Numerical Algorithms

, Volume 22, Issue 2, pp 157–165

# Accelerating infinite products

• Alan M. Cohen
• David Levin
Article

## Abstract

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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