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