Let's say I have a covariance matrix $\Sigma$ computed using a set of vectors $\{X_1, .. X_n\}$. Given a set of new vectors $\{Y_1, .. Y_m\}$ where $m<<n$, is there a way to do a kind of "adaptation" to $\Sigma$ and make it take into account the $Y_i$ vectors without having to recompute the covariance matrix using the whole vectors set $\{X_1, .. X_n, Y_1, .. Y_m\}$ ?
My goal is just to do the computation faster without loosing a lot in terms of precision (in my case $n$ is around 15000 and $m$ is around 30 and the vectors dimension is 1000).
Thanks !