[Octave-bug-tracker] [bug #50846] Unexpected results with ordered qz decomposition

[Johannes Pfeifer]

URL:
  <http://savannah.gnu.org/bugs/?50846>

                 Summary: Unexpected results with ordered qz decomposition
                 Project: GNU Octave
            Submitted by: jpfeifer
            Submitted on: Fri 21 Apr 2017 12:50:38 PM UTC
                Category: Octave Function
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Incorrect Result
                  Status: None
             Assigned to: None
         Originator Name: Johannes Pfeifer
        Originator Email: 
             Open/Closed: Open
         Discussion Lock: Any
                 Release: 4.2.1
        Operating System: Microsoft Windows

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Details:

According to  https://octave.sourceforge.io/octave/function/qz.html
the 'S' flag of the qz-decomposition should return a leading block has all
eigenvalues |lambda|≤ 1

But running 

load octave_qz.mat
[ss,tt,w,eigval] = qz(e,d,'S');
abs(eigval)-1

returns


ans =

  -1.00000000000000e+000
  -5.71920035902214e-001
  -2.00000000000000e-001
  -1.00000000000000e-001
  2.62626262626263e-001
  -1.11022302462516e-016
  1.22334455667789e-001
  1.10880152430664e+016
  1.35960823868476e+000
  1.01010101010102e-002

Thus, the fifth eigenvalue has |lambda|>1 while the sixth one again has
|lambda|<1 and should therefore still be in the first block.





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File Attachments:


-------------------------------------------------------
Date: Fri 21 Apr 2017 12:50:38 PM UTC  Name: octave_qz.mat  Size: 2kB   By:
jpfeifer
data file with matrices for QZ
<http://savannah.gnu.org/bugs/download.php?file_id=40465>

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