Acceleration of Fourier series (Q549553)

Several sequence acceleration methods are tested on the partial sums of Fourier series. It turns out that in some cases the convergence is not accelerated, but it is completely destroyed. The present author outlines in a more efficient way the proofs of certain results in [\textit{A. J. Boggess}, \textit{B. E. Bunch} and \textit{C. C. N. Moore}, Numer. Algorithms 47, No. 2, 133--142 (2008; Zbl 1140.65095)] and [\textit{E. Abebe}, \textit{J. Graber} and \textit{C. N. Moore}, J. Comput. Appl. Math. 224, No. 1, 146--151 (2009; Zbl 1159.65111)].