Suppose $A\in\mathbb{R}^{n\times c}$,$u\in\mathbb{R}^n$,$n\gg c$. The time complexity of eigenvalue decomposing directly for matrix $AA^T+\text{diag}(u)$ is $O(n^3)$. And it is easy to avoid $O(n^3)$ for matrix $AA^T+I$. So can we avoid $O(n^3)$ for matrix $AA^T+\text{diag}(u)$? Thanks.
Regards.
Jay.