A Linearly Convergent Algorithm for Computing the Petz-Augustin Mean

Chun-Neng Chu, Wei-Fu Tseng, Yen-Huan Li

We study the computation of the Petz-Augustin mean of order $\hat{I}\pm \in (0,1)\cup (1,\infty )$, defined as the minimizer of a weighted sum of $n$ Petz-Rényi divergences of order $\hat{I}\pm$ o…