Gauss-Markov Linear Model

Let $A$ be an $n\times m$ matrix, $B$ an $n\times p$ matrix, and $d$ an $n$ vector, with the condition $m\leqslant n\leqslant m+p$, this application solves the general Gauss-Markov linear model problem (GLM): \[ \min_{x} \| y \|_2 \quad\mbox{subject to}\quad Ax+By=d \] In the special cases, the GLM problem reduces to an ordinary linear least squares problem when $B=I$ or to the weighted linear least squares problem when $B$ is square and nonsingular. In the latter case it is written in the form \[ \min_{x} \| B^{-1}(d-Ax) \|_2 \]

See Input Data for the description of how to enter matrix or just click Example for a simple example.

GLM Calculator