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MathGroup Archive 2005

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Re: Numerical Eigenvalues for a 11x11 matrix

  • To: mathgroup at smc.vnet.net
  • Subject: [mg57050] Re: Numerical Eigenvalues for a 11x11 matrix
  • From: David Bailey <dave at Remove_Thisdbailey.co.uk>
  • Date: Thu, 12 May 2005 22:44:39 -0400 (EDT)
  • References: <d5sjll$no6$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Fabian Bodoky wrote:
> 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
> 
Try to post some actual code, so people can reproduce your problem.

David Bailey
http://www.dbaileyconsultancy.co.uk


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