[Octave-bug-tracker] [bug #31773] numerical instability in the pinv (Moore-Penrose inverse) function

[Sven Serneels]

URL:
  <http://savannah.gnu.org/bugs/?31773>

                 Summary: numerical instability in the pinv (Moore-Penrose
inverse) function 
                 Project: GNU Octave
            Submitted by: svens
            Submitted on: Fri 03 Dec 2010 09:04:31 PM GMT
                Category: Configuration and Build System
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Incorrect Result
                  Status: None
             Assigned to: None
         Originator Name: Sven Serneels
        Originator Email: 
             Open/Closed: Open
         Discussion Lock: Any
                 Release: 3.2.4
        Operating System: GNU/Linux

    _______________________________________________________

Details:

In the following lines sigmas and sigmac are both singular values of the same
matrix computed by different algorithms. The values these variables return in
the Shell prompt are identical, i.e. for a given data set: 


sigmas = 
8.6534  

sigmac = 
8.6534
 

Using these values in the following lines: 

 
kron(wKs',pinv(sigmac**2*eye(q)-Zs'*Zs)*Zs')
kron(wKs',pinv(sigmas**2*eye(q)-Zs'*Zs)*Zs')
 

should theoretically yield identical results. Nonetheless the first line
yields values in the order of magnitude 1E-3, whereas the second yields values
in the order of magnitude 1E+12. 

Checked several times. 
Likely due to numertical instability in the 'pinv' function. 




    _______________________________________________________

Reply to this item at:

  <http://savannah.gnu.org/bugs/?31773>

_______________________________________________
  Message sent via/by Savannah
  http://savannah.gnu.org/