A fixed-point iteration computes the Petz-Augustin mean with linear convergence in the Thompson metric for alpha > 1/2, giving the first non-asymptotic guarantees for this quantity and for the Petz capacity.
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A Linearly Convergent Algorithm for Computing the Petz-Augustin Mean
A fixed-point iteration computes the Petz-Augustin mean with linear convergence in the Thompson metric for alpha > 1/2, giving the first non-asymptotic guarantees for this quantity and for the Petz capacity.