I have a $n\times m$ matrix, $C$, and a $m\times m$ matrix, $B$. Is there any computational trick that allows me to calculate $(CBC^T)^{-1}$ without first calculating $Z=CBC^T$? Specifically, when $m<<n$, I want to avoid storing the $n\times n$ matrix $Z$.
This reminds me of the Sherman-Woodbury-Morrison Identity for $(A+CBC^T)^{-1}$ if $A$ were a matrix of zeros, however, because $A$ would have no inverse, this doesn't seem to help. Any ideas?