QR decomposition of submatrix

Question

I would like to ask you whether you know, given the QR decomposition $A=QR,A\in\mathbb{R}^{N\times M}$, if it is possible to faster derive the QR decomposition of a partition of A, that contains a subset of rows of A. The reason why I am asking is that I have to apply CCA on a set of a million $B$ matrices with $B\in \mathbb{R}^{N\times K},K\in\{1,2\}$, that contain missing rows, and the same matrix A. I am using canoncorr Matlab implementation, which makes use of QR decomposition on the two matrices followed by SVD. More information on the CCA algorithm can be found at this document. There is currently a method in Matlab, named qrdelete, that removes a column by finding an optimal set of Givens rotations, but I would like to ask if there is a more general way to do it, with an arbitrary subset of A rows.

Answer 1

Work from Hammarling et. al (2008) explains some ways with which what I was asking can be done. The main idea here is the deletion of a number of groups of rows, so the section 2.1 summarizes plenty of ways to do this, however the computational gains I could get from this, particularly in the case of high missingness, seem to be non-existent. If I could intercalate a method that finds the best permutation of matrices B , so that the minimum number of rows is required to be added or deleted at any given iteration, namely minimizing the edit distance between sets, then I would possibly be able to get a speed-up of the total process.