Re: Eigenvalue bug in Mathematica 7.0.0
- To: mathgroup at smc.vnet.net
- Subject: [mg101237] Re: Eigenvalue bug in Mathematica 7.0.0
- From: Alois Steindl <Alois.Steindl at tuwien.ac.at>
- Date: Sat, 27 Jun 2009 06:05:52 -0400 (EDT)
- Organization: Inst. f. Mechanics II, TU Vienna
- References: <h22974$hqb$1@smc.vnet.net>
Hello,
I tried your example with Mathematica 7.0.1 and cannot find any mistake.
Mathematica returns the Eigenvalues
{138.983, 138.983, 134.545, 134.545, 132.139, 132.139, 130.106, \
130.106, 127.7, 127.7, 125.685, 125.667, 125.306, 125.236, 123.261, \
123.261, 121.271, 120.907, 120.797, 118.89, 118.822, 118.385, \
118.269, 116.492, 116.359, 114.048, 113.83, 112.135, 111.94, 109.619, \
109.391, 105.158, 105.134, -62.1433, -56.109, -56.1087, -49.9294, \
-49.9193, -43.7204, -43.679, 42.6088, 42.6088, 39.1564, 39.1564, \
37.4483, 37.4483, -37.4396, -37.4207, 33.9956, 33.9956, 32.3605, \
32.3605, 32.2878, 32.2878, -31.2147, -31.0896, 28.9063, 28.9062, \
28.8348, 28.8347, 27.1637, 27.1637, 27.1274, 27.1274, 23.7099, \
23.7098, 23.6741, 23.674, 21.967, 21.9669, 21.9669, 21.9669, 18.5135, \
18.5134, 18.5134, 18.5132, 16.8509, 16.8509, 16.7702, 16.7702, \
13.3985, 13.3985, 13.3171, 13.3169, 11.6985, 11.6985, 11.5893, \
11.5893, 8.24605, 8.24605, 8.13687, 8.13687, 6.38447, 6.38447, \
2.93206, 2.93206, -2.27249, -2.27249, 1.17992, 1.17992}
As you can see, all the eigenvalues occur twice, which indicates, that
you have some symmetry in your equations, which you didn't use to reduce
the size of the system.
Also the Jordan matrix, which you obtain by
{ev, em} = Eigensystem[H];
eb=Transpose[em];
jor=Inverse[eb].H.eb;
looks reasonable. The numeric errors are quite small.
Since the computation of eigenvalues is quite standard and has bin in
Mathematica for decades, I doubt, that the program does something wrong.
Good luck
Alois