Least Absolute Deviation solution of a linear system

[James R. Van Zandt]

Ben Abbott <bpabbott at mac.com> wrote:
>On Jan 22, 2009, at 9:17 PM, James R. Van Zandt wrote:
>>
>> 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.

>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?

The concept of a "least absolute deviation" solution certainly applies
to non-linear problems too.  However, I don't know of any efficient
algorithm to find it.  Instead, one would have to use a
general-purpose optimization algorithm like Nelder-Mead or simulated
annealing.

       - Jim Van Zandt