Accelerating infinite products

Slowly convergent infinite products are considered, where 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 . For complicated sequences it involves the solution of some linear systems, but it is still effective. This revised version was published online in June 2006 with corrections to the Cover Date.