Let $A$ be a symmetric matrix with eigenvalue decomposition $UDU^T$. Golub, et al. and Bunch, et al. have shown that given such an $A$, the eigenvalue decomposition of $A+\rho xx^t$ may be computed efficiently.

Has anything similar been done for the case where the update is of the form $A+B$, where $B=uv^t+vu^t$ is a rank-two symmetric matrix (note we can't just do two rank-one symmetric updates)?

What if we relaxed the insistence that $B$ be symmetric and asked instead for an efficient computation of the SVD of the update $A+B$?

References or thoughts would be greatly appreciated.