For the discussion of math. Duh.
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If I'm doing least squares optimization with a linear system of n parameters, but at most m<n of them are allowed to be non-zero, is there any way of finding the optimal subset of parameters that's more efficient than just brute-forcing all (n choose m) of them? The only vague idea I've got is to start with the solution with all n parameters and do some sort of iteration from there that gets the parameter vector closer and closer to some m-plane while minimizing the growth of the error, but my brain is starting to fry.
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