Let $A$ be a symmetric matrix with eigenvalue decomposition $UDU^T$. Golub, et al.1 and Bunch, et al.2 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 $A+B$?
2Bunch, J.R., Nielsen, C.P. & Sorensen, D.C. Rank-one modification of the symmetric eigenproblem. Numer. Math. 31, 31–48 (1978). DOI:10.1007/BF01396012, eudml, ZBL0369.65007