Fwd: RE: Problems with Jama Eigenvalues

[Ronald Boisvert <boisvert@nist.gov>]

Sender: Cleve Moler<Cleve.Moler@mathworks.com>
Subject: RE: Problems with Jama Eigenvalues


Put a small value, e = 1.e-15, in the upper right hand corner of your 6-by-6 matrix.  The EXACT eigenvalues are now complex numbers equally spaced around the circle with radius e^(1/6) = .0032.  Any good eigenvalues routine -- JAMA, MATLAB, or anything else -- will find eigenvalues of this magnitude.   Is this what you mean by "much larger than zero"?
    -- Cleve Moler

-----Original Message-----
From: jama@nist.gov [mailto:jama@nist.gov] On Behalf Of Welf Wustlich
Sent: Thursday, January 13, 2011 1:32 AM
To: Multiple recipients of list
Subject: Problems with Jama Eigenvalues

In case of a randomly generated matrix it seems to work well (not proven in
any case).

In case of a matrix where the size of all Eigenvalues is equal, e.g. "1.0" on
main diagonal and then random permutations of lines, the Eigenvalue
calculation of Jama1.0.2 hangs in an endless loop, consuming computing power
but never comes to an end.
This problem could be worked around by adding a slight noise on the
Eigenvalues, but this is not a good solution.
In case of a certain matrix, where the values put on a diagonal beyond main
diagonal:
    0 0 0 0 0 0
    1 0 0 0 0 0
    0 1 0 0 0 0
    0 0 1 0 0 0
    0 0 0 1 0 0
    0 0 0 0 1 0

Where the Eigenvalues are all zero, Jama comes up with Eigenvalues much larger
than zero, the larger the matrix the larger the Eigenvalues, the larger the
error Jama makes.

I have not done a detailed analysis of other cases, just compared the
described cases with Matlab results, but I wonder how somebody can use a
package with these crucial wrong behaviour.
I would be interested if there is a reason or solution for this.

Best regards, Welf

-- 
Welf Wustlich
Chief Research and Development
PLANET intelligent systems GmbH
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Germany
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