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