  We propose an iterative algorithm that computes the maximum-likelihood
estimate in quantum state tomography. The optimization error of the algorithm
converges to zero at an $O ( ( 1 / k ) \log D )$ rate, where $k$ denotes the
number of iterations and $D$ denotes the dimension of the quantum state. The
per-iteration computational complexity of the algorithm is $O ( D ^ 3 + N D ^2
)$, where $N$ denotes the number of measurement outcomes. The algorithm can be
considered as a parameter-free correction of the $R \rho R$ method [A. I.
Lvovsky. Iterative maximum-likelihood reconstruction in quantum homodyne
tomography. \textit{J. Opt. B: Quantum Semiclass. Opt.} 2004] [G.
Molina-Terriza et al. Triggered qutrits for quantum communication protocols.
\textit{Phys. Rev. Lett.} 2004.].
