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2019 Aug 13
0
behaviour and documentation of qr.solve
...bind(
c(1,1,1,1,1),
c(1,2,2,2,2),
c(1,2,3,3,3)
)
The system has infinitely many solutions. The minimal norm solution is x=c(1,0,2/3,2/3,2/3).
But qr.solve(A,b) yielded the solution x=(1,0,2,0,0) which is destinguished only by being sparse and I do not think qr.solve
tries to compute the sparsest solution. So what does qr.solve do in case of an underdetermined system?
It is not documented.
Then I tried to figure out what qr.coef, qr.resid, and qr.fitted do. I had to do actual experiments to figure out that it seems to solve the
problem x=argmin_u||Au-y|| with...