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argmin
2019 Aug 13
0
behaviour and documentation of qr.solve
...ion or behaviour of qr.solve, qr.coef, qr.resid, and qr.fitted is not easily comprehensible and unfortunate.
We all know that a linear system Ax=b can have 0, one or infinitely many solutions. To treat all these cases uniformly we can rephrase the problem
as
x = argmin_u||Au-b||,
where ||.|| denotes the Euclidean norm. There is then exactly one natural and distinguished solution x, the minimizer x which is itself of minimal
Euclidean Norm. So if we want to return only one solution, I think we can agree that this should be it....