I'm trying to understand how to solve a least squares problem of the form:
$$\begin{bmatrix}A& B \end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix} = [b]$$
where I only explicitly solve for $y$ and not $x$. I have access to some c code which performs a QR factorization on $A$ and uses $Q_A$ on $B$ and $b$. Least squares is then applied to $\tilde{B}$ and $\tilde{b}$ to find $y$.
Could someone please help me with a description of this method? Researching this on the web, I am having a difficult time finding information since I don't know what this method would be called.
So I've discovered the name is the Generalized QR Factorization: http://www.netlib.org/lapack/lug/node46.html