[Octave-bug-tracker] [bug #57145] backslash vs. pinv

[Michael Leitner]

Follow-up Comment #1, bug #57145 (project octave):

Is this a recent change of how matlab interprets its backslash operator?
Indeed, its documentation says that multiplication by the pinv gives the
minimum-norm solution (that's guaranteed by the properties of the
Moore-Penrose pseudoinverse), while the backslash operator according to the
mldivide documentation "is not necessarily the minimum norm solution", and
only according to the pinv documentation "is special because it has only three
nonzero elements" in the present example. I do not find a general rule, so I
would say it is undocumented what matlab really computes in the case of
underdetermined problems. If it is the solution with the least number of
non-zero entries, then this is not unique as I see it. Perhaps it is the one
with the smallest norm among those with the smallest number of non-zero
entries (but I am not sure if even that is unique in general).

In contrast, for octave it is well-defined: it is the minimum-norm solution,
just as what you would get by pinv (but computed more efficiently). So your
point a) is valid (but as I said, does matlab even define its behaviour in
this case?), but b) is not true in general (I would even estimate that the
minimum-norm solution gives a smaller error in general).

    _______________________________________________________

Reply to this item at:

  <https://savannah.gnu.org/bugs/?57145>

_______________________________________________
  Message sent via Savannah
  https://savannah.gnu.org/