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