deletions | additions       diff --git a/methods.tex b/methods.tex  index f4eaee7..45a7895 100644  --- a/methods.tex  +++ b/methods.tex 
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\vec{R_z'} \end{array} \right)\] where $R_x'$ and $R_z'$ are $m \times 1$ and $n \times 1$ arrays, respectively, yields  \[ Q' = ||\left( \begin{array}{c}  \vec{R_x'} + A'\vec{\delta x} \\  \vec{R_z'} \end{array}|| \right)\] \end{array} \right)||\]  This is clearly minimized when \[ \vec{R_x'} = -A'\vec{\delta x} \] or \[ \vec{\delta x} = -A'^{-1} \vec{R_x'}\]  Note that since $A'$ is upper triangular, its inverse can be easily calculated.