How to reduce the complexity of matrix inversion of sum of rank 1 matrices, not only arithmetic but also run time?
$M^{-1} = \left( I + \sum \limits_{i=1}^{K} \alpha_i A_i \right)^{-1} $
where $A_i \in \mathbb{C}^{N \times N}$, ${\rm rank}\left(A_i \right) = 1$, and $\alpha_i \in \mathbb{R}$.
For instance, the suggestion here is apprently reducing the arithmetic complexity but not the run time (I mean it will take $N$ iterations to find the matrix inverse)? What other alternatives do we have?
