Least Absolute Deviation solution of a linear system

[Ben Abbott]

On Jan 22, 2009, at 9:17 PM, James R. Van Zandt wrote:

>
> Octave has a function ols which find the least squares solution of an
> overdetermined linear system.  I propose the following function, which
> finds the "least abolute deviation" solution - the one that minimizes
> the sum of the absolute values of the deviations.  It is more work to
> find (requiring solution of a linear program), but is more robust to
> outliers.  See below for references.
>
> The LAD solution is the analog of the median.  You will recall that
> the median of an odd number of values is well defined, but for an even
> number of values we normally add a condition so we get the center of
> the interval between the centermost values.  This implementation of
> the LAD does not have this kind of rule.  If there is more than one
> solution that minimizes the sum of absolute values of the deviations,
> it doesn't attempt to return the "middle" one.
>
>            - Jim Van Zandt

Jim,

I've been wondering if this approach might be applied to non-linear  
problems as well.  Essentially, could it be applied to implement the  
equivalent of the non-linear regression routine on Octave-Forge?

	http://octave.sourceforge.net/doc/f/leasqr.html

Ben