Matlab says the command A\B finds a solution to Ax=B which has the smallest number of non-zero components. If A is nxm with n>m the system does not have an exact solution, in general, so A\B returns an approximate solution.
My problem is this: I have a system for which I know that a very sparse solution x0 should exist. However, A\B is not returning that solution. I imagine this can only be because Matlab finds a different solution x which is a "better" approximation in the sense that norm(Ax-B) < norm(Ax0-B).
I would like to "trade" the quality in the approximation for the sparsity in the solution. Namely, I want A\B to return the "worse" solution x0 instead of x, because x0 is more sparse than x. Is this possible?