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From: Alois Steindl on 8 Feb 2010 07:40
Hello,
why does the eigenvalue in your case become small?
There could be several reasons, which might possibly be avoided:
Bad scaling: If the quantities in the system have different orders of
magnitude, the matrix could become ill conditioned. (Rescaling shouldn't
change the eigenvalues, but it might help to improve the computation of
the eigenvectors.)
If these small eigenvalues occur for some special parameter values, you
could view the problem as bifurcation problem and directly calculate the
critical parameter values, where you have an exact zero eigenvalue.
Also approximate symmetries could cause small eigenvalues.

However, for the difficulties in finding the proper eigenvectors the
size of the eigenvalues is usually not so critical as if you have
closely spaced eigenvalues.

Alois


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