I wonder if it's possible to find the $Q$ and $R$ matrices from this QR-equation with only compute QR at one time only:
$$A = QR$$
if, the first column of $A$ got removed and then a new column got added to $A$.
I take it again: Assume that we first got our data matrix $A$ and we compute $Q$ and $R$. Then we change our data matrix $A$ by remove first column and add new data column to $A$. That means $Q$ and $R$ are going to change. Can we compute the new $Q$ and $R$ if we know the new data column of $A$ and the past $Q$ and $R$?
If you wonder what I got this question from. I got this from the paper Recursive Subspace Identification Algorithm using the Propagator Based Method, 2017.