There is a lot of work done on low rank updates to inverses or SVDs (or similar decompositions), but I am wondering what can be said about the inverse or SVD
$(A + c \times B)$
in terms of $(A + d \times B)$ for some other $d$. That is, in general full-rank updates, but along very particular dimensions.
$c$ and $d$ are positive scalars, and $A$ and $B$ are symmetric, positive definite matrices. Quantities like this arise in MLE-like computations in linear mixed models (e.g. http://onlinelibrary.wiley.com/doi/10.1111/1467-9868.00092/abstract).