I was wondering if Lapack implements rank-one updates of the thin QR factorization, that is, an update
Q'R' := QR + v*u^T, with Q -- m x n, R -- n x n, v -- m x 1 and v -- n x 1.
I am interested in the setting m >> n.
An algorithm is proposed in the 1976 paper
J.W Daniel, W.B. Gragg, L. Kaufman, G.W. Stewart
Reorthogonalization and Stable Algorithms for Updating the Gram-Schmidt QR Factorization
I have already found a topic on this forum about adding/deleting columns/rows to the QR factorization, but nothing about rank one updates.
If lapack does not implement such an algorithm (or at least its basic building blocks), does someone known if there is an efficient implementation available ?
Thank you in advance !