volume 22, Issue 2, pp 157–165

Accelerating infinite products

  • Alan M. Cohen
  • David Levin


Slowly convergent infinite products \(\prod\nolimits_{n - 1}^\infty {b_n }\) are considered, where \(\left\{ {b_n } \right\}\) 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 \(\left\{ {b_n } \right\}\). For complicated sequences \(\left\{ {b_n } \right\}\) it involves the solution of some linear systems, but it is still effective.

convergence acceleration infinite products 


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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Alan M. Cohen
  • David Levin

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