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

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

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

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

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 $A$.

Susan Blackford 2001-08-19