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MathGroup Archive 2005

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Numerical Eigenvalues for a 11x11 matrix

  • To: mathgroup at smc.vnet.net
  • Subject: [mg57071] Numerical Eigenvalues for a 11x11 matrix
  • From: Fabian Bodoky <fabian.bodoky at stud.unibas.ch>
  • Date: Sat, 14 May 2005 04:58:09 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi all,

as I am new to the MathGroup, I encountered some technical problems in posting 
my question, especially in posting the notebook with my problem. I was 
notified, that my first attempt to put it on mathematica-users.org did not 
work, but now the link should be up and working, so I am looking forward to 
helpful solutions!
Here the link:
http://www.mathematica-users.org/mediawiki/images/c/cb/fabMatrix.nb

For the problem description see my earlier message included at the end and the 
comments in the notebook itself. Thank you very much!

Regards, Fabian




----------  Forwarded Message  ----------

Subject: [mg57071] Numerical Eigenvalues for a 11x11 matrix
From: Fabian Bodoky <fabian.bodoky at stud.unibas.ch>
To: mathgroup at smc.vnet.net

Hi everyone,

I am using MAthematica to perform some physical simulations, i. e. solving
master equations for the smallest eigenvalue, and I encounter a problem.

I have a 11x11 matrix and should find numerically it's smallest eigenvalue
and plot it as a function of x. The entries of the matrix are sums of Fermi
functions [f(x) = 1 / (1-exp(x))]. Now there occurs always an overflow error
("General::ovfl: Overflow occurred in computation"). I can bypass this error
by not using the normal plot function, but rather ListPlot and calculate the
the matrix and its eigenvalue using a higher precision. The precision I have
to use varies between 500 and 1000, or even more for some settings, which
slows down my calculations very badly.
Since an 11x11 matrix is not so huge and there are quite good procedures for
numerically finding roots, I am somewhat puzzled by this behaviour of my
calculations, and it seems to me (after discussion with some other physicis
even more) that there should be some way to do such calculations without
using such enormous precision.

I am very thankful for any suggestions and help!
Regards and cheers,
Fabian

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