Is there a known way to calculate matrix $Z$ such that $e^Z=e^Xe^Y$ in an efficient and numerically stable way? $X$ and $Y$ are square matrices and can be complex.
Naively computing it is numerically unstable as the matrix exponential can easily get overflow or underflow. Another alternative is to use BCH formula. However, the series in BCH formula might be slow to converge (and I’m not even sure if the convergence is guaranteed for all matrices).