For linear nonexpansive operators, Boţ-Nguyen acceleration coincides with weighted mean ergodic iterations whose weights derive from the beta-binomial distribution, yielding the projection as weak limit and strong convergence at parameter value 4.
Bauschke:Projection Algorithms and Monotone Operators, PhD thesis, Simon Fraser Uni- versity, 1996.https://summit.sfu.ca/item/7015
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Bo\c{t}-Nguyen Acceleration, Weighted Mean Ergodic Iteration, and the Beta-Binomial Distribution
For linear nonexpansive operators, Boţ-Nguyen acceleration coincides with weighted mean ergodic iterations whose weights derive from the beta-binomial distribution, yielding the projection as weak limit and strong convergence at parameter value 4.