The Matrix Division operator,
\ according to Julia’s documentation uses, for this case, the Pivoted QR algorithm to return the Minimum Norm Solution.
In MATLAB’s documentation for the algorithms it says it uses also the QR solver, yet it doesn’t say what kind. Yet MATLAB doesn’t guarantee to return the Minimum Norm solution and indeed in most cases doesn’t.
My questions are:
- Does Julia return the Minimum Norm solution since it uses the Pivoted QR or is there an additional step on top of that?
- Performance wise, does it have any effect on the speed of the operation? Could it be faster if there was no requirements for the minimum norm solution?