Convergence acceleration of alternating series

02/23/2017

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by   Rafał Nowak, et al.

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A new simple convergence acceleration method is proposed for a certain wide range class of convergent alternating series. The method has some common features with Smith's and Ford's modification of Levin's and Weniger's sequence transformations, but it leads to less computational and memory cost. The similarities and differences between all three methods are analyzed and some common theoretical results are given. Numerical examples confirm a similar performance of all three methods.