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.
Toeplitz: ¨Uber allgemeine lineare Mittelbildungen,Prace Matematyczno-Fizyczne22 (1911), 113–119.https://eudml.org/doc/215310 31
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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.