Hi,

my question is similar to this one. I have to compute $B^TC^{−1}B$, where $C$ is a strictly positive definite $n\times n$ matrix and $B$ is $n\times m$. The matrix $C$ is huge ($n$ up to a hundred thousand) and sparse. If $m$ is small I compute $b^TC^{−1}b$ for all columns $b$ of $B$ using CG which is really fast (much faster than Cholesky decomposition). However this becomes problematic if $m$ gets larger.

Are there methods from numerical optimization to compute $B^TC^{−1}B$ more efficient?

Thank you very much!

Manuel