Quote:
Originally Posted by Michael Hill
I'm using the l1eq_pd.m function
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That's the wrong solver.
Code:
% l1eq_pd.m
%
% Solve
% min_x ||x||_1 s.t. Ax = b
Firstly, you cannot find a min L1 norm vector x such that Ax=b because
there is no vector x such that Ax=b, since the system is overdetermined.
Secondly, what you want to find is the min L1 norm
of the residuals, not of the solution vector itself.
For the set of overdetermined linear equations Ax ≈ b, x is the solution vector. The residuals are b-Ax. So you want find a solution vector x which minimizes the L1 norm of b-Ax.