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MathGroup Archive 2005

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Numerical Eigenvalues for a 11x11 matrix

  • To: mathgroup at smc.vnet.net
  • Subject: [mg56951] Numerical Eigenvalues for a 11x11 matrix
  • From: Fabian Bodoky <fabian.bodoky at stud.unibas.ch>
  • Date: Wed, 11 May 2005 05:24:06 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

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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