# Updating the qr factorization and the least squares problem Mob sex chat

This is achieved by updating the factors Q and R, and we show this can be much faster than computing the factorization of A1 from scratch.

We consider algorithms that exploit the Level 3 BLAS where possible and place no restriction on the dimensions of A or the number of rows and columns added or deleted.

The following table gives the number of operations in the k-th step of the QR-decomposition by the Householder transformation, assuming a square matrix with size n.

Analogously, we can define QL, RQ, and LQ decompositions, with L being a lower triangular matrix.

More generally, the first k columns of Q form an orthonormal basis for the span of the first k columns of A for any 1 ≤ k ≤ n.

More generally, we can factor a complex m×n matrix A, with m ≥ n, as the product of an m×m unitary matrix Q and an m×n upper triangular matrix R.

Despite searching for days a couple of months ago, i've not been able to find an equivalent in R (beware there are many qr.update functions in cran but when you look under the hood they're just fake --i.e. I've been also looking since long time for an equivalent to the matlab qr update, leaps seems a nice way!

In R, you could look at the recresid() function in package strucchange, that will give recursive residuals when you add an observation (not variable! My guess is that this will require little modification to obtain recursive betas (the betar in the code?

Q = I) and R is an upper triangular matrix (also called right triangular matrix).