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.
Silverman:On the Definition of the Sum of a Divergent Series, PhD thesis, University of Michigan, 1913.https://quod.lib.umich.edu/u/umhistmath/AHE6267.0001.001
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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.