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A Linearly Convergent Algorithm for Petz-Augustin Means with Applications to Computing Petz-Augustin Capacity and Equilibrium Prices in Fisher Markets
We study the computation of the Petz-Augustin mean of order $α\in (0,1) \cup (1,\infty)$, defined as the minimizer of a weighted sum of $n$ Petz-Rényi divergences of order $α$ over the set of $d$-by-$d$ quantum states, where the Petz-Rényi divergence is a quantum generalization of the classical Rény
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