[Octave-bug-tracker] [bug #40057] exit criterion in pcg

[Marco Caliari]

URL:
  <http://savannah.gnu.org/bugs/?40057>

                 Summary: exit criterion in pcg
                 Project: GNU Octave
            Submitted by: caliari
            Submitted on: Wed 18 Sep 2013 09:40:46 AM GMT
                Category: Octave Function
                Severity: 2 - Minor
                Priority: 5 - Normal
              Item Group: Matlab Compatibility
                  Status: None
             Assigned to: None
         Originator Name: 
        Originator Email: 
             Open/Closed: Open
         Discussion Lock: Any
                 Release: 3.6.2
        Operating System: GNU/Linux

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Details:

Dear all,

the exit criterion in pcg is


norm (B - A * X) <= TOL * norm (B - A * X0)


On the other hand, in C.T. Kelley (quoted as reference book), p.23, it is
used


norm (B - A * X) <= TOL * norm (B)


and the same in matlab (as I understand from the description of
[X,FLAG,RELRES] output). Of course, Octave criterion is a valid one and they
coincide for X0 = zeros (the default value). I think it should be changed for
compatibility. If one really needs the current behavior, he can give TOL *
norm (B - A * X0) / norm (B) as input tolerance.

Cheers,

Marco




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