Convergence acceleration of alternating series

2017/02/23 by Rafał Nowak, Nowak, Rafał · 1 citation
Computer Science · Earth and Planetary Sciences · Physics and Astronomy · #65B10 #Computational Physics and Python Applications #FOS: Mathematics #G.1.0 #G.1.10 #Geophysics and Gravity Measurements #Numerical Analysis (math.NA) #Scientific Research and Discoveries

paper · pdf · doi:10.48550/arxiv.1702.07199

openalex publication_date 2017/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a new simple convergence acceleration method for wide range class of convergent alternating series. It has some common features with Smith's and Ford's modification of Levin's and Weniger's sequence transformations, but its computational and memory cost is lower. We compare all three methods and give some common theoretical results. Numerical examples confirm a similar performance of all of them.

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• Positive rational series for reciprocal powers of Catalan's constant and Dirichlet beta values

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