Unfortunately, in my case, the generalized inverse of AA' is the preconditioner for the system, which is why I need the factorization of A'. Essentially, I tak

Unfortunately, in my case, the generalized inverse of AA' is the preconditioner for the system, which is why I need the factorization of A'. Essentially, I take this factorization and then run it through my own iterative method. When I run tests in MATLAB, SPQR scales fine for matrices of at least a few hundred thousand rows and columns. For larger, it would be nice to essentially have an incomplete Q-less QR factorization, which I don't think exists, but should be an extension of the incomplete Choleski work. But, yes, LSQR or more fitting LSMR solves a similar problem, but they're the iterative solver and I need the preconditioner, which I'm using the factorization for.