Purpose

LA_GGLSE solves the linear equality-constrained least squares (LSE) problem:

$$\min \Vert c - A\,x \Vert _2 \;\;\mbox{subject} \; \mbox{ to}\;\; B\,x = d,$$

where $A$ and $B$ are real or complex rectangular matrices and $c$ and $d$ are real or complex vectors. Further, $A$ is $m \times n$, $B$ is $p \times n$, $c$ is $m \times 1$ and $d$ is $p \times 1$, and it is assumed that

$$p \leq n \leq m+p, \;\;\;\; \mbox{rank}(B) = p, \; \;\;\; \mb... ...\small\left( \begin{array}{c} A \\ B \end{array} \right)} = n.$$

These conditions ensure that the $LSE$ problem has a unique solution $x$. This is obtained using the generalized $RQ$ factorization of the matrices $B$ and $A$.