Given a matrix $A=I+K^{-1}BB^TK^{-1}$ where K is a discrete Laplacian, and B is a sparse uniformly distributed random matrix, how can I calculate matrix-vector products $Av$ efficiently without any inverse operations?
I'm supposed to use the \ operator, but not sure where that fits in, given that $Av=b$, but I know $v$, i.e. unlike usual $Ax=b$ problems where you solve for $x$ given b.
$A$ is positive definite so can be split into $RR^T$, giving:
$(I+RR^T)v=b$
where $R=K^{-1}B$